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Preview of Algebra 1
Polynomials
12A Introduction to
Polynomials
12-1 Polynomials
LAB Model Polynomials
12-2 Simplifying Polynomials
12B Polynomial
Operations
LAB
Model Polynomial
Addition
Adding Polynomials
Model Polynomial
Subtraction
Subtracting Polynomials
Multiplying Polynomials
by Monomials
Multiply Binomials
Multiplying Binomials
12-3
LAB
12-4
12-5
LAB
12-6
KEYWORD: MT8CA Ch12
Polynomials can be used
to calculate the height of
fireworks.
Walt Disney
Concert Hall,
Los Angeles
586
Chapter 12
Associative
Property
Vocabulary
Choose the best term from the list to complete each sentence.
coefficient
1. __?__ have the same variables raised to the same powers.
2. In the expression 4x 2, 4 is the __?__.
Distributive
Property
3. 5 (4 3) (5 4) 3 by the __?__.
like terms
4. 3 2 3 4 3(2 4) by the __?__.
Commutative
Property
Complete these exercises to review skills you will need for this chapter.
Integer Operations
Add or subtract.
5. 12 4
6. 8 10
7. 14 (4)
8. 9 5
9. 9 (5)
10. 9 (5)
11. 17 8
12. 12 (19)
13. 23 (5)
Evaluate Expressions
Evaluate the expression for the given value of the variable.
14. (x y ) z for x 8, y 3, z 4
15. 7ab 5 for a 3, b 4
16. 2(n 3)2 for n 1
17. 6(t 4)2 for t 2
Simplify Algebraic Expressions
Simplify each algebraic expression.
18. 8 4x x 9
19. 9b a 11 3a 12
20. n 10m 9n 4
Area of Squares, Rectangles, and Triangles
Find the area of each figure.
21.
22.
23.
15 cm
6 in.
36 cm
24 m
15 in.
24 m
Polynomials
587
The information below “unpacks” the standards. The Academic Vocabulary is
highlighted and defined to help you understand the language of the standards.
Refer to the lessons listed after each standard for help with the math terms and
phrases. The Chapter Concept shows how the standard is applied in this chapter.
California
Standard
10.0
Preview of Algebra 1
Students add, subtract, multiply, and divide
monomials and polynomials. Students solve
multistep problems, including word
problems, by using these techniques .
(Lessons 12-3, 12-4, 12-5, 12-6; Labs 12-3,
12-4, 12-6)
Academic
Vocabulary
multistep more than one step
technique a way of doing something
Chapter
Concept
You use your knowledge of
exponents to add, subtract, and
multiply polynomials, and you
use polynomials to solve
problems.
Example:
You simplify expressions such
as 3x 2 2x 5x 2 1 and
x(3x 4 5x 3 x 2).
Standards AF1.2 and AF1.3 are also covered in this chapter. To see these standards unpacked, go to Chapter 1, p. 4 (AF1.2) and
Chapter 3, p. 114 (AF1.3).
588
Chapter 12
Study Strategy: Study for a Final Exam
A cumulative final exam will cover material you have learned over the
course of the year. You must be prepared if you want to be successful.
It may help you to make a study timeline like the one below.
2 weeks before the final:
•
Look at previous exams and homework to
determine areas I need to focus on; rework
problems that were incorrect or incomplete.
•
Make a list of all formulas I need to know
for the final.
•
Create a practice exam using problems
from the book that are similar to problems
from each exam.
1 week before the final:
•
Take the practice exam and check it. For
each problem I miss, find two or three
similar problems and work those.
•
Work with a friend in the class to quiz
each other on formulas from my list.
1 day before the final:
• Make sure I have pencils and scratch
paper.
Try This
Complete the following to help you prepare for your cumulative test.
1. Create a timeline that you will use to study for your final exam.
Polynomials
589
12-1
Why learn this? You can use polynomials
to find the height of a firework when it
explodes. (See Example 4.)
California
Standards
Preview of Algebra 1
Preparation for
10.0
Students add, subtract, multiply,
and divide monomials and
polynomials. Students solve
multistep problems, including
word problems, by using these
techniques.
Also covered: 7AF1.2
EXAMPLE
Polynomials
Recall that a monomial is a number, variable,
or a product of numbers and variables with
exponents that are whole numbers.
1
Monomials
2n, x3, 4a4b3, 7
Not monomials
5
p2.4, 2x, x
, 2
g
Identifying Monomials
Determine whether each expression is a monomial.
Vocabulary
polynomial
bionomial
trinomial
degree of a polynomial
1
x 4y 7
3
10xy 0.3
monomial
not a monomial
4 and 7 are whole numbers.
0.3 is not a whole number.
A polynomial is one monomial or the sum or difference of monomials.
A simplified polynomial can be classified by the number of monomials,
or terms, that it contains. A monomial has 1 term, a binomial has
2 terms, and a trinomial has 3 terms.
EXAMPLE
2
Classifying Polynomials by the Number of Terms
Classify each expression as a monomial, a binomial, a trinomial, or
not a polynomial.
35.55h 19.55g
binomial
Polynomial with 2 terms
2x 3y
monomial
Polynomial with 1 term
2
6x 2 4xy x
not a polynomial
7mn 4m 5n
trinomial
590
Chapter 12 Polynomials
2
x can be written as 2x1, where the
exponent is not a whole number.
Polynomial with 3 terms
The degree of a term is the sum of the exponents of the variables in
the term. The degree of a polynomial is the same as the degree of
the term with the greatest degree. A polynomial can be classified by
its degree.
2
5
4x
123
2x
xy
5
123
{
{
Degree 2
5
Degree 2
0
1
444444Degree
4444
24
444444Degree
4443
Degree 5
EXAMPLE
3
Classifying Polynomials by Their Degrees
Find the degree of each polynomial.
6x 2 3x 4
6x 2
Degree 2
3x
Degree 1
4
Degree 0
The greatest degree is 2, so the degree of 6x 2 3x 4 is 2.
6 3m2 4m5
6
Degree 0
3m 2
Degree 2
4m 5
Degree 5
The greatest degree is 5, so the degree of 6 3m 2 4m5 is 5.
To evaluate a polynomial, substitute the given number for each variable.
EXAMPLE
4
Physics Application
The height in feet of a firework launched straight up into the air
from s feet off the ground at velocity v after t seconds is given by
the polynomial 16t 2 vt s. Find the height of a firework
launched from a 10 ft platform at 200 ft/s after 5 seconds.
A polynomial is an
algebraic expression.
For help with
evaluating algebraic
expressions, see
Lesson 1-1.
16t 2 vt s
16(5)2 200(5) 10
400 1000 10
610
Write the polynomial expression for height.
Substitute 5 for t, 200 for v, and 10 for s.
Simplify.
The firework is 610 feet high 5 seconds after launching.
Think and Discuss
1. Describe two ways you can classify a polynomial. Give a
polynomial with three terms, and classify it two ways.
2. Explain why 5x2 3 is a polynomial but 5x 2 3 is not.
12-1 Polynomials
591
12-1 Exercises
California
Standards Practice
Preparation for Algebra 1
10.0;
7AF1.2
KEYWORD: MT8CA 12-1
KEYWORD: MT8CA Parent
GUIDED PRACTICE
See Example 1
Determine whether each expression is a monomial.
1. 2x 2y
See Example 2
4. 9
6. 5r 3r 2 6
3
7. 2 2x
8. 2
x
Find the degree of each polynomial.
9. 7m5 3m8
See Example 4
3. 3x
Classify each expression as a monomial, a binomial, a trinomial, or
not a polynomial.
3
5. 4x y
See Example 3
4
2. 3
x
10. x 4 4
11. 52
12. The trinomial 16t 2 24t 72 describes the height in feet of a ball
thrown straight up from a 72 ft platform with a velocity of 24 ft/s after
t seconds. What is the ball’s height after 2 seconds?
INDEPENDENT PRACTICE
See Example 1
See Example 2
See Example 3
See Example 4
Determine whether each expression is a monomial.
5y 4
13. 5.2x 3
14. 3x4
15. 6
x
4
16. 7x 4y 2
17. 210
18. 3x
Classify each expression as a monomial, a binomial, a trinomial, or
not a polynomial.
1
19. 9m2n6
20. 6g 3h2
21. 4x 3 2x 5 3
22. a 3
23. 2x
24. 5v 3s
Find the degree of each polynomial.
25. 2x 2 7x 1
26. 3m2 4m3 2
27. 2 3x 4x 4
28. 6p 4 7p2
29. n 2
30. 3y 8
31. The volume of a box with height x, length x 2, and width 3x 5 is given
by the trinomial 3x 3 x 2 10x. What is the volume of the box if its height
is 2 inches?
PRACTICE AND PROBLEM SOLVING
Extra Practice
See page EP24.
592
32. Transportation The distance in feet required for a car traveling at
r2
r mi/h to come to a stop can be approximated by the binomial 2
r.
0
About how many feet will be required for a car to stop if it is traveling at
70 mi/h?
Chapter 12 Polynomials
Classify each expression as a monomial, a binomial, a trinomial, or not a
polynomial. If it is a polynomial, give its degree.
33. 4x3
34. 7x0.7 3x
37. 2f 3 5f 5 f
38. 3 x
5
2
3
35. 6x 5x 2
36. 7y 2 6y
39. 6x 4x
40. 6x4
1
43. 2x 2 3x 4 5
41. 3b 2 9b 8b 3 42. 4 5x
44. 5
45. Transportation Gas mileage at speed s in miles per hour can be
estimated using the given polynomials. Evaluate the polynomials to
complete the table.
Gas Mileage (mi/gal)
40 mi/h
Compact
– 0.025s2 + 2.45s – 30
Midsize
– 0.015s2 + 1.45s – 13
Van
– 0.03s2 + 2.9s – 53
50 mi/h
60 mi/h
46. Reasoning Without evaluating, tell which of the following binomials has
the greatest value when x 10. Explain what method you used.
A
3x 5 8
B
3x 8 8
C
3x 2 8
D
3x 6 8
47. What’s the Error? A student says that the degree of the polynomial
4b5 7b9 6b is 5. What is the error?
48. Write About It Give some examples of words that start with mono-, bi-,
tri-, and poly-, and relate the meaning of each to polynomials.
49. Challenge The base of a triangle is described by the binomial x 2, and
its height is described by the trinomial 2x 2 3x 7. What is the area of
the triangle if x 5?
NS1.1, NS2.4, AF1.2
50. Multiple Choice The height in feet of a soccer ball kicked straight up into
the air from s feet off the ground at velocity v after t seconds is given by the
trinomial 16t 2 vt s. What is the height of the soccer ball kicked from
2 feet off the ground at 90 ft/s after 3 seconds?
A
3 ft
B
15 ft
C
90 ft
D
128 ft
51. Gridded Response What is the degree of the polynomial 6 7k 4 8k 9?
Write each number in scientific notation. (Lesson 4-5)
52. 4,080,000
53. 0.000035
54. 5,910,000,000
Find the two square roots of each number. (Lesson 4-6)
55. 49
56. 9
57. 81
58. 169
12-1 Polynomials
593
Model Polynomials
12-1
Use with Lesson 12-1
KEYWORD: MT8CA Lab12
KEY
REMEMBER
x2
x 2
0
x
x
0
1
1
0
California
Standards
Preview of Algebra 1
Preparation for
10.0 Students add, subtract,
multiply, and divide monomials and polynomials.
Students solve multistep problems, including word
problems, by using these techniques.
You can use algebra tiles to model polynomials. To model the polynomial
4x 2 x 3, you need four x 2-tiles, one x-tile, and three 1-tiles.
+
+
+
+
+
4x 2
−
−
−
x 3
Activity 1
1
Use algebra tiles to model the polynomial 2x 2 4x 6.
All signs are positive, so use all yellow tiles.
+
+
2x 2
594
Chapter 12 Polynomials
+ + + +
4x
+ +
+ +
+ +
6
2 Use algebra tiles to model the polynomial x 2 6x 4.
Modeling x 2 6x 4 is similar to modeling 2x 2 4x 6. Remember
to use red tiles for negative values.
−
− −
− −
+ + + + + +
x 2
6x
4
Think and Discuss
1. How do you know when to use red tiles?
Try This
Use algebra tiles to model each polynomial.
1. 2x 2 3x 5
2. 4x 2 5x 1
3. 5x 2 x 9
Activity 2
1 Write the polynomial modeled by the algebra tiles below.
+
+
2x 2
+ + + +
+ + + +
+ +
− − − − −
5x
10
The polynomial modeled by the tiles is 2x 2 5x 10.
Think and Discuss
1. How do you know the coefficient of the x 2-term in Activity 2?
Try This
Write a polynomial modeled by each group of algebra tiles.
1.
+
− −
2.
3.
+
12-1 Hands-On Lab
595
12-2
Why learn this? You can simplify polynomials
to determine the amount of lumber that can be
harvested from a tree. (See Example 4.)
California
Standards
Preview of Algebra 1
Preparation for
10.0
Students add, subtract, multiply,
and divide monomials and
polynomials. Students solve
multistep problems, including
word problems, by using these
techniques.
Also covered:
7AF1.3
Simplifying Polynomials
You can simplify a polynomial by adding or subtracting like terms.
The variables have the same powers.
Like terms
Not like terms
EXAMPLE
1
The variables have different powers.
Identifying Like Terms
Identify the like terms in each polynomial.
2a 4a2 3 5a 6a2
2a 4a2 3 5a 6a2
Identify like terms.
Like terms: 2a and 5a; 4a2 and 6a2
4x 5y 3 12x 5y 3 4x 3 6x 5y 3
4x 5y 3 12x 5y 3 4x 3 6x 5y 3
5 3
5 3
Identify like terms.
5 3
Like terms: 4x y , 12x y , and 6x y
5m2 3mn 4m
5m2 3mn 4m
There are no like terms.
Identify like terms.
To simplify a polynomial, combine like terms. First arrange the terms from
highest degree to lowest degree by using the Commutative Property.
EXAMPLE
2
Simplifying Polynomials by Combining Like Terms
Simplify.
x 2 5x 4 – 6 7x 2 3x 4 – 4x 2
When you rearrange
terms, move the
operation symbol in
front of each term
with that term.
596
x 2 5x4 6 7x 2 3x4 4x 2
Identify like terms.
5x 4 3x 4 x 2 7x 2 4x 2 6
8x 4 4x 2 6
Commutative Property
Chapter 12 Polynomials
Combine coefficients:
5 3 8 and 1 7 4 4.
Simplify.
5a2b 12ab 2 4a2b ab 2 3ab
5a2b 12ab 2 4a2b ab 2 3ab Identify like terms.
5a2b 4a2b 12ab 2 ab 2 3ab Commutative Property
9a2b 11ab2 3ab
Combine coefficients:
5 4 9 and 12 1 11.
You may need to use the Distributive Property to simplify a polynomial.
EXAMPLE
3
Simplifying Polynomials by Using the Distributive Property
Simplify.
4(3x 2 5x)
4(3x 2 5x)
4(3x 2) 4(5x)
12x 2 20x
Distributive Property
No like terms
2(4ab 2 5b) 3ab 2 6
2(4ab 2 5b) 3ab 2 6
2(4ab 2) 2(5b) 3ab 2 6
8ab 2 10b 3ab 2 6
11ab 2 10b 6
EXAMPLE
4
Distributive Property
Identify like terms.
Combine coefficients.
Business Application
A board foot is equal to the volume of a 1 ft by 1 ft by 1 in. piece of
lumber. The amount of lumber that can be harvested from a tree with
diameter d in. is approximately 20 0.005(d 3 30d 2 300d 1000)
board feet. Use the Distributive Property to write an equivalent
expression.
20 0.005(d 3 30d2 300d 1000) 20 0.005d 3 0.15d2 1.5d 5
15 0.005d 3 0.15d 2 1.5d
Think and Discuss
1. Tell how you know when you can combine like terms.
2. Give an example of an expression that you could simplify by
using the Distributive Property. Then give an expression that you
could simplify by combining like terms.
12-2 Simplifying Polynomials
597
12-2 Exercises
California
Standards Practice
Preparation for Algebra 1
10.0;
7AF1.3
KEYWORD: MT8CA 12-2
KEYWORD: MT8CA Parent
GUIDED PRACTICE
See Example 1
Identify the like terms in each polynomial.
1. 3b2 5b 4b2 b 6
2. 7mn 5m2n 2 8m2n 4m2n 2
See Example 2
Simplify.
3. 2x 2 3x 5x 2 7x 5
4. 6 3b 2b4 7b2 9 4b 3b 2
6. 7(2x 2 4x)
7. 5(3a2 5a) 2a2 4a
See Example 3
5. 4(3x 8)
See Example 4
8. The level of nitric oxide emissions, in parts per million, from a car engine is
approximated by the polynomial 40,000 5x(800 x2), where x is the
air-fuel ratio. Use the Distributive Property to write an equivalent expression.
INDEPENDENT PRACTICE
See Example 1
Identify the like terms in each polynomial.
9. t 4t 2 5t 2 5t 2
10. 8rs 3r 2s2 5r 2s 2 2rs 5
See Example 2
Simplify.
11. 2p 3p 2 5p 12p 2
12. 3fg f 2g fg 2 3fg 4f 2g 6fg 2
14. 2(b 3) 5b 3b 2
1
15. 2(6y 3 8) 3y 3
See Example 3
13. 5(x 2 5x) 4x 2 7x
See Example 4
16. The concentration of a certain medication in an average person’s
bloodstream h hours after injection can be estimated using the
expression 6(0.03h 0.002h 2 0.01h 3). Use the Distributive Property
to write an equivalent expression.
PRACTICE AND PROBLEM SOLVING
Extra Practice
See page EP24.
Simplify.
17. 2s2 3s 10s2 5s 3
18. 5gh 2 4g 2h 2g 2h g 2h
19. 2(x2 5x 4) 3x 7
20. 5(x x 5 x 3) 3x
21. 4(2m 3m2) 7(3m2 4m)
22. 6b4 2b 2 3(b 2 6)
23. 5mn 3m3n2 3(m3n2 4mn)
24. 3(4x y) 2(3x 2y)
25. Life Science The rate of flow in cm/s of blood in an artery at d cm
from the center is given by the polynomial 1000(0.04 d 2). Use the
Distributive Property to write an equivalent expression.
598
Chapter 12 Polynomials
Art
Abstract artists often use geometric shapes,
such as cubes, prisms, pyramids, and
spheres, to create sculptures.
26. Suppose the volume of a
sculpture is approximately
s 3 0.52s 3 0.18s 3 0.33s 3 cm3
and the surface area is approximately
6s 2 3.14s 2 7.62s 2 3.24s 2 cm2.
a. Simplify the polynomial expression
for the volume of the sculpture,
and find the volume of the
sculpture for s 5.
b. Simplify the polynomial
expression for the surface area of
the sculpture, and find the surface
area of the sculpture for s 5.
Balanced/Unbalanced O
by Fletcher Benton
27. A sculpture features a large ring with
an outer lateral surface area of about
44xy in2, an inner lateral surface area
of about 38xy in2, and 2 bases, each
with an area of about 41y in2. Write and
simplify a polynomial that expresses
the surface area of the ring.
28.
Challenge The volume of the ring on the
sculpture from Exercise 27 is 49πxy 2 36πxy 2 in3.
Simplify the polynomial, and find the volume for
x 12 and y 7.5. Give your answer both in terms
of π and to the nearest tenth.
Pyramid Balancing Cube and Sphere, artist unknown
KEYWORD: MT8CA Art
NS1.3, AF3.1
29. Multiple Choice Simplify the expression 4x 2 8x 3 9x 2 2x.
A
8x 3 5x 4 2x
B
8x 3 13x2 2x
C
8x 3 5x2 2x
D
5x 3
30. Short Response Identify the like terms in the polynomial
3x 4 5x2 x 4 4x 2. Then simplify the polynomial.
Find each percent to the nearest tenth. (Lesson 6-3)
31. What percent of 82 is 42?
32. What percent of 195 is 126?
Create a table for each quadratic function, and use it to graph the function. (Lesson 7- 4)
33. y x 2 1
34. y x 2 2x 1
12-2 Simplifying Polynomials
599
Quiz for Lessons 12-1 Through 12-2
12-1 Polynomials
Determine whether each expression is a monomial.
1
1. 5x2
1
2. 3x2 x 3
3. 7c 2d 8
Classify each expression as a monomial, a binomial, a trinomial, or not
a polynomial.
1
4. x x 2
5. a3 2a 17
6. y 2
Find the degree of each polynomial.
7. u 6 7
8. 3c 2 c5 c 1
9. 43
10. The depth, in feet below the ocean surface, of a submerging exploration
submarine after y minutes can be approximated by the polynomial
0.001y 4 0.12y 3 3.6y 2. Estimate the depth after 45 minutes.
12-2 Simplifying Polynomials
Identify the like terms in each polynomial.
11. 5x 2 y 2 4xy x 2y 2
12. z 2 7z 4z2 z 9
13. t 8 2t 6
14. 8ab 3ac 5bc 4ac 6ab
Simplify.
15. 6 3b5 2b3 7 5b3
16. 6y 2 y 7y 2 4y 5
17. 6(x 2 7x) 2x 2 7x
18. y 5 5y 4(5y 2)
19. The area of one face of a cube is given by the expression 3s 2 5s.
Write a polynomial to represent the total surface area of the cube.
20. The area of each lateral face of a regular square pyramid is given by
the expression 12b 2 2b. Write a polynomial to represent the lateral
surface area of the pyramid.
600
Chapter 12 Polynomials
California
Standards
MR2.1 Use estimation to verify the
reasonableness of calculated results.
Also covered:
NS1.7
Look Back
• Estimate to check that your answer is reasonable
Before you solve a word problem, you can often read through the
problem and make an estimate of the correct answer. Make sure
your answer is reasonable for the situation in the problem. After
you have solved the problem, compare your answer with the
original estimate. If your answer is not close to your estimate,
check your work again.
Each problem below has an incorrect answer given.
Explain why the answer is not reasonable, and
give your own estimate of the correct answer.
1 The perimeter of rectangle ABCD is 48 cm.
What is the value of x?
A
2x 9
B
x2
C
D
Answer: x 5
2 A patio layer can use 4x 6y ft of accent
edging to divide a patio into three sections
measuring x ft long by y ft wide. If each
section must be at least 15 ft long and
have an area of at least 165 ft2, what is
the minimum amount of edging needed
for the patio?
y ft
x ft
3 A baseball is thrown straight up from a
height of 3 ft at 30 mi/h. The height of
the baseball in feet after t seconds is
16t 2 44t 3. How long will it take the
baseball to reach its maximum height?
Answer: 5 minutes
4 Jacob deposited $2000 in a savings account
that earns 6% simple interest. How much
money will he have in the account after
7 years?
Answer: $1925
Answer: 52 ft
Focus on Problem Solving
601
Model Polynomial
Addition
12-3
Use with Lesson 12-3
KEYWORD: MT8CA Lab12
KEY
REMEMBER
x2
x 2
0
x
x
0
1
1
0
California
Standards
Preview of Algebra 1
10.0 Students add, subtract, multiply, and divide
monomials and polynomials. Students solve multistep
problems, including word problems, by using these techniques.
You can use algebra tiles to model polynomial addition.
Activity
1
Use algebra tiles to find (2x 2 2x 3) (x 2 x 5).
2x
2x 2
x2
x
3
5
Use tiles to represent all terms from
both expressions.
Remove any zero pairs.
The remaining tiles represent the sum
3x 2 x 2.
3x 2
x
2
Think and Discuss
1. Explain what happens when you add the x-terms in (2x 5) (2x 4).
Try This
Use algebra tiles to find each sum.
1. (3m2 2m 6) (4m2 m 3)
602
Chapter 12 Polynomials
2. (5b2 4b 1) (b 1)
12-3
Adding Polynomials
Why learn this? You can add
polynomials to find the amount of
material needed to mat and frame a
picture. (See Example 3.)
California
Standards
Preview of Algebra 1
10.0 Students add, subtract,
multiply, and divide monomials and
polynomials. Students solve
multistep problems, including
word problems, by using these
techniques.
Also covered:
7AF1.3
EXAMPLE
Adding polynomials is similar to
simplifying polynomials. One way to
add polynomials is to write them
horizontally. First write the
polynomials as one polynomial,
and then use the Commutative
Property to combine like terms.
1
Adding Polynomials Horizontally
Add.
(6x 2 3x 4) (7x 6)
6x 2 3x 4 7x 6
Write as one polynomial.
6x 2 3x 7x 4 6
Commutative Property
6x 2 4x 2
Combine like terms.
(4cd 2 3cd 6) (7cd 6cd 2 6)
4cd 2 3cd 6 7cd 6cd 2 6
2
2
Write as one polynomial.
4cd 6cd 3cd 7cd 6 6
Commutative Property
10cd 2 4cd
Combine like terms.
(ab 2 4a) (3ab 2 4a 3) (a 5)
ab 2 4a 3ab 2 4a 3 a 5
2
2
ab 3ab 4a 4a a 3 5
2
4ab 9a 2
Write as one polynomial.
Commutative Property
Combine like terms.
You can also add polynomials in a vertical format. Write the second
polynomial below the first one. Be sure to line up the like terms.
If the terms are rearranged, remember to keep the correct sign with
each term.
12-3 Adding Polynomials
603
EXAMPLE
2
Adding Polynomials Vertically
Add.
(5a2 4a 2) (4a2 3a 1)
5a 2 4a 2
4a 2 3a 1
Place like terms in columns.
9a 2 7a 3
Combine like terms.
(2xy 2 3x 4y) (8xy 2 2x 3)
2xy 2 3x 4y
8xy 2 2x
3
Place like terms in columns.
2
10xy x 4y 3
Combine like terms.
(4a2b 2 3a2 6ab) (4ab a 2 5) (3 7ab)
4a 2b 2 3a 2 6ab
a 2 4ab 5
7ab 3
Place like terms in columns.
Combine like terms.
4a 2b 2 4a 2 3ab 2
EXAMPLE
Reasoning
3
Art Application
f
m
14 in.
Mina is putting a mat of width m
and a frame of width f around
f m 11 in.
m f
an 11-inch by 14-inch picture. Find
an expression for the amount of
m
framing material she needs.
f
The amount of material Mina
needs equals the perimeter of the outside of the frame. Draw a
diagram to help you determine the outer dimensions of the frame.
Width 14 m m f f
14 2m 2f
Length 11 m m f f
11 2m 2f
P 2(11 2m 2f ) 2(14 2m 2f )
P 2w 2
22 4m 4f 28 4m 4f
Simplify.
50 8m 8f
Combine like terms.
She will need 50 8m 8f inches of framing material.
Think and Discuss
1. Compare adding (5x 2 2x) (3x 2 2x) vertically with adding
it horizontally.
2. Explain how adding polynomials is similar to simplifying
polynomials.
604
Chapter 12 Polynomials
12-3 Exercises
California
Standards Practice
Preview of Algebra 1
10.0;
7AF1.3
KEYWORD: MT8CA 12-3
KEYWORD: MT8CA Parent
GUIDED PRACTICE
See Example 1
Add.
1. (5x 3 6x 1) (3x 7)
2. (22x 6) (14x 3)
3. (r 2s 3rs) (4r 2s 8rs) (6r 2s 14rs)
See Example 2
4. (4b 2 5b 10) (6b 2 7b 8)
5. (9ab 2 5ab 6a 2b) (8ab 12a 2b 6) (6ab 2 5a 2b 14)
6. (h4j hj 3 hj 6) (5hj 3 5) (6h4j 7hj)
See Example 3
7. Colette is putting a mat of width 3w and a frame of width w around a
16-inch by 48-inch poster. Find an expression for the amount of frame
material she needs.
16 in.
3w
w
48 in.
w
3w
INDEPENDENT PRACTICE
See Example 1
Add.
8. (5x 2y 4xy 3) (7xy 3x 2y)
9. (5g 9) (7g 2 4g 8)
10. (6bc 2b 2c 2 8bc 2) (6bc 3bc 2)
11. (9h4 5h 4h6) (h6 6h 3h4)
12. (4pq 5p 2q 9pq 2) (6p 2q 11pq 2) (2pq 2 7pq 6p 2q)
See Example 2
13. (8t 2 4t 3) (5t 2 8t 9)
14. (5b 3c 2 3b 2c 2bc) (8b 3c 2 3bc 14) (b 2c 5bc 9)
15. (w 2 3w 5) (2w 3w 2 1) (w 2 w 6)
See Example 3
16. Each side of an equilateral triangle has
length w 3. Each side of a square
has length 4w 2. Write an expression
for the sum of the perimeter of the
equilateral triangle and the perimeter
of the square.
w3
4w 2
12-3 Adding Polynomials
605
PRACTICE AND PROBLEM SOLVING
Extra Practice
Add.
See page EP25.
17. (3w 2y 3wy 2 4wy) (5wy 2wy 2 7w 2y) (wy 2 5wy 3w 2y)
18. (2p 2t 3pt 5) (p 2t 2pt 2 3pt) (1 5pt 2 p 2t)
19. Geometry Write and simplify an expression for the combined volumes
of a sphere with volume 43πr 3, a cube with volume r 3, and a prism with
volume r 3 4r 2 5r 2. Use 3.14 for π.
Business
20. Business The cost of producing n toys at a factory is given by the polynomial
0.5n 2 3n 12. The cost of packaging is 0.25n2 5n 4. Write and simplify an
expression for the total cost of producing and packaging n toys.
21. Reasoning Two airplanes depart from the same airport, traveling in opposite
directions. After 2 hours, one airplane is x 2 2x 400 miles from the airport,
and the other airplane is 3x 2 50x 100 miles from the airport. How could
you determine the distance between the two planes? Explain.
According to the
Toy Industry
Association,
$24.6 billion was
spent on toys
worldwide in 2000.
22. Write two polynomials whose sum is 3m2 4m 6.
23. Choose a Strategy What is the missing term?
(6x 2 4x 3) (3x 2 5) 3x 2 6x 8
KEYWORD: MT8CA Toys
A
2x
B
2x
C
10x
D
10x
24. Write a Problem A plane leaves an airport heading north at x 3 mi/h.
At the same time, another plane leaves the same airport, heading south at
x 4 mi/h. Write a problem using the speeds of both planes.
25. Write About It Explain how to add polynomials.
26. Challenge What polynomial would have to be added
to 6x 2 4x 5 so that the sum is 3x 2 4x 7?
NS1.5, MG1.2
27. Multiple Choice Debbie is putting a deck of width 5w around her 20 foot
by 80 foot pool. Which is the expression for the perimeter of the pool and
deck combined?
A
100 10w
B
150 15w
C
200 20w
D
250 25w
28. Gridded Response What is the sum of (10x 3 4x 4 3x 5 10),
(9x 3 8x 4 20x 5 15), and (x 3 4x 4 17x 5 2)?
Find the fraction equivalent of each decimal. (Lesson 2-1)
29. 1.1
30. 0.08
31. 0.24
32. 4.05
Using the scale 1 in. 6 ft, find the height or length of each object. (Lesson 5-7)
33. a 14 in. tall model of an office building
606
Chapter 12 Polynomials
34. a 2.5 in. long model of a train
Model Polynomial
Subtraction
12-4
Use with Lesson 12-4
KEYWORD: MT8CA Lab12
KEY
REMEMBER
x2
x 2
0
x
x
0
1
1
0
California
Standards
Preview of Algebra 1
10.0 Students add, subtract, multiply, and divide
monomials and polynomials. Students solve multistep
problems, including word problems, by using these techniques.
You can use algebra tiles to model polynomial subtraction.
Activity
1 Use algebra tiles to find (2x 2 2x 3) (x 2 x 3).
2x 2
2x
3
x 2
x
3
Remember, subtracting is the same
as adding the opposite. Use the
opposite of each term in x 2 x 3.
x2
Remove any zero pairs.
3x
6
The remaining tiles represent the
difference x 2 3x 6.
Think and Discuss
1. Why do you have to add the opposite when subtracting?
Try This
Use algebra tiles to find each difference.
1. (6m 2 2m) (4m2)
2. (5b 2 9) (b 9)
12-4 Hands-On Lab
607
12-4
Who uses this? Manufacturers
can subtract polynomials to
estimate the cost of making a
product and the revenue from
sales. (See Example 4.)
California
Standards
Preview of Algebra 1
10.0 Students add, subtract,
multiply, and divide monomials and
polynomials. Students solve
multistep problems, including
word problems, by using these
techniques.
Also covered:
7AF1.3
EXAMPLE
Subtracting Polynomials
Recall that to subtract an integer,
you add its opposite. To subtract
a polynomial, you first need to find
its opposite.
1
Finding the Opposite of a Polynomial
Find the opposite of each polynomial.
8x 3y 6z
(8x 3y 6z)
8x 3y 6z
is a negative term.
12x 2 5x
(12x 2 5x)
12x 2 5x
Distributive Property
3ab 2 4ab 3
(3ab 2 4ab 3)
3ab 2 4ab 3
Distributive Property
The opposite of a positive term
To subtract a polynomial, add its opposite.
EXAMPLE
2
Subtracting Polynomials Horizontally
Subtract.
(n3 n 5n2) (7n 4n2 9)
(n3 n 5n2) (7n 4n2 9)
n3 5n2 4n2 n 7n 9
n3 9n2 8n 9
(2cd 2 cd 4) (7cd 2 2 5cd )
(2cd 2 cd 4) (7cd 2 2 5cd)
2cd 2 7cd 2 cd 5cd 4 2
5cd 2 6cd 2
608
Chapter 12 Polynomials
Add the opposite.
Commutative Property
Combine like terms.
Add the opposite.
Commutative Property
Combine like terms.
You can also subtract polynomials in a vertical format. Write the
second polynomial below the first one, lining up the like terms.
EXAMPLE
3
Subtracting Polynomials Vertically
Subtract.
(x 3 4x 1) (6x 3 3x 5)
(x 3 4x 1)
x 3 4x 1
(6x 3 3x 5)
6x 3 3x 5
3
5x x 4
Add the opposite.
(4m2n 3mn 4m) (8m2n 6mn 3)
(4m2n 3mn 4m)
4m2n 3mn 4m
(8m2n 6mn 3)
8m2n 6mn
3 Add the
12m2n 3mn 4m 3 opposite.
(4x 2y 2 xy 6x) (7x 5xy 6)
(4x 2y 2 xy 6x)
4x 2y 2 xy 6x
(7x 5xy 6)
5xy 7x 6
2
2
4x y 4xy 13x 6
EXAMPLE
4
Rearrange terms
as needed.
Business Application
Suppose the cost in dollars of producing x model kits is given by
the polynomial 3x 400,000 and the revenue generated from
sales is given by the polynomial 0.00004x 2 20x. Find a
polynomial expression for the profit from making and selling x
model kits, and evaluate the expression for x 200,000.
0.00004x 2 20x (3x 400,000)
0.00004x 2 20x (3x 400,00)
0.00004x 2 20x 3x 400,000
0.00004x 2 17x 400,000
revenue cost
Add the opposite.
Commutative Property
Combine like terms.
The profit is given by the polynomial 0.00004x2 17x 400,000.
For x 200,000,
0.00004(200,000)2 17(200,000) 400,000 1,400,000.
The profit is $1,400,000, or $1.4 million.
Think and Discuss
1. Explain how to find the opposite of a polynomial.
2. Compare subtracting polynomials with adding polynomials.
12-4 Subtracting Polynomials
609
12-4 Exercises
California
Standards Practice
Preview of Algebra 1
10.0;
7AF1.3
KEYWORD: MT8CA 12-4
KEYWORD: MT8CA Parent
GUIDED PRACTICE
See Example 1
See Example 2
Find the opposite of each polynomial.
1. 4x2y
2. 5x 4xy5
3. 3x2 8x 5
4. 5y2 2y 4
5. 8x3 5x 6
6. 6xy2 4y 2
Subtract.
7. (2b 3 5b 2 8) (4b 3 b 12)
8. 7b (4b 2 3b 12)
9. (4m2n 7mn 3mn2) (5mn 4m2n)
See Example 3
10. (8x 2 4x 1) (5x 2 2x 3)
11. (2x 2y xy 3x 4) (4xy 7x 4)
12. (5ab 2 4ab 3a 2b) (7 5ab 3ab 2 4a 2b)
See Example 4
13. The volume of a rectangular prism, in cubic inches, is given by the
expression x 3 3x 2 5x 7. The volume of a smaller rectangular prism
is given by the expression 5x 3 6x 2 7x 14. How much greater is the
volume of the larger rectangular prism? Evaluate the expression for x 3.
INDEPENDENT PRACTICE
See Example 1
See Example 2
Find the opposite of each polynomial.
14. 4rn2
15. 3v 5v2
16. 4m2 6m 2
17. 4xy2 2xy
18. 8n6 5n3 n
19. 9b2 2b 9
Subtract.
20. (6w 2 3w 6) (3w 2 4w 5)
21. (14a a2) (8 a 2 9a)
22. (7r 2s 2 5rs 2 6r 2s 7rs) (3rs 2 3r 2s 8rs)
See Example 3
23. (4x 2 6x 1) (3x 2 9x 5)
24. (3a2b 2 4ab 2a 4) (4a 2b 2 5a 3b 6)
25. (4pt 2 6p 3 5p 2t 2) (5p 2 6pt 2 7p 2t 2)
See Example 4
610
26. The current in an electrical circuit at t seconds is 4 t 3 5t 2 2t 200
amperes. The current in another electrical circuit is 3t 3 2t 2 5t 100
amperes. Write an expression to show the difference in the two currents.
Chapter 12 Polynomials
PRACTICE AND PROBLEM SOLVING
Extra Practice
See page EP25.
Subtract.
27. (6a 3b 5ab) (6a 5b 7ab)
28. (4pq 2 6p 2q 3pq) (7pq 2 7p 2q 3pq)
29. (9y 2 5x 2y x 2) (3y 2 7x 2y 4x 2)
30. The area of the rectangle is 2a 2 4a 5 cm2.
The area of the square is a 2 2a 6 cm2.
What is the area of the shaded region?
31. The area of the square is 4x 2 2x 6 in2. The
area of the triangle is 2x 2 4x 5 in2. What is
the area of the shaded region?
32. Business The price in dollars of one share of stock after y years is
modeled by the expression 3y 3 6y 4.25. The price of one share of
another stock is modeled by 3y 3 24y 25.5. What expression shows the
difference in price of the two stocks after y years?
33. Choose a Strategy Which polynomial has the greatest value when x 6?
A
x 2 3x 8
C
x 3 30x 200
B
2x 4 7x 14
D
x 5 100x 4 10
34. Write About It Explain how to subtract the polynomial
5x 3 3x 6 from 4x 3 7x 1.
35. Challenge Find the values of a, b, c, and d that make the equation true.
(2t 3 at 2 4bt 6) (ct 3 4t 2 7t 1) 4t 3 5t 2 15t d
AF1.2,
AF1.3, AF2.2
36. Multiple Choice What is the opposite of the polynomial
4a2b 3ab2 5ab?
A
4a2b 3ab2 5ab
C
4a2b 3ab2 5ab
B
4a2b 3ab2 5ab
D
4a2b 3ab2 5ab
37. Extended Response A square has an area of x 2 10x 25. A triangle
inside the square has an area of x 2 4. Create an expression for the area of
the square minus the area of the triangle. Evaluate the expression for x 8.
Multiply. (Lesson 4-4)
38. (3x)(6x)
39. (9m3)(7m2)
40. (8ab4)(5a4)
41. (4r4s)(2r 6s 9)
Simplify. (Lesson 12-2)
42. x 3y 2 2x 2y 4x 3y 2
43. 4(zy 3 2zy) 3zy 5zy 3 44. 6(3x 2 6x 1)
12-4 Subtracting Polynomials
611
12-5
Why learn this? You can multiply polynomials
and monomials to determine the dimensions of a
planter box. (See Example 3.)
California
Standards
Preview of Algebra 1
10.0 Students add, subtract,
multiply, and divide monomials
and polynomials. Students solve
multistep problems, including
word problems, by using these
techniques.
Also covered: 7AF1.2,
7AF1.3, 7AF2.2
EXAMPLE
Multiplying Polynomials
by Monomials
Remember that when you multiply two powers with
the same bases, you add the exponents. To multiply
two monomials, multiply the coefficients and add
the exponents of the variables that are the same.
(5m2n3)(6m3n6) 5 6 m 2 3n 3 6 30m5n9
1
Multiplying Monomials
Multiply.
(4r 3s4)(6r 5s 6)
4 6 r 3 5 s4 6
24r 8s 10
Multiply coefficients. Add exponents that
(9x 2y)(2x 3yz 6)
9 2 x 2 3 y1 1 z 6
18x 5y 2z 6
Multiply coefficients. Add exponents that
have the same base.
have the same base.
To multiply a polynomial by a monomial, use the Distributive Property.
Multiply every term of the polynomial by the monomial.
EXAMPLE
2
Multiplying a Polynomial by a Monomial
Multiply.
1
x(y z)
4
1
x(y z)
4
1
1
xy xz
4
4
When multiplying a
polynomial by a
negative monomial,
be sure to distribute
the negative sign.
612
5a 2b(3a4b 3 6a 2b 3)
5a 2b(3a 4b 3 6a 2b 3) Multiply each term in the parentheses
15a 6b 4 30a 4b 4
by 5a2b.
Chapter 12 Polynomials
1
Multiply each term in the parentheses by 4x.
Multiply.
5rs 2(r 2s4 3rs 3 4rst)
5rs 2(r 2s 4 3rs 3 4rst)
5r 3s 6 15r 2s 5 20r 2s 3t
EXAMPLE
3
Multiply each term in the
parentheses by 5rs 2.
PROBLEM SOLVING APPLICATION
Chrystelle is making a planter box with
a square base. She wants the height of
the box to be 3 inches more than the
side length of the base. If she wants the
volume of the box to be 6804 in3, what
should the side length of the base be?
Reasoning
1 Understand the Problem
1.
If the side length of the base is s, then the height is s 3. The volume
is s s (s 3) s2(s 3). The answer will be a value of s that makes
the volume of the box equal to 6804 in3.
1.2 Make a Plan
You can make a table of values for the polynomial to try to find the
value of s. Use the Distributive Property to write the expression
s 2(s 3) another way. Use substitution to complete the table.
1.3 Solve
s2(s 3) s3 3s2
s
s 3 3s 2
15
Distributive Property
16
17
18
153 3(15)2 163 3(16)2 173 3(17)2 183 3(18)2
4050
4864
5780
6804
The side length of the base should be 18 inches.
1.4 Look Back
If the side length of the base were 18 inches and the height
were 3 inches more, or 21 inches, then the volume would be
18 18 21 6804 in3. The answer is reasonable.
Think and Discuss
1. Compare multiplying two monomials with multiplying a
polynomial by a monomial.
12-5 Multiplying Polynomials by Monomials
613
12-5 Exercises
California
Standards Practice
Preview of Algebra 1
10.0;
7AF1.2,
7AF1.3, 7AF2.2
KEYWORD: MT8CA 12-5
KEYWORD: MT8CA Parent
GUIDED PRACTICE
See Example 1
See Example 2
Multiply.
1. (5s 2t 2)(3st 3)
2. (x 2y 3)(6x 4y 3)
3. (5h2j 4)(7h 4j 6 )
4. 6m(4m 5)
5. 7p 3r(5pr 4)
6. 13g 5h3(10g 5h2)
8. 4ab(a 2b ab 2)
7. 2h(3m 4h)
9. 3x(x 2 5x 10)
See Example 3
10. 6c 2d(3cd 3 5c 3d 2 4cd )
11. The formula for the area of a trapezoid is A 12h(b1 b2), where h is the
trapezoid’s height and b1 and b2 are the lengths of its bases. Use the
Distributive Property to simplify the expression. Then use the expression to
find the area of a trapezoid with height 12 in. and base lengths 9 in. and 7 in.
INDEPENDENT PRACTICE
See Example 1
See Example 2
See Example 3
Multiply.
12. (6x 2y 5)(3xy 4)
13. (gh3)(2g 2h5)
15. (s 4t 3)(2st)
1
16. 12x 9y 7 2x 3y
14. (4a 2b)(2b 3)
17. 2.5j 3(3h 5j 7)
18. (3m3n4)(1 5mn5)
19. 3z(5z 2 4z)
20. 3h2(6h 3h3)
21. 3cd(2c 3d 2 4cd 2)
22. 2b(4b 4 7b 10)
23. 3s 2t 2(4s 2t 5st 2s 2t 2)
24. A rectangle has a base of length 3x 2y and a height of 2x 3 4xy 3.
Write and simplify an expression for the area of the rectangle. Then
find the area of the rectangle if x 2 and y 1.
PRACTICE AND PROBLEM SOLVING
Extra Practice
See page EP25.
Multiply.
25. (3b 2)(8b 4)
26. (4m2n)(2mn4)
27. (2a 2b2)(3ab 4)
28. 7g(g 5)
29. 3m2(m3 5m)
30. 2ab(3a 2b 3ab2)
31. x 4(x x 3y 5)
32. m(x 3)
33. f 2g 2(3 f g 3)
34. x 2(x 2 4x 9)
35. (4m 2p 4)(5m 2p 4 3mp 3 6m 2p)
36. 3wz(5w 4z 2 4wz 2 6w 2z 2)
37. Felix is building a cylindrical-shaped storage container. The height of the
container is x 3 y 3. Write and simplify an expression for the volume
using the formula V πr 2h. Then find the volume with r 112 feet,
x 3, and y 1.
614
Chapter 12 Polynomials
38. Health The table gives some formulas for finding the target heart rate for
a person of age a exercising at p percent of his or her maximum heart rate.
Target Heart Rate
Nonathletic
Male
Female
p(220 a)
p(226 a)
1
p(410
2
Fit
a)
1
p(422
2
a)
a. Use the Distributive Property to simplify each expression.
b. Use your answer from part a to write an expression for the difference
between the target heart rate for a fit male and for a fit female. Both
people are age a and are exercising at p percent of their maximum
heart rates.
39. What’s the Question? A square prism has a base area of x 2 and a
height of 3x 4. If the answer is 3x 3 4x 2, what is the question? If the
answer is 14x 2 16x, what is the question?
40. Write About It If a polynomial is multiplied by a monomial, what can
you say about the number of terms in the answer? What can you say
about the degree of the answer?
41. Challenge On a multiple-choice test, if the probability of guessing each
question correctly is p, then the probability of guessing two or more
correctly out of four is 6p2(1 2p p 2) 4p 3(1 p) p 4. Simplify the
expression. Then write an expression for the probability of guessing fewer
than two out of four correctly.
AF1.3, MG2.1
42. Multiple Choice The width of a rectangle is 13 feet less than twice its length.
Which of the following shows an expression for the area of the rectangle?
A
22 13
B
22 13
C
2 13
D
6 26
43. Short Response A triangle has base 10cd2 and height 3c2d2 4cd2.
Write and simplify an expression for the area of the triangle. Then evaluate
the expression for c 2 and d 3.
Combine like terms. (Lesson 3-2)
44. 8x 3y x 7
45. 4m n 7 2n 5
46. 9a 11 6b 10a 7b
Find the surface area of each figure. Use 3.14 for π. (Lesson 10-4)
47. a rectangular prism with base 4 in. by 3 in. and height 2.5 in.
48. a cylinder with radius 10 cm and height 7 cm
12-5 Multiplying Polynomials by Monomials
615
Multiply Binomials
12-6
Use with Lesson 12-6
KEYWORD: MT8CA Lab12
KEY
REMEMBER
x2
x 2
x
x
1
1
The area of a rectangle
with base b and height
h is given by A bh.
California
Standards
Preview of Algebra 1
10.0 Students add, subtract, multiply, and divide
monomials and polynomials. Students solve multistep
problems, including word problems, by using these techniques.
You can use algebra tiles to find the product of two binomials.
Activity 1
x3
1 To model (x 3)(2x 1) with
algebra tiles, make a rectangle
with base x 3 and height 2x 1.
2x 1
Area (x 3)(2x 1)
2x 2 7x 3
x2
2 Use algebra tiles to find
(x 2)(x 1).
x 1
Think and Discuss
1. Explain how to determine the signs of each term in the product
when you are multiplying (x 3)(x 2).
2. How can you use algebra tiles to find (x 3)(x 3)?
616
Chapter 12 Polynomials
Area (x 2)(x 1)
x 2 3x 2
Try This
Use algebra tiles to find each product.
1. (x 4)(x 4)
2. (x 3)(x 2)
3. (x 5)(x 3)
Activity 2
Write two binomials whose product is modeled by the algebra tiles below,
and then write the product as a polynomial expression.
The base of the rectangle is x 5 and the height is x 2, so the binomial
product is (x 5)(x 2).
The model shows one x 2-tile, seven x-tiles, and ten 1-tiles, so the
polynomial expression is x 2 7x 10.
Think and Discuss
1. Write an expression modeled by the algebra tiles below. How many
zero pairs are modeled? Describe them.
Try This
Write two binomials whose product is modeled by each set of algebra
tiles below, and then write the product as a polynomial expression.
1.
2.
3.
12-6 Hands-On Lab
617
12-6
Why learn this? You can
multiply binomials to determine
the area of a walkway around a
cactus garden. (See Example 2.)
California
Standards
Preview of Algebra 1
10.0 Students add, subtract,
multiply, and divide monomials and
polynomials. Students solve
multistep problems, including
word problems, by using these
techniques.
Vocabulary
FOIL
Multiplying Binomials
You can use the Distributive
Property to multiply two
binomials.
678
(x y)(x z) x(x z) y(x z)
x 2 xz yx yz
The product can be simplified using the FOIL method: multiply the
First terms, the Outer terms, the Inner terms, and the Last terms of
the binomials.
First
Last
F
O
I
L
Inner
Outer
EXAMPLE
1
Multiplying Two Binomials
Multiply.
(p 2)(3 q)
(p 2)(3 q)
When you multiply
two binomials,
you will get four
products. Then
combine like terms.
(m n)(p q)
FOIL
3p pq 6 2q
mp mq np nq
(x 2)(x 5)
(3m n)(m 2n)
(x 2)(x 5)
FOIL
x 2 5x 2x 10
x 2 7x 10
Combine like terms.
618
(m n)(p q)
Chapter 12 Polynomials
(3m n)(m 2n)
3m 2 6mn mn 2n 2
3m 2 5mn 2n 2
EXAMPLE
2
Landscaping Application
Find the area of a bark walkway of width x ft
around a 12 ft by 5 ft cactus garden.
Area of
Walkway Total Area
(5 2x)(12 2x)
Area of
Flower Bed
(5)(12)
60 10x 24x 4x 2 60
34x 4x 2
The walkway area is 4x 2 34x ft2.
Binomial products of the form (a b)2, (a b)2, and (a b)(a b)
are often called special products.
EXAMPLE
3
Special Products of Binomials
Multiply.
(x 3)2
(a b)2
(x 3)(x 3)
(a b)(a b)
x 2 3x 3x 32
x 2 6x 9
a 2 ab ab b 2
a2 2ab b2
(n 3)(n 3)
(n 3)(n 3)
n2 3n 3n 32
n2 9
3n 3n 0
Special Products of Binomials
(a b)2 a2 ab ab b2 a2 2ab b2
(a b)2 a2 ab ab b2 a2 2ab b2
(a b)(a b) a2 ab ab b2 a2 b2
Think and Discuss
1. Give an example of a product of two binomials that has 4 terms,
one that has 3 terms, and one that has 2 terms.
12-6 Multiplying Binomials
619
12-6 Exercises
California
Standards Practice
Preview of Algebra 1
10.0
KEYWORD: MT8CA 12-6
KEYWORD: MT8CA Parent
GUIDED PRACTICE
See Example 1
See Example 2
See Example 3
Multiply.
1. (x 5)(y 4)
2. (x 3)(x 7)
3. (3m 5)(4m 9)
4. (h 2)(3h 4)
5. (m 2)(m 7)
6. (b 3c)(4b c)
7. A courtyard is 20 ft by 30 ft. There is a walkway of width x all the way
around the courtyard. Find the area of the walkway.
Multiply.
8. (x 2)2
9. (b 3)(b 3)
10. (x 4)2
11. (3x 5)2
INDEPENDENT PRACTICE
See Example 1
Multiply.
12. (x 4)(x 3)
13. (v 1)(v 5)
14. (w 6)(w 2)
15. (3x 5)(x 6)
16. (4m 1)(3m 2)
17. (3b c)(4b 5c)
18. (3t 1)(t 1)
19. (3r s)(4r 5s)
20. (5n 3b)(n 2b)
See Example 2
21. Construction The Gonzalez family is having a pool to swim laps built in
their backyard. The pool will be 25 yards long by 5 yards wide. There will
be a cement deck of width x yards around the pool. Find the total area of
the pool and the deck.
See Example 3
Multiply.
22. (x 5)2
23. (b 3)2
24. (x 4)(x 4)
25. (2x 3)(2x 3)
26. (4x 1)2
27. (a 7)2
PRACTICE AND PROBLEM SOLVING
Extra Practice
See page EP25.
Multiply.
28. (m 6)(m 6)
29. (b 5)(b 12)
30. (q 6)(q 5)
31. (t 9)(t 4)
32. (g 3)(g 3)
33. (3b 7)(b 4)
34. (3t 1)(6t 7)
35. (4m n)(m 3n)
36. (3a 6b)2
37. (r 5)(r 5)
38. (5q 2)2
39. (3r 2s)(5r 4s)
40. A metalworker makes a box from a 15 in. by 20 in. piece of tin by cutting
a square with side length x out of each corner and folding up the sides.
Write and simplify an expression for the area of the base of the box.
620
Chapter 12 Polynomials
Life Science
A. V. Hill (1886–1977) was a biophysicist and pioneer in the study
of how muscles work. He studied muscle contractions in frogs
and came up with an equation relating the force generated by
a muscle to the speed at which the muscle contracts. Hill
expressed this relationship as
(P a)(V b) c,
where P is the force generated by the muscle, a is the force needed to
make the muscle contract, V is the speed at which the muscle contracts,
b is the smallest contraction rate of the muscle, and c is a constant.
41. Use the FOIL method to simplify Hill’s equation.
42. Suppose the force a needed to make the muscle
contract is approximately 14 the maximum force
the muscle can generate. Use Hill’s equation
to write an equation for a muscle
generating the maximum possible
force M. Simplify the equation.
43.
Write About It In Hill’s equation,
what happens to V as P increases?
What happens to P as V increases?
(Hint: You can substitute the value of
1 for a, b, and c to help you see the
relationship between P and V.)
44.
Challenge Solve Hill’s equation
for P. Assume that no variables equal 0.
The muscles on opposite
sides of a bone work as a pair.
Muscles in pairs alternately
contract and relax to move
your skeleton.
AF1.3,
AF4.1
45. Multiple Choice Which polynomial shows the result of using the FOIL
method to find (x 2)(x 6)?
A
x 2 12
B
x 2 6x 2x 12
C
2x 2x 12
D
x2 4
46. Gridded Response Multiply 3a 2b and 5a 8b. What is the coefficient of ab?
Solve. (Lesson 2-8)
47. 5x 33.6 91.9
48. 14 1.2j 16.4
49. 4.4 0.6y 6.82
50. 3.7 26.2x 9.4
Simplify. (Lesson 12-2)
51. 4(m2 3m 6)
52. 3(a2b 4a 3ab) 2ab 53. x 2y 4(xy 2 3x 2y 4xy)
12-6 Multiplying Binomials
621
Quiz for Lessons 12-3 Through 12-6
12-3 Adding Polynomials
Add.
1. (8x 3 6x 3) (2x 6)
3 2
2
2. (30x 7) (12x 5)
3 2
3. (7b c 6b c 3bc) (8b c 5bc 13) (4b 2c 5bc 9)
4. (2w 2 4w 6) (3w 4w 2 5) (w 2 4)
5. Each side of an equilateral triangle has
length w 2. Each side of a square has
length 3w 4. Write an expression for the
sum of the perimeter of the equilateral
triangle and the perimeter of the square.
12-4 Subtracting Polynomials
w2
3w 4
Find the opposite of each polynomial.
6. 3x 4xy 3
7. 2m2 6m 3
8. 5v 7v 2
Subtract.
9. 10b2 (3b2 6b 8)
10. (13a a2) (9 a 7a) 11. (6x 2 6x) (3x 2 7x)
12. The population of a bacteria colony after h hours is 4h3 5h2 2h 200.
The population of another bacteria colony is 3h3 2h2 5h 200.
Write an expression to show the difference between the two populations.
Evaluate the expression for h 1000.
12-5 Multiplying Polynomials by Monomials
Multiply.
13. (4x 3y 3 )(3xy6 )
14. (3hj 5)(6h4j 5 )
15. 4s 2t 2(4s2t 3st s 2t 2)
16. A triangle has a base of length 2x 2 y and a height of x 3 xy 2. Write
and simplify an expression for the area of the triangle. Then find the
area of the triangle if x 2 and y 1.
12-6 Multiplying Binomials
Multiply.
17. (x 2)(x 6)
18. (3m 4)(2m 8)
19. (n 5)(n 3)
20. (x 6)2
21. (x 5)(x 5)
22. (3x 2)(3x 2)
23. A rug is placed in a 10 ft 20 ft room so that there is an uncovered strip
of width x all the way around the rug. Find the area of the rug.
622
Chapter 12 Polynomials
Cooking Up a New Kitchen
Javier is a contractor who remodels
kitchens. He drew the figure to help
calculate the dimensions of a
countertop surrounding a
sink that is x inches long
and y inches wide.
6 in.
1. Write a polynomial that Javier can use to
find the perimeter of the outer edge of
the countertop.
4 in.
y
x
6 in.
4 in.
2. Someone orders a countertop for a sink that
is 18 inches long and 12 inches wide. Javier
puts tape around the outer edge of the
countertop to protect it while it is being
moved. Use the polynomial to determine
how many inches of tape are needed.
3. Write a polynomial that Javier can use to find
the area of the countertop for any size sink.
4. The marble for the countertop costs $1.25
per square inch. Write a polynomial that
gives the cost of the countertop.
5. Find the cost of the countertop for the
18-inch by 12-inch sink. Explain your answer.
Concept Connection
623
Short Cuts
You can use properties of algebra to explain many arithmetic
shortcuts. For example, to square a two-digit number that ends
in 5, multiply the first digit by one more than the first digit,
and then place a 25 at the end.
To find 352, multiply the first digit, 3, by one more than
the first digit, 4. You get 3 4 12. Place a 25 at the end,
and you get 1225. So 352 1225.
Why does this shortcut work? You can use FOIL to multiply 35 by itself:
352 35 35 (30 5)(30 5) 900 150 150 25
900 300 25
1200 25
1200 30 40
1225
First use the shortcut to find each square. Then use FOIL to multiply the
number by itself.
1. 152
2. 452
3. 852
4. 652
5. 252
6. Can you explain why the shortcut works?
Use FOIL to multiply each pair of numbers.
7. 11 14
8. 12 16
9. 13 15
10. 14 17
11. 18 19
12. Write a shortcut for multiplying two-digit numbers with a first digit of 1.
RRolling
olling for
for T
Tiles
iles
For this game, you will need a number cube,
a set of algebra tiles, and a game board.
Roll the number cube, and draw an algebra tile:
1
, 2
, 3
, 4
, 5
, 6
.
The goal is to model expressions that can be added,
subtracted, multiplied, or divided to equal the
polynomials on the game board.
A complete set of rules and a game board are available online.
624
Chapter 12 Polynomials
KEYWORD: MT8CA Games
Materials
• 3 sheets of
decorative paper
• ruler
• compass
• scissors
• glue
• markers
PROJECT
Polynomial Petals
A
Pick a petal and find a fact about polynomials!
Directions
1 Draw a 5-inch square on a sheet of decorative
paper. Use a compass to make a semicircle on
each side of the square. Cut out the shape.
Figure A
2 Draw a 312-inch square on another sheet of
decorative paper. Use a compass to make a
semicircle on each side of the square. Cut out
the shape.
B
3 Draw a 212-inch square on the last sheet of
decorative paper. Use a compass to make a
semicircle on each side of the square. Cut out
the shape.
4 Glue the medium square onto the center of the
large square so that the squares are at a 45°
angle to each other. Figure B
5 Glue the small square onto the center of
the medium square in the same way.
Taking Note of the Math
Write examples of different types of
polynomials on the petals. Then use
the remaining petals to take notes on
the key concepts from the chapter.
When you’re done, fold up the petals.
625
Vocabulary
binomial . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590
polynomial . . . . . . . . . . . . . . . . . . . . . . . . . 590
degree of a polynomial . . . . . . . . . . . . . . . 591
trinomial . . . . . . . . . . . . . . . . . . . . . . . . . . . 590
FOIL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618
Complete the sentences below with vocabulary words from the
list above.
1. The expression 4x 3 10x 2 4x 12 is an example of a ___?___
whose ___?___ is 3.
2. Use the ___?___ method to find the product of two ___?___.
3. A polynomial with 2 terms is called a ___?___. A polynomial
with 3 terms is called a ___?___.
12-1 Polynomials
(pp. 590–593)
EXAMPLE
Classify each expression as a monomial,
a binomial, a trinomial, or not a
polynomial.
■
■
■
Classify each expression as a monomial,
a binomial, a trinomial, or not a
polynomial.
4. 5t 2 7t 8
4xy 34 7x 2y 4
6. 12g 7g 3 2
not a polynomial
7. 4a 2b 3c 5
x
x 3 2x 1
degree 3
n 3n4 16n2
degree 4
5. r 4 3r 2 5
5
g
8. x
2xy
9. 6st 7s
Find the degree of each polynomial.
10. 3x 5 6x 8 5x
11. x 4 4x 2 3x 1
12. 14 8r 2 9r 3
1
1
7
13. 3m 3 6m 5 9m 2
14. 3x 6 5x 5 9x
626
Chapter 12 Polynomials
1A10.0; 7AF1.2
EXERCISES
4x 5 2x 3 7
trinomial
Find the degree of each polynomial.
■
Preview of
12-2 Simplifying Polynomials
(pp. 596–599)
EXAMPLE
7AF1.3
Simplify.
2x 4 5x 3 15. 4t 2 6t 3t 4t 2 7t 2 1
4x 2
16. 4gh 5g 2h 7gh 4g 2h
5x 2 2x 4 5x 3 4x 2
17. 4(5mn 3m)
18. 4(2a 2 4b) 6b
9x 2 7x 1
■
1A10.0;
EXERCISES
Simplify.
■ 5x 2
Preview of
19. 5(4st 2 6t) 16st 2 7t
4(2x 7) 5x 4
8x 28 5x 4
3x 24
12-3 Adding Polynomials
(pp. 603–606)
EXAMPLE
2x 5x 2
8x 2 x 2
■
20. (4x 2 3x 7) (2x 2 5x 12)
21. (5x 4 3x 2 4x 2) (4x2 5x 9)
3x 2
Identify
like terms.
Combine like terms.
22. (5h 5) (2h2 3) (3h 1)
23. (3xy 2 5x 2y 4xy) (3x 2y 6xy xy 2)
(8t 3 4t 6) (4t 2 7t 2)
8t 3
4t 6 Place like terms
4t 2 7t 2 in columns.
8t 3 4t 2 3t 4 Combine like terms.
12-4 Subtracting Polynomials
24. (4n2 6) (3n2 2) (8 6n2)
(pp. 608–611)
EXAMPLE
■
7AF1.3
Add.
(3x 2 2x) (5x 2 3x 2)
3x 2
1A10.0;
EXERCISES
Add.
■
Preview of
Preview of
7AF1.3
EXERCISES
Subtract.
Subtract.
(6x 2 4x 5) (7x 2 8x 2)
6x 2 4x 5 (7x 2 8x 2) Add the
25. (x 2 4) (4 5x 2)
opposite.
Associative
Property
Combine like terms.
6x 2 4x 5 7x 2 8x 2
x 2 4x 3
1A10.0;
26. (w 2 4w 6) (2w 2 8w 8)
27. (3x 2 8x 9) (7x 2 8x 5)
28. (4ab 2 5ab 7a 2b) (3a 2b 6ab)
29. (3p 3q 2 4p 2q 2) (2pq 2 4p 3q 2)
Study Guide: Review
627
12-5 Multiplying Polynomials by Monomials
EXAMPLE
(pp. 612–615)
EXERCISES
Preview of
1A10.0; 7AF1.2,
7AF1.3, 7AF2.2
Multiply.
Multiply.
■ (3x 2y 3)(2xy 2)
30. (4st 3 )(s 3st 8)
(3x 2y 3)(2xy 2)
3 2 x2 1 y3 2
6x 3y 5
■ (2ab 2)(4a 2b 2
Multiply the
coefficients and
add the exponents.
31. 6a 2b(2a 2b 2 5ab 2 6a 4b)
32. 2m(m 2 8m 1)
33. 5h(3gh 4 2g 3h 2 6h 4g)
1
34. 2j 3k 2(4j 2k 3jk 2 2j 3k 3 )
3ab 6a 8)
35. 3x 2y 5(5x 4y 7 6x 5y 9 8xy 4xy 2 )
(2ab 2)(4a 2b 2 3ab 6a 8)
8a3b 4 6a 2b 3 12a 2b 2 16ab 2
12-6 Multiplying Binomials
(pp. 618–621)
EXAMPLE
EXERCISES
Multiply.
Multiply.
■
(r 8)(r 6)
36. (p 6)(p 2)
37. (b 4)(b 6)
■
(r 8)(r 6)
FOIL
r 2 6r 8r 48
r 2 2r 48
Combine like terms.
38. (3r 1)(r 4)
39. (3a 4b)(a 5b)
40. (m 7)2
41. (3t 6)(3t 6)
42. (3b 7t)(2b 4t)
(b 6)2
43. (10 3x)(4 x)
628
(b 6)(b 6)
FOIL
b 2 6b 6b 36
b 2 12b 36
Combine like terms.
Chapter 12 Polynomials
44. ( y 11)2
Preview of
1A10.0
Classify each expression as a monomial, a binomial, a trinomial,
or not a polynomial.
1
1. t 2 2t 0.5 4
2. 2a 3b 6
3. 4m 4 5m 8
Find the degree of each polynomial.
4. 6 9b 2m 4
6. 4 y
5. 54
7. The volume of a cube with side length x 2 is given by the polynomial
x 3 6x 2 12x 8. What is the volume of the cube if x 3?
Simplify.
9. 3(x 2 6x 10)
8. 2a 4b 5b 6a 2b
10. 2x 2y 3xy2 4x 2y 2x 2y
11. 6(4b 2 7b) 3b 2 5b
12. The area of one face of a cube is given by the expression 2s 2 9s. Write a
polynomial to represent the total surface area of the cube.
Add.
13. (4x 2 2x 1) (2x 5)
2 2
2
14. (12x 5) (9x 5)
2
15. (3bc b c 5bc ) (2bc bc )
16. (6h 5 3h3 2h6 ) (h6 2h 5h4 )
17. (b 3c 2 8b2c 5bc) (6b 3c 2 4bc 3) (b2c 3bc 11)
18. Harold is placing a mat of width w 4 around a 16 in. by 20 in. portrait.
Write an expression for the perimeter of the outer edge of the mat.
Subtract.
19. (4m2n 5mn mn2) (2mn 4m2n)
20. (12a a2) (6 a2 8a)
21. (3a2b 5a2b2 6ab2) (2a2b2 7a2b)
22. ( j 4 7j 2 4j) (5j 3 2j 2 6j 1)
23. A circle whose area is 2x 2 3x 4 is cut from a rectangular piece of plywood
with area 4x 2 3x 1 and discarded. Write an expression for the area of the
remaining plywood. Evaluate the expression for x 4 in.
Multiply.
24. (3x)(5x4)
25. (4x 2y)(5xy 3)
26. (2a2b4)(5a4b5)
27. a(a3 4a 5)
28. 3m3n4(2m3n4 5m2n2)
29. 3a3(ab2 2ab 8a)
30. (x 2)(x 12)
31. (x 2)(x 4)
32. (a 3)(a 7)
33. A student forms a box from a 10 in. by 15 in. piece of cardboard by cutting
a square with side length x out of each corner and folding up the sides.
Write and simplify an expression for the area of the base of the box.
Chapter 12 Test
629
KEYWORD: MT8CA Practice
Cumulative Assessment, Chapters 1–12
Multiple Choice
1. Jerome walked on a treadmill for
45 minutes at a speed of 4.2 miles per
hour. How far did Jerome walk?
A
1.89 miles
3.15 miles
C
B 2.1 miles
5. If rectangle MNQP is similar to
rectangle ABDC, then what is the
area of rectangle ABDC?
18 cm
M
N
x3
A
10 cm
x
2. Which line has a slope of 3?
A
3
C
y
B
0
-3
3
y
0
x
P
y
x
-3
0
D
3
x
-5
0
C
D
A
44 cm2
C
120 cm2
B
66 cm2
D
270 cm2
6. Which statement is modeled by
3f 2 16?
y
4
Q
x
-4
-3
A
Two added to 3 times f is at
least 16.
B
Three times the sum of f and 2 is at
most 16.
C
The sum of 2 and 3 times f is more
than 16.
D
The product of 3f and 2 is no more
than 16.
3
-3
3. How much water can the cone-shaped
cup hold? Use 3.14 for π.
4 cm
7. If the area of a circle is 49π and the
circumference of the circle is 14π,
what is the diameter of the circle?
10 cm
A
41.9 cm3
C
167.47 cm3
B
502.4 cm3
D
1507.2 cm3
4. Twenty-two percent of the sales of a
general store are due to snack sales. If
the store sold $1350 worth of goods,
how much of the total was due to
snack sales?
630
B
D 5.6 miles
A
$167
C
B
$297
D $2970
Chapter 12 Polynomials
$1053
A
7 units
C
21 units
B
14 units
D
49 units
8. Nationally, there were 217.8 million
people age 18 and over and 53.3
million children ages 5 to 17 as of
July 1, 2003, according to the U.S.
Census Bureau. How do you write the
number of people age 5 and older in
scientific notation?
A
2.711 102
C
2.711 107
B
2.711 106
D
2.711 108
9. There are 36 flowers in a bouquet.
Two-thirds of the flowers are roses.
One-fourth of the roses are red. What
percent of the bouquet is made up of
red roses?
A
9%
B
163%
2
C
25%
D
663%
Short Response
14. A quilt is made by connecting squares
like the one below.
2x 4
3x 4
2
If a problem involves decimals, you may
be able to eliminate answer choices that
do not have the correct number of places
after the decimal point.
x
a. Write an expression for the area of
the triangle and an expression for
the area of the square.
b. Write an expression for the area of
the gray region.
Gridded Response
10. The floor in the entrance way of Kendra’s
house is square and measures 6.5 feet
on each side. Colored tiles have been set
in the center of the floor in a square
measuring 4 feet on each side. The
remaining floor consists of white tiles.
15. Draw a model for the product of the
two binomials (x 3) and (2x 5)
with the following tiles. Use the
model to determine the product.
x2
6.5 ft
4 ft
x
1
Extended Response
16. A cake pan is made by cutting four
squares from a 18 cm by 24 cm piece of
tin and folding the sides as shown.
24 cm
How many square feet of the entrance
way floor consists of white tiles?
11. Rosalind purchased a sewing machine
discounted 20%. The original selling
price of the machine was $340. What
was the sale price in dollars?
12. What is the length, in centimeters, of
the diagonal of a square with side
length 8 cm? Round your answer to the
nearest hundredth.
13. The length of a rectangle is 2 units
greater than the width. The area of the
rectangle is 24 square units. What is its
width?
x
x
x
x
18 cm
x
x
x
x
a. Write an expression for the length,
width, and height of the cake pan
in terms of x.
b. Multiply the expressions from part a
to find a polynomial that gives the
volume of the cake pan.
c. Evaluate the polynomial for x 1,
x 2, x 3, and x 4. Which value
of x gives the cake pan with the
largest volume? Give the dimensions
and the volume of the largest
cake pan.
Cumulative Assessment, Chapters 1–12
631
Student
Handbook
Extra Practice
EP2
Skills Bank
SB2
Place Value to the Billions . . . . . . . . . . . . . . . . . . . . . . . . . . . SB2
Round Whole Numbers and Decimals . . . . . . . . . . . . . . . . . SB2
Compare and Order Whole Numbers. . . . . . . . . . . . . . . . . . SB3
Compare and Order Decimals. . . . . . . . . . . . . . . . . . . . . . . . SB3
Divisibility Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB4
Factors and Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB4
Prime and Composite Numbers . . . . . . . . . . . . . . . . . . . . . . SB5
Prime Factorization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB5
Greatest Common Divisor (GCD) . . . . . . . . . . . . . . . . . . . . . SB6
Least Common Multiple (LCM). . . . . . . . . . . . . . . . . . . . . . . SB6
Multiply and Divide by Powers of Ten . . . . . . . . . . . . . . . . . SB7
Dividing Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB7
Plot Numbers on a Number Line . . . . . . . . . . . . . . . . . . . . . SB8
Simplest Form of Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . SB8
Mixed Numbers and Improper Fractions . . . . . . . . . . . . . . SB9
Finding a Common Denominator . . . . . . . . . . . . . . . . . . . . SB9
Adding Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB10
Subtracting Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB10
632
Student Handbook
Multiplying Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB11
Dividing Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB11
Adding Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB12
Subtracting Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB12
Multiplying Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB13
Dividing Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB13
Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB14
Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB15
Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB16
Geometric Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB16
Classify Triangles and Quadrilaterals . . . . . . . . . . . . . . . . SB17
Bar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB18
Line Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB19
Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB20
Circle Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB21
Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB22
Bias. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB22
Compound Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SB23
Inductive and Deductive Reasoning . . . . . . . . . . . . . . . . . SB24
Selected Answers
Glossary
Index
Table of Formulas and
Symbols
SA1
G1
I2
inside back cover
633
Extra Practice
Chapter 1
LESSON 1-1
Evaluate each expression for the given value(s) of the variable(s).
1. 3 x for x 5
2. 6m 2 for m 3
3. 2(p 3) for p 8
4. 4x y for x 1, y 3
5. 2y x for x 3, y 6
6. 5x 1.5y for x 2, y 4
LESSON 1-2
Write an algebraic expression for each word phrase.
7. seven less than a number b
8. eight more than the product of 7 and a
9. a quotient of 8 and a number m
10. five times the sum of c and 18
Write a word phrase for each algebraic expression.
x
11. 9 3
12. 19x 14
1
13. 3(x 1)
4
14. x 100
15. Write a word problem that can be evaluated by the algebraic expression
x 122, and then evaluate the expression for x 225.
LESSON 1-3
16. In a miniature golf game the scores of four brothers relative to par are Jesse 3,
Jack 2, James 5, and Jarod 1. Use , , or to compare Jack’s and Jarod’s
scores. Then list the brothers in order from the lowest score to the highest.
Write the integers in order from least to greatest.
17. 4, 6, 2
18. 1, 16, 9
19. 14, 2, 19
20. ⏐9⏐ ⏐4⏐
21. ⏐3⏐ ⏐19⏐
22. ⏐52 12⏐
23. ⏐5 7⏐⏐8 6⏐
24. ⏐4⏐ ⏐1 3⏐
25. ⏐13 9⏐ ⏐15⏐
Simplify each expression.
LESSON 1-4
Add.
26. 4 6
27. 3 (8)
28. 6 (2)
29. 7 (11)
Evaluate each expression for the given value of the variable.
30. x 9 for x 8
31. x 3 for x 3
33. The middle school registrar is checking her
records. Use the information in the table to
find the net change in the number of students
for this school for the week.
EP2
Extra Practice
32. x 5 for x 7
Day
Students
Students
Registering Withdrawing
Monday
4
2
Tuesday
6
7
Wednesday
5
5
Thursday
1
4
Friday
4
0
Extra Practice
Chapter 1
LESSON 1-5
Subtract.
34. 6 4
35. 8 (3)
36. 6 (3)
37. 5 8
Evaluate each expression for the given value of the variable.
38. 7 x for x 4
39. 8 s for s 6
40. 8 b for b 12
41. ⏐3 x⏐for x 2
42. ⏐7 b⏐4 for b 10
43. ⏐5 m⏐⏐6⏐for m 3
44. An elevator rises 351 feet above ground level and then drops 415 feet to
the basement. What is the position of the elevator relative to ground level?
LESSON 1-6
Multiply or divide.
63
46. 7
47. 7(3)
52
48. 4
50. 5(9) 11
51. 4(16 4)
52. 3 7(10 14)
53. 4 x 13
54. t 3 8
55. 17 m 11
56. 5 a 7
57. p 5 23
58. 31 y 50
59. 18 k 34
60. g 16 23
45. 8(6)
Simplify.
49. 8(4 5)
LESSON 1-7
Solve.
61. Richard biked 39 miles on Saturday. This distance is 13 more miles than
Trevor biked. How many miles did Trevor bike on Saturday?
LESSON 1-8
Solve and check.
62.
a
4
2
66. 8b 64
63. 49 7d
67. 144 9y
c
8
64. 2
x
68. 2 78
65. 57 3p
69. 19c 152
70. Jessica hiked a total of 36 miles on her vacation. This distance is 4 times as far as
she typically hikes. How many miles does Jessica typically hike?
LESSON 1-9
Translate each sentence into an equation.
71. 8 less than the product of 5 and a number x is 53.
72. 7 more than the quotient of a number t and 6 is 9.
Solve.
73. 3m 5 23
x
74. 9 4 31
75. 1 6y 11
m
76. 16 7 5
Extra Practice
EP3
Extra Practice
Chapter 2
LESSON 2-1
Write each fraction as a decimal.
1
1. 8
7
2. 1
2
5
9
4. 2
0
3. 3
Write each decimal as a fraction in simplest form.
5. 0.4
6. 0.05
7. 0.125
8. 0.625
Write each repeating decimal as a fraction in simplest form.
10. 0.25
11. 0.45
9. 0.7
12. 0.009
LESSON 2-2
Compare. Write , , or .
6
13. 7
4
5
5
2
17. 18
13
9
11
14. 1
10
5
1
1
18. 28
25
1
15. 3
5
6
12
19. 1
7
4
0.75
1
8
16. 5
7
20. 58
5.9
21. In a sewing class, students were instructed to measure and cut cloth to a
width of 3 yards. While checking four students’ work, the teacher found
that the four pieces of cloth were cut to the following measurements:
11
3
3.5 yards, 2.75 yards, 21
yards, and 38 yards. List these measurements
6
from least to greatest.
LESSON 2-3
22. Hannah and Elizabeth drove to Niagara Falls for vacation. Hannah drove
9834 miles, and Elizabeth drove 106.44 miles. How far did they drive
together?
Add or subtract. Write each answer in simplest form.
3
7
23. 4 4
19
11
24. 8 8
5
15
25. 4 4
26. 4 4
7
11
9
15
27. 2 2
11
14
28. 2 2
9
22
29. 4 4
30. 3 3
21
16
Evaluate each expression for the given value of the variable.
31. 32.9 x for x 15.8
32. 21.3 a for a 37.6
3
1
33. 5 z for z 35
LESSON 2-4
Multiply. Write each answer in simplest form.
5
7
3
35. 1
5
2
36. 5 1
0
38. 4.7(8)
39. 4.1(8.6)
40. 0.06(5.2)
3
4
9
34. 4 9
3 13
37. 7 1
4
41. 0.003(2.6)
42. Rosie ate 212 bananas on Saturday. On Sunday she ate 12 as many bananas as
she ate on Saturday. How many bananas did Rosie eat over the weekend?
EP4
Extra Practice
Extra Practice
Chapter 2
LESSON 2-5
Divide. Write each answer in simplest form.
3
1
1
43. 24 3
47. 5.68 0.2
7
5
44. 55 8
48. 7.65 0.05
3
1
45. 39 4
49. 1.76 0.8
2
46. 38 5
50. 0.744 8
Evaluate each expression for the given value of the variable.
7.4
51. x for x 0.5
11.88
52. x for x 0.08
15.3
53. x for x 1.2
54. Yolanda is making bows that each take 2112 inches of ribbon to make.
She has 344 inches of ribbon. How many bows can she make?
LESSON 2-6
Add or subtract. Write each answer in simplest form.
8
2
55. 9 7
1
3
2
56. 8 3
1
59. 45 27
2
1
57. 3 7
2
7
60. 33 18
1
5
4
58. 6 9
3
61. 48 15
1
1
62. 87 41
0
Evaluate each expression for the given value of the variable.
1
2
1
63. 82 x for x 49
7
64. n 9 for n 18
1
4
65. 18 y for y 7
66. A container has 1012 gallons of milk. If the children at a preschool drink
734 gallons of milk, how many gallons of milk are left in the container?
LESSON 2-7
Solve.
67. x 3.2 5.1
1
5
71. m 3 8
68. 3.1p 15.5
3
1
72. x 7 9
a
7.9
69. 2.3
70. 4.3x 34.4
4
2
73. 5w 3
9
5
74. 1
z 8
0
75. Peter estimates that it will take him 934 hours to paint a room. If he gets
two of his friends to help him and they work at the same rate as he
does, how long will they take to paint the room?
LESSON 2-8
76. A bill from the plumber was $383. The plumber charged $175 for parts
and $52 per hour for labor. How long did the plumber work at this job?
Solve.
a
77. 2 3 8
78. 2.4 0.8x 3.2
79. 0.9m 1.6 5.2
b
80. 5 2 3
x4
81. 3 7
82. 8.6 3.4k 1.8
83. 6c 1.2 4.2
84. 7 4d 8
85. 3 2
y9
Extra Practice
EP5
Extra Practice
Chapter 3
LESSON 3-1
Name the property that is illustrated in each equation.
1. 5 (6 x) (5 6) x
3. 4 m m 4
2. 8 (1) (1) 8
Simplify each expression. Justify each step.
1
4. 5 9 35
2
5
6. 7 6 7
5. 23 14 7
Write each product using the Distributive Property. Then simplify.
7. 3(94)
8. 8(47)
9. 6(52)
LESSON 3-2
Combine like terms.
10. 5x 4x 7x
11. 6x 4x 9 5x 7
12. 2x 3 2x 5
13. 7a 2b 6 4b 5a
14. 4s 9t 9
15. 6m 4n 6m n
17. 3(3b 3) 3b
18. 4(x 2) 3x 8
19. 4a 5 2a 9 28
20. 5 8b 6 2b 61
21. 4x 6 8x 9 21
22. g 9 4g 6 12
23. 2 3f 5 5f 6
24. 4r 8 7 6r 9
4a
7
3
25. 5 5 5
1
2b
7
26. 3 3 3
4z
3
27. 1
1
1
1
1
10c
16
56
29. 4 2 8
9x
45
36x
126
30. 3 9 6 9
Simplify.
16. 6(y 4) y
LESSON 3-3
Solve.
2f
24
28. 4 4 1
2
31. A round-trip car ride took 12 hours. The first half of the trip took 7 hours
at a rate of 45 miles per hour. What was the average rate of speed on the
return trip?
LESSON 3-4
Solve.
32. 4z 2 z 1
33. 4a 4 a 11 34. 4p 6 3 4p 35. 6 5c 3c 4
36. 7d 3 2d 5d 8 1
37. 3f 4 5f f 4 f
38. 5k 4 k 3k 6 2k
w
5
2w
7
2w
39. 4 8 2 8 4
a
1
5a
9
2a
a
40. 3 6 6 6 3 3
2
5
41. 3 9 6 6 1
8
2q
42. A cafeteria charges a fixed price per ounce for the salad bar. A sandwich
costs $3.10, and a large drink costs $1.75. If a 7-ounce salad and a drink
cost the same as a 4-ounce salad and a sandwich, how much does the
salad cost per ounce?
EP6
Extra Practice
q
5q
Extra Practice
Chapter 3
LESSON 3-5
Write an inequality for each situation or statement.
43. The cafeteria could hold no more than 50 people.
44. There were fewer than 20 boats in the marina.
45. A number n decreased by 4 is more than 13.
46. A number x divided by 5 is at most 28.
Graph each inequality.
47. y 2
48. f 3
49. n 1.5
50. x 4
Write a compound inequality for each statement.
51. A number m is both less than 8.5 and greater than or equal to 0.
52. A number c is either greater than 1.5 or less than or equal to 1.
LESSON 3-6
Solve and graph.
1
53. x 3.5 7
54. h 5 13
55. 5 q 32
56. m 1 0.25
2
1
57. n 43 53
58. q 0.5 1
59. 30 h 23
60. 7 x 65
61. 5 2
62. 40 4q
63. 9x 72
64. 2 3
65. 3 6
66. 3 5
67. f 4
68. 5y 55
4
LESSON 3-7
Solve and graph.
v
p
w
s
69. Reese is running for student council president. In order for a student
to be elected president, at least 13 of the students must vote for him. If
there are 432 students in a class, at least how many students must
vote for Reese in order for him to be elected class president?
LESSON 3-8
Solve and graph.
70. 3a 6 12
71. 5 4x 7
72. 2b 8 16
73. 4z 8 4
x
1
2
74. 6 3 3
1
75. 2k 8 9
d
4
76. 2 5 2
2
7
77. 3 6 6
p
78. Nikko wants to make flyers promoting a library book sale. The printer
charges $40 plus $0.03 per flyer. How many flyers can Nikko make
without spending more than the library’s $54 budget?
Extra Practice
EP7
Extra Practice
Chapter 4
LESSON 4-1
Write in exponential form.
1. 3 3 3 3
2. 6a 6a 6a 6a 6a 3. (9) (9)
4. b
6. 34
8. (3)5
Simplify.
5. 25
7. (6)2
Evaluate each expression for the given values of the variables.
x
9. s 4 y(s 3) for s 1 and y 2
10. 10 x 2 2(y 4) for x 3 and y 2
LESSON 4-2
Simplify the powers of 10.
11. 101
12. 102
13. 103
14. 104
Simplify.
15. (4)2
2
3
18. 4 (9 3)0
3
16. 33
17. (5)4
19. 13 (3) 19(1 2)2
20. 45 32 (3)3
LESSON 4-3
Simplify each expression. Write your answer in exponential form.
21. 24 25
3
x
25. 3
y
9
6
22. w7 w7
4
23. 9
c
24. 2
26. (30)4
27. (32)3
28. (a 3)4
4
c
LESSON 4-4
Multiply or divide. Assume that no denominator equals zero.
29. (x5)(4x4)
30. (7a4b2)(3b4)
31. (8m6n3)(5mn7)
10
22m
32. 5
8 7
18x
y
33. 8
5 9
45a
b
34. 2 5
36. (9p3r)2
37. (4a7b4)3
2m
12x y
9a b
Simplify.
35. (3y)5
LESSON 4-5
Write each number in scientific notation.
38. 0.00384
39. 1,450,000,000
40. 0.654
Write each number in standard form.
41. 2.4 103
42. 3.62 105
43. 5.036 104
44. 8.93 102
45. The population of the United States was approximately 2.9 108 people in July
2006. In the same month, the population of Canada was approximately 3.3 107
people. Which country had the greater population in July 2006?
EP8
Extra Practice
Extra Practice
Chapter 4
LESSON 4-6
Find the two square roots of each number.
46. 25
47. 49
48. 289
49. 169
50. The area of a square garden is 1,681 square feet. What are the
dimensions of the garden?
Simplify each expression.
400x20
51. 52. 49y6
53. m14n12
54. 196a16
b8
LESSON 4-7
Each square root is between two integers. Name the integers. Explain your answer.
55. 30
56. 61
58. 124
57. 93
59. Each tile on Michelle’s patio is 18 square inches. If her patio is square
shaped and consists of 81 tiles, about how big is her patio?
Approximate each square root to the nearest hundredth.
60. 52
61. 83
62. 166
63. 246
LESSON 4-8
Write all classifications that apply to each number.
64. 5
16
66. 2
65. 61.2
67. 6
State if the number is rational, irrational, or not a real number.
68.
25
4
69. 9
13
71. 0
70. 17
Find a real number between each pair of numbers.
1
2
1
72. 58 and 58
2
5
73. 43 and 43
6
74. 37 and 37
LESSON 4-9
Use the Pythagorean Theorem to find each missing measure.
75.
76.
77.
78.
b
c
y
5 in.
25 ft
20 ft
12 km
8 km
9 cm
10 cm
12 in.
x
Tell whether the given side lengths form a right triangle.
79. 6, 8, 10
80. 8, 11, 13
81. 7, 10, 12
82. 0.8, 1.5, 1.7
Extra Practice
EP9
Extra Practice
Chapter 5
LESSON 5-1
Write each ratio in simplest form.
1. 2 cups of milk to 8 eggs
2. 36 inches to 2 feet
3. 4 feet to 20 yards
Simplify to tell whether the ratios are equivalent.
5
3
and 1
4. 3
0
8
12
16
5. 2
and 2
1
8
91
52
7. 6
and 112
4
15
10
6. 2
and 1
1
6
LESSON 5-2
8. Nikko jogs 3 miles in 30 minutes. How many miles does she jog per hour?
9. A penny has a mass of 2.5 g and a volume of approximately 0.442 cm3.
What is the approximate density of a penny?
Estimate the unit rate.
10. 384 mg of calcium for 8 oz of yogurt
11. $57.50 for 5 hours
12. Determine which brand of detergent
has the lower unit rate.
Detergent Brand
LESSON 5-3
Size (oz)
Price ($)
Pizzazz
128
3.08
Spring Clean
64
1.60
Bubbling
196
4.51
Tell whether the ratios are proportional.
7
3
13. 8 and 4
3
24
14. 4 and 3
2
32
18
15. 4
and 2
8
7
6
12
16. 2
and 1
2
0
17. Mark is making 35 sandwiches for a luncheon. He made the first 15 sandwiches in
45 minutes. If he continues to work at the same rate, how many more minutes will he
take to complete the job?
18. An 18-pound weight is positioned 6 inches from a fulcrum. At what distance from the
fulcrum must a 24-pound weight be positioned to keep the scale balanced?
LESSON 5-4
19. A water fountain dispenses 8 cups of water per minute. Find this rate
in pints per minute.
20. Jo’s car uses 1664 quarts of gas per year. Find this rate in gallons per week.
21. Toby walked 352 feet in one minute. What is his rate in miles per hour?
22. A three-toed sloth has a top speed of 0.22 feet per second. A giant tortoise
has a top speed of 2.992 inches per second. Convert both speeds to miles
per hour, and determine which animal is faster.
23. There are markers every 1000 feet along the side of a road. While cycling,
Ben passes marker number 6 at 3:35 P.M. and marker number 24 at 3:47 P.M.
Find Ben’s average speed in feet per minute. Use dimensional analysis to
check the reasonableness of your answer.
EP10
Extra Practice
Extra Practice
Chapter 5
LESSON 5-5
24. Which triangles are similar?
A
B
A
C D
G
11 ft 30° 11.2 ft
C
60°
B
5 ft
10 ft
E
60°
45°
10 ft
14.1 ft
45°
I
10 ft
22 ft
22.4 ft
30°
H
25. Khaled scans a photo that is 5 in. wide by 7 in. long into his computer. If
the length of the scanned photo is reduced to 3.5 in., how wide should the
scanned photo be for the two photos to be similar?
F
26. Mutsuko drew an 8.5-inch-wide by 11-inch-tall picture that will be
turned into a 34-inch-wide poster. How tall will the similar poster be?
27. A right triangle has legs that measure 3 cm and 4 cm. The shorter leg of a
similar right triangle measures 6 cm. What is the length of the other leg of
the similar triangle?
LESSON 5-6
28. Brian casts a 9 ft shadow at the same time that Carrie casts an 8 ft
shadow. If Brian is 6 ft tall, how tall is Carrie?
29. A telephone pole casts an 80 ft shadow, and a child standing nearby
who is 3.5 ft tall casts a 6 ft shadow. How tall is the pole?
LESSON 5-7
Use the map to answer each question.
30. On the map, the distance from State College to
Belmont is 2 cm. What is the actual distance
between the two locations?
31. Henderson City is 83 miles from State College.
How many centimeters apart should the two
locations be placed on the map?
Belmont
State College
Scale: 1 cm:5 mi
32. What is the scale of a drawing in which a building that is 95 ft tall is drawn 6 in. tall?
33. A model of a skyscraper was made using a scale of 0.5 in:5 ft. If the
actual skyscraper is 570 feet tall, what is the height of the model?
34. Julio uses a scale of 81 inch 1 foot when he paints landscapes. In one
painting, a giant sequoia tree is 34.375 inches tall. How tall is the actual tree?
35. On a scale drawing of a house plan, the master bathroom is 112 inches
wide and 258 inches long. If the scale of the drawing is 136 inches 1 foot, what are the actual dimensions of the bathroom?
Extra Practice
EP11
Extra Practice
Chapter 6
LESSON 6-1
Compare. Write , , or .
3
1. 5
2
2. 3
62%
2
663%
3. 24%
4. 1%
0.25
0.11
Order the numbers from least to greatest.
5. 0.11, 11.5%, 10%, 8
1
1
2
6. 5, 100%, 263%, 0.3
7
7. 6, 115%, 83, 83.3%
8. 67.5%, 3, 160%, 2.2
7
9. A molecule of ammonia is made up of 3 atoms of hydrogen and 1 atom of
nitrogen. What percent of an ammonia molecule is made up of hydrogen
atoms?
LESSON 6-2
Estimate.
10. 51% of 1019
11. 33% of 60
12. 60% of 79
2
13. 663% of 211
14. Approximately 23% of each class walks to school. A student said that in
a class of 20 students, approximately 2 students walk to school.
Estimate to determine if the student’s number is reasonable. Explain.
LESSON 6-3
15. What percent of 364 is 92?
16. What percent of 48 is 5?
17. What percent of 164 is 444?
18. What percent of 50 is 4?
19. Mt. McKinley in Alaska is 20,320 feet tall. The height of Mt. Everest is
about 143% of the height of Mt. McKinley. Estimate the height of Mt.
Everest. Round to the nearest thousand.
20. A restaurant bill for $64.45 was split among four people. Dona paid
25% of the bill. Sandy paid 15 of the bill. Mara paid $14.25. Greta paid
the remainder of the bill. Who paid the most money?
LESSON 6-4
21. 38 is 42% of what number?
22. 46 is 74% of what number?
23. 23 is 8% of what number?
24. 93 is 62% of what number?
25. 315 is 92% of what number?
26. 52 is 120% of what number?
27. A certain rock is a compound of several minerals. Tests show that the
sample contains 17.3 grams of quartz. If 27.5% of the rock is quartz,
find the mass in grams of the entire rock.
28. The Alabama River is 729 miles in length, or about 31% of the length of
the Mississippi River. Estimate the length of the Mississippi River.
Round to the nearest mile.
EP12
Extra Practice
Extra Practice
Chapter 6
LESSON 6-5
Find each percent of increase or decrease to the nearest percent.
29. from 10 to 17
30. from 38 to 65
31. from 91 to 44
32. from 3 to 25
33. from 86 to 27
34. from 38 to 46
35. from 19 to 60
36. from 88 to 23
37. A stereo that sells for $895 is on sale for 20% off the regular price. What
is the discounted price of the stereo?
38. Mr. Schultz’s hardware store marks up merchandise 28% over warehouse
cost. What is the selling price for a wrench that costs him $12.45?
LESSON 6-6
Find each sales tax to the nearest cent.
39. total sales: $12.89
sales tax rate: 8.25%
40. total sales: $87.95
sales tax rate: 6.5%
41. total sales: $119.99
sales tax rate: 7%
Find the total sales.
42. commission: $127.92
commission rate: 8%
43. commission: $32.45
commission rate: 5%
44. An electronics salesperson sold $15,486 worth of computers last
month. She makes 3% commission on all sales and earns a monthly
salary of $1200. What was her total pay last month?
45. Jon bought a printer for $189 and a set of printer cartridges for $129. Sales
tax on these items was 6.5%. How much tax did Jon pay for those items?
46. In her shop, Stephanie earns 16% profit on all of the clothes she sells. If
total sales were $3920 this month, what was her profit?
LESSON 6-7
Find the simple interest and the total amount to the nearest cent.
47. $3000 at 5.5% per year for 2 years
48. $15,599 at 9% per year for 3 years
49. $32,000 at 3.6% per year for 5 years
50. $124,500 at 8% per year for 20 years
51. Rebekah invested $15,000 in a mutual fund at a yearly rate of 8%. She
earned $7200 in simple interest. How long was the money invested?
52. Shu invested $6000 in a savings account for 4 years at a rate of 5%.
a. What would be the value of the investment if the account is
compounded semiannually?
b. What would be the value of the investment if the account is
compounded quarterly?
Extra Practice
EP13
Extra Practice
Chapter 7
LESSON 7-1
Identify the quadrant that contains each point. Plot each
point on a coordinate plane.
1. M(–1, 1)
2. N(4, 4)
y
A
2
3. Q(3, –1)
B
x
Give the coordinates of each point.
4. A
2
5. B
6. C
4
C
–2
LESSON 7-2
Determine if each relationship represents a function.
y
7.
8.
4
O
x
4
x
3
1
1
1
0
2
2
0
y
9.
y
2
O
x
2
LESSON 7-3
Graph each linear function.
10. y 2x 2
11. y x 3
12. y x 2
13. The outside temperature is 52°F and is increasing at a rate of 6°F per hour.
Write a linear function that describes the temperature over time. Then make a
graph to show the temperature over the first 3 hours.
LESSON 7-4
Create a table for each quadratic function, and use the table to graph the function.
14. y x2 2
15. y x2 x 8
16. y x2 x 6
LESSON 7-5
Create a table for each cubic function, and use the table to graph the function.
17. y x3 1
1
18. y 4x3
19. y 4x3
Tell whether each function is linear, quadratic, or cubic.
20.
21.
y
x
EP14
Extra Practice
22.
y
x
y
x
Extra Practice
Chapter 7
LESSON 7-6
Find the slope of each line.
23.
4
24.
y
2
⫺4
⫺2
x
O
⫺2
3
x
2
⫺4
25.
y
2
O
2
1
4
⫺2
⫺2
4
⫺2
y
O
1
x
2
4
⫺3
⫺4
LESSON 7-7
Find the slope of the line that passes through each pair of points.
26. (3, 4) and (2, 2)
27. (6, 2) and (2, 6) 28. (3, 3) and (1, 4) 29. (2, 4) and (1, 1)
30. The table shows how much money Andy and Margie made while working at
the concession stand at a baseball game one weekend. Use the data to make
a graph. Find the slope of the line, and explain what the slope means.
Time (h)
2
4
6
8
Money Earned ($)
15
30
45
60
LESSON 7-8
31. Abby rode her bike to the park. She had a picnic there with friends and
then rode home. Which graph best shows the situation?
Graph A
Distance
from home
Distance
from home
Distance
from home
Time
Graph C
Graph B
Time
Time
32. Greg walked to a café for lunch. Then he walked across the street to a store
before returning home. Sketch a graph to show Greg’s distance compared
to time.
LESSON 7-9
33. Instructions for a chemical-concentrate swimming-pool cleaner state that
2 ounces of concentrate should be added to every 112 gallons of water used.
How many ounces of concentrate should be added to 18 gallons of water?
34. The distance d that an object falls varies directly with the square of the time
t of the fall. This relationship is expressed by the formula d k t 2. An
object falls 90 feet in 3 seconds. How far will the object fall in 15 seconds?
Extra Practice
EP15
Extra Practice
Chapter 8
LESSON 8-1
C
Use the diagram to name each figure.
N
A
1. a line
2. three rays
3. a plane
4. three segments
B
Use the diagram to name each figure.
5. a right angle
6. two acute angles
7. an obtuse angle
8. a pair of complementary angles
B
C
55° 35°
90°
D
E
A
LESSON 8-2
A
Identify two lines that have the given relationship.
B
D
9. perpendicular lines
C
10. skew lines
E
11. parallel lines
H
Identify two planes that appear to have the given relationship.
I
12. parallel planes
13. perpendicular planes
D
E
G
14. neither parallel nor perpendicular
F
LESSON 8-3
Use the diagram to find each angle measure.
15. If m1 107°, find m3.
4 1
3 2
16. If m2 46°, find m4.
In the figure, line d⏐⏐line f. Find the measure of each angle.
17. 1
18. 2
19. 3
g
1 120°
2
d
f
LESSON 8-4
3
Find the missing angle measures in each triangle.
20.
21.
22.
43°
1 23 x°
54°
66°
x°
and
23. In the figure, B is the midpoint of AC
is perpendicular to AC
. Find the length
BD
of AD .
EP16
Extra Practice
x°
y°
A
16 m
m
16
B
6m
D
4x°
C
Extra Practice
Chapter 8
LESSON 8-5
Give all of the names that apply to each figure.
A
24.
B
2 cm
AB || CD
D
2 cm
25.
2 cm
2 cm
C
Find the coordinates of the missing vertex. Then tell which lines are parallel and which
lines are perpendicular.
26. rhombus ABCD with A(2, 3), B(3, 0), and D(1, 0)
27. square JKLM with J(1, 1), K(4, 1), and L(4, 2)
28. rectangle ABCD with A(4, 3), B(1, 3), and D(4, 1)
29. trapezoid JKLM with J(2, 1), K(2, 1), and L(1, 1)
LESSON 8-6
In the figure, quadrilateral ABCD quadrilateral KLMN.
30. Find x.
A
125°
31. Find y.
D
32. Find z.
M
B
x2
10
32
C
8y
L
95
K
z°
N
LESSON 8-7
Graph each transformation.
33. Rotate PQR 90° counterclockwise about vertex R.
4
P
34. Reflect the figure across
the y-axis.
y
Q
4
2
y
E
R
D
4
y
S
2
x
R
O
35. Translate RST
3 units right and
3 units down.
2
G x
F
2
O
2
4
x
2
O
T2
4
LESSON 8-8
Create a tessellation with each figure.
36.
37.
Extra Practice
EP17
Extra Practice
Chapter 9
LESSON 9-1
Find the perimeter of each figure.
1.
2.
3.
1
6m
14 m
3 3 in.
11 m
1
3 3 in.
9m
Graph and find the area of each figure with the given vertices.
4. (2, 1), (5, 1), (2, 4), (5, 4)
5.
(1, 2), (2, 1), (5, 2), (6, 1)
6. Find the perimeter and area of the figure.
10
4
4 6
6
6
6
10
LESSON 9-2
Find the missing measurement for each figure with the given perimeter.
7. perimeter 27 cm
8. perimeter 92 ft
9. perimeter 16 units
3
16 ft
5 cm
10 cm
4
c
16 ft
a
d
5
32 ft
Graph and find the area of each figure with the given vertices.
10. (4, 3), (2, 3), (2, 1)
11. (2, 1), (5, 3), (0, 1), (3, 3)
12. The sail of a toy sailboat forms a right triangle with legs that measure
5 inches each. Find the perimeter and area of the sail.
LESSON 9-3
Name the parts of circle I.
M
L
13. radii
14. diameters
J
15. chords
I
K
H
Find the central angle measure of the sector of a circle that represents
the given percent of a whole.
16. 12%
EP18
17. 40.5%
Extra Practice
18. 82%
19. 50%
Extra Practice
Chapter 9
LESSON 9-4
Find the circumference and area of each circle, both in terms of π
and to the nearest hundredth. Use 3.14 for π.
20.
21.
4 cm
22.
14 in.
14 ft
23. A wheel has a radius of 14 in. Approximately how far does a point on the wheel
travel if it makes 15 complete revolutions? Use 272 for π.
LESSON 9-5
Find the shaded area. Round to the nearest tenth, if necessary.
24.
3 ft
25.
9 ft
3 ft
13 m
5m
3 ft
3 ft
26.
27.
8m
3 yd
4 yd
8m
1 yd
7 yd
4m
LESSON 9-6
Find the area of each figure.
28.
29.
Use composite figures to estimate the shaded area.
30.
31.
Extra Practice
EP19
Extra Practice
Chapter 10
LESSON 10-1
Describe the bases and faces of each figure. Then name the figure.
1.
2.
3.
Classify each figure as a polyhedron or not a polyhedron. Then name the figure.
4.
5.
6.
LESSON 10-2
Find the volume of each figure to the nearest tenth. Use 3.14 for π.
7.
8.
9.
2 cm
5 ft
7 in.
4 cm
2 ft
8 ft
15 in.
5 in.
10. A can has a diameter of 3 in. and a height of 5 in. Explain whether
doubling only the height of the can would have the same effect on the
volume as doubling only the diameter.
11. A shoe box is 6.8 in. by 5.9 in. by 16 in. Estimate the volume of the shoe box.
4
12. Find the volume of the composite figure.
2
3
7
5
LESSON 10-3
9
Find the volume of each figure to the nearest tenth. Use 3.14 for π.
10 m
13.
14.
4.2 yd
15.
46 mm
31 mm
15 m
15 m
8 yd
16. A rectangular pyramid has a height of 15 ft and a base that measures
5 ft by 7.5 ft. Find the volume of the pyramid.
EP20
Extra Practice
31 mm
Extra Practice
Chapter 10
LESSON 10-4
Find the surface area of each prism to the nearest tenth.
17.
18.
19.
3m
9 cm
21 ft
9 cm
3m
6m
9 cm
20 ft
40 ft
Find the surface area of each cylinder to the nearest tenth. Use 3.14 for π.
20.
21. 6 m
22.
7 ft
20 m
4 cm
9 ft
12 mm
14 mm
LESSON 10-5
Find the surface area of each figure to the nearest tenth. Use 3.14 for π.
23.
24.
1m
15 in.
25.
17 yd
1m
10 yd
13 in.
13 in.
10 yd
10 yd
Find the surface area of each figure with the given dimensions. Use 3.14 for π.
26. cone:
diameter 4 in.
slant height 3 in.
27. regular square pyramid:
base area 64 ft2
slant height 8 ft
LESSON 10-6
Find the volume of each sphere, both in terms of π and to the nearest
tenth. Use 3.14 for π.
28. r 5 ft
29. d 40 cm
Find the surface area of each sphere, both in terms of π and to the
nearest tenth. Use 3.14 for π.
30. r 3.8 mm
31. d 1.5 ft
LESSON 10-7
An 8 cm cube and a 5 cm cube are both part of a demonstration kit for
architects. Compare the following values of the two cubes.
32. edge length
33. surface area
34. volume
Extra Practice
EP21
Extra Practice
Chapter 11
LESSON 11-1
1. Use a line plot to organize the data showing the number of miles that
students cycled over a weekend. What number of miles did students
cycle the most?
Number of Miles Cycled by Students
12 21 12 8 10 15 15 18 12 11 9 10 9 6 0 5 12 5 14 14 10 8 12 10 9
2. Use the given data to make a back-to-back stem-and-leaf plot.
World Series Win/Loss Records of Selected Teams (through 2001)
Team
Yankees
Pirates
Giants
Tigers
Cardinals
Dodgers
Orioles
Wins
26
5
5
4
9
6
3
Losses
12
2
11
5
6
12
4
LESSON 11-2
Find the mean, median, mode, and range of each data set.
3. 13, 8, 40, 19, 5, 8
4. 21, 19, 23, 26, 15, 25, 25
5. The table shows the number of points a player scored in ten games.
Find the mean and median of the data. Which measure best describes
the typical number of points scored in a game? Justify your answer.
Points a Player Scored in Ten Games
Game
1
2
3
4
5
6
7
8
9
10
Points
36
34
28
50
30
30
31
47
55
29
LESSON 11-3
Find the lower and upper quartiles for each data set.
6. 27, 31, 26, 24, 33, 31, 24, 28,
31, 24, 22, 27, 31, 28, 26
7. 84, 79, 77, 72, 81, 82, 89, 94, 72,
80, 76, 80, 83, 86, 73
Use the given data to make a box-and-whisker plot.
8. 11, 4, 9, 17, 16, 12, 5, 16, 9, 11, 13
9. 57, 53, 52, 31, 48, 59, 64, 86, 56, 54, 55
LESSON 11-4
10. The table shows the relationship between the number of years of post
high school education and salary. Use the given data to make a scatter
plot. Then describe the relationship between the data sets.
Number of Years of Post High School Education and Salary
Years
1
3
4
4
4
5
5
6
6
8
Salary ($1000’s)
18 20.5 28
35
51
43
58
52
64
58
75 73.5
EP22
Extra Practice
1
8
Extra Practice
Chapter 11
LESSON 11-5
Refer to the spinner at right. Give the probability for each outcome.
11. not red
12. blue
13. not yellow
A game consists of randomly selecting four colored marbles from a jar
and counting the number of red marbles in the selection. The table gives
the experimental probability of each outcome.
Number of Red Marbles
Probability
0
1
2
3
4
0.043
0.248
0.418
0.248
0.043
14. What is the probability of selecting 2 or more red marbles?
15. What is the probability of selecting at most 1 red marble?
LESSON 11-6
A utensil is drawn from a drawer and replaced. The
table shows the results after 100 draws.
16. Estimate the probability of drawing a spoon.
17. Estimate the probability of drawing a fork.
A sales assistant tracks the sales of a particular sweater.
The table shows the data after 1000 sales.
18. Use the table to compare the probability that the next
customer will buy a brown sweater to the probability that
the next customer will buy a beige sweater.
Outcomes
Draws
Spoon
33
Knife
36
Fork
31
Outcomes
Sales
White
361
Beige
207
Brown
189
Black
243
LESSON 11-7
An experiment consists of rolling a fair number cube. There are six possible
outcomes: 1, 2, 3, 4, 5, and 6. Find the probability of each event.
19. P(rolling an odd number)
20. P(rolling a 2)
21. P(rolling a number greater than 3)
22. P(rolling a 7)
An experiment consists of rolling two fair number cubes. Find each probability.
23. P(rolling a total of 4)
24. P(rolling a total less than 2)
25. P(rolling a total greater than 12)
26. P(rolling a total of 9)
LESSON 11-8
27. An experiment consists of rolling a fair number cube three times. For
each toss, all outcomes are equally likely. What is the probability of
rolling a 2 three times in a row?
28. A jar contains 3 blue marbles and 9 red marbles. What is the
probability of drawing 2 red marbles at the same time?
Extra Practice
EP23
Extra Practice
Chapter 12
LESSON 12-1
Determine whether each expression is a monomial.
1
1. 4r 2st 5
2. 6xy 3
3. 2 yx 4
3
3m
4. 5
n
Classify each expression as a monomial, a binomial, a trinomial, or not a polynomial.
1
5. 4x 3 x 2 4
9. xw7 7wz
6. 9x 5y 2z4
4
7. 5m4n3 m3
3
z
2
11. 3a 4 a3 5
10. 4
8. h 2h0.5 1
12. 13st 6
Find the degree of each polynomial.
13. 3x 3 4x 5 8
14. b 2 9b3 b 4 8 15. z 2 5z 6 9z 3
16. 4 t
17. The trinomial 16t 2 vt 12 describes the height in feet of a baseball
thrown straight up from a 12-foot platform with a velocity of v ft/s after
t seconds. What is the height of the ball after 3 seconds if v 55 ft/s?
18. The trinomial 4x 2 270x 2000 gives the net profit in dollars that a
custom bicycle manufacturer earns by selling x bikes in a given month.
What is the net profit for a month if x 15 bicycles?
LESSON 12-2
Identify the like terms in each polynomial.
19. s 5r 2 7r 9r 2 3s
20. 4x 2 9 7x x 5 10
21. 5x 2y 7x 2z 7yz 2 3x 2y xz 2
22. 3mn 3p 2 3p 5p 2 3mn
23. 8s 2 6 7s 6s4 13
24. 25 15xy 10x 2 3xy 5y 2 5
Simplify.
25. 5z 2 2z z 2 11z 9
26. 5 7(a 2 9) 3a 2 7
27. y 2z 8xz 6xy 2 10y 2z xy 2
28. 5c 2 11cd d 2 5(c 2 d 2) 2c(c d)
29. 5(a 2b 2 3ab) 3(ab 2 5ab)
30. 2s 2t 2 st 2 5s 2t 2 7s 2t 3st 2 s 2t
31. A rectangle has a width of 12 cm and a length of (2x 2 6) cm. The area
is given by the expression 12(2x 2 6) cm2. Use the Distributive
Property to write an equivalent expression.
32. A parallelogram has a base of (3x 2 4) in. and a height of 4 in. The area
is given by the expression 4(3x 2 4) in2. Use the Distributive Property
to write an equivalent expression.
EP24
Extra Practice
Extra Practice
Chapter 12
LESSON 12-3
Add.
33. (2x 2y 3 7x3y 2 xy) (x 2y 3 2x 3y 2 3xy) 34. (3a 2 4ab 2) (a 2b 2b2) (a2b 7ab2)
35. (m3 3m2n2 4) (6m2n2 9)
36. (10r 3s2 7r 2s 4r) (4r 3s 2 3r)
37. A rectangle has a width of (x 7) cm and a length of (3x 5) cm. An
equilateral triangle has sides of length x 2 2x 3. Write an expression
for the sum of the perimeters of the rectangle and the triangle.
LESSON 12-4
Find the opposite of each polynomial.
38. 6xy 2y 3
39. 4a 3b 7ab 8
40. 2x 6 3x x 3
41. 7g 5 gh4
Subtract.
42. (5x 2 2xy 3y 2) (3x 2 2y 2 8)
43. 14a (5a 3 3a 6)
44. (5r 2s 2 9r 2s rs) (3r 2s 7rs 2r 2)
45. (12y 3 6xy 1) (8xy 2x 1)
46. The area of the larger rectangle is (10x 2 2x 15) cm2.
The area of the smaller rectangle is (5x 2 3x) cm2.
What is the area of the shaded region?
LESSON 12-5
Multiply.
47. (5xy 2)(7x 3y 2)
48. (2a 2bc 2 )(5a 3b 2 )
49. (6m3n4 )(2mn)
50. 6t(9s 5t )
51. p (2p 2 pq 5)
52. 3xy 2(2x 3y 2 4x 2 y xy 6 11xy)
53. A rectangle has a width of 3x 2 y ft and a length of (2x 2 4xy 7) ft. Write
and simplify an expression for the area of the rectangle. Then find the
area of the rectangle if x 2 and y 3.
LESSON 12-6
Multiply.
54. (y 5)(y 3)
55. (s 3)(s 5)
56. (3m 2)(4m 3)
57. (y 1)2
58. (d 5)2
59. (a 9)(a 9)
60. (x 11)(x 5)
61. (7b 2)(7b 2)
62. (2m n)(6m 8n)
Extra Practice
EP25
Skills Bank
Review Skills
Place Value to the Billions
4NS1.1
A place-value chart can help you read and write numbers. The number
345,012,678,912.5784 (three hundred forty-five billion, twelve million, six
hundred seventy-eight thousand, nine hundred twelve and five thousand
seven hundred eighty-four ten-thousandths) is shown.
Billions Millions Thousands Ones
345,
012,
678,
912
Tenths Hundredths Thousandths Ten-Thousandths
.
5
7
8
4
EXAMPLE
Name the place value of the digit.
A the 7 in the thousands column
7
ten thousands place
B the 0 in the millions column
0
hundred millions place
C the 5 in the billions column
5
one billion, or billions, place
D the 8 to the right of the decimal point
8
thousandths
PRACTICE
Name the place value of the underlined digit.
1. 123,456,789,123.0594
2. 123,456,789,123.0594
3. 123,456,789,123.0594
4. 123,456,789,123.0594
5. 123,456,789,123.0594
6. 123,456,789,123.0594
Round Whole Numbers and Decimals
4NS1.3, 5NS1.1
To round to a certain place, follow these steps.
1. Locate the digit in that place, and consider the next digit to the right.
2. If the digit to the right is 5 or greater, round up. Otherwise, round down.
3. Change each digit to the right of the rounding place to zero.
EXAMPLE
A Round 125,439.378 to the nearest
thousand.
125,439.378 Locate the digit.
The digit to the right, 4, is less than 5,
so round down.
125,000.000 125,000
B Round 125,439.378 to the nearest
tenth.
125,439.378 Locate the digit.
The digit to the right, 7, is greater
than 5, so round up.
125,439.400 125,539.4
PRACTICE
Round 259,345.278 to the place indicated.
1. hundred thousand
SB2
Skills Bank
2. ten thousand
3. thousand
4. hundredth
Compare and Order Whole Numbers
4NS1.2
You can use place values to compare and order whole numbers.
EXAMPLE
Order the numbers from least to greatest: 42,810; 142,997; 42,729; 42,638.
Start at the left most place value.
There is one number with a digit in the greatest place.
It is the greatest of the four numbers.
42,810
Compare the remaining three numbers. All values in
the next two places, the ten thousands and thousands,
are the same.
142,997
In the hundreds place, the values are different.
Use this digit to order the remaining numbers.
42,729
42,638
42,638; 42,729; 42,810; 142,997
PRACTICE
Order the numbers in each set from least to greatest.
1. 2,564; 2,546; 2,465; 2,654
2. 6,237; 6,372; 6,273; 6,327
3. 132,957; 232,795; 32,975; 31,999
4. 9,614; 29,461; 129,164; 129,146
Compare and Order Decimals
4NS1.2
You can also use place values to compare and order decimals.
EXAMPLE
Order the decimals from least to greatest: 14.35, 14.3, 14.05.
14.35
14.30
14.30 14.35
Compare two of the numbers at a time.
Write 14.3 as “14.30.”
14.35
14.05
14.05 14.35
Start at the left and compare the digits.
Look for the first place the digits are different.
14.30 14.05 14.30
14.05
Graph the numbers on a number line.
14.05
14.30 14.35
14 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15
The numbers are in order from left to right: 14.05, 14.3, and 14.35.
PRACTICE
Order the decimals in each set from least to greatest.
1. 9.5, 9.35, 9.65
2. 4.18, 4.1, 4.09
3. 1.56, 1.62, 1.5
4. 6.7, 6.07, 6.23
Skills Bank
SB3
Divisibility Rules
4NS4.1
A number is divisible by another number if the division results in a
remainder of 0. Some divisibility rules are shown below.
A number is divisible by . . .
2 if the last digit is an even number.
Divisible
Not Divisible
11,994
2175
216
79
1028
621
15,195
10,007
1332
44
25,016
14,100
144
33
2790
9325
3 if the sum of the digits is divisible by 3.
4 if the last two digits form a number divisible by 4.
5 if the last digit is 0 or 5.
6 if the number is even and divisible by 3.
8 if the last three digits form a number divisible by 8.
9 if the sum of the digits is divisible by 9.
10
if the last digit is 0.
PRACTICE
Determine whether each number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10.
1. 56
2. 200
3. 75
7. 784
8. 501
9. 2345
4. 324
5. 42
10. 555,555
11. 3009
6. 812
12. 2001
Factors and Multiples
4NS4.1
When two numbers are multiplied to form a third, the two numbers are
said to be factors of the third number. Multiples of a number can be
found by multiplying the number by 1, 2, 3, 4, and so on.
EXAMPLE
A List all the factors of 48.
The possible factors are whole numbers
from 1 to 48.
1 48 48, 2 24 48, 3 16 48,
4 12 48, and 6 8 48
The factors of 48 are
1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
B Find the first five multiples of 3.
3 1 3, 3 2 6, 3 3 9,
3 4 12, and 3 5 15
The first five multiples of 3 are
3, 6, 9, 12, and 15.
PRACTICE
List all the factors of each number.
1. 8
2. 20
3. 9
4. 51
5. 16
6. 27
Find the first five multiples of each number.
7. 9
SB4
8. 10
Skills Bank
9. 20
10. 15
11. 7
12. 18
Prime and Composite Numbers
A prime number has exactly two factors,
1 and the number itself.
2
A composite number has more than two
factors.
Factors: 1 and 2; prime
4
11
Factors: 1 and 11; prime
47
Factors: 1 and 47; prime
4NS4.2
Factors: 1, 2, and 4; composite
12
Factors: 1, 2, 3, 4, 6, and 12;
composite
63
Factors: 1, 3, 7, 9, 21, and 63;
composite
EXAMPLE
Determine whether each number is prime or composite.
B 16
A 17
Factors
1, 17
prime
C 51
Factors
1, 2, 4, 8, 16
Factors
1, 3, 17, 51
composite
composite
PRACTICE
Determine whether each number is prime or composite.
1. 5
2. 14
3. 18
4. 2
7. 13
8. 39
9. 72
10. 49
5. 23
11. 9
6. 27
12. 89
Prime Factorization
5NS1.4
A composite number can be expressed as a product of prime numbers.
This is the prime factorization of the number. To find the prime
factorization of a number, you can use a factor tree.
EXAMPLE
Find the prime factorization of 24.
24
2 • 12
2•3•4
2•3•2•2
24
3• 8
3•2•4
3•2•2•2
24
4• 6
2•2•2•3
The prime factorization of 24 is 2 2 2 3, or 23 3.
PRACTICE
Find the prime factorization of each number.
1. 25
2. 16
3. 56
4. 18
5. 72
6. 40
Skills Bank
SB5
Greatest Common Divisor (GCD)
6NS2.4
The greatest common divisor (GCD) of two or more whole numbers is the
greatest whole number that divides evenly into each number.
EXAMPLE
Find the greatest common divisor of 24 and 32.
Method 1: List all the factors of both
numbers. Then find all the common factors.
Method 2: Find the prime factorization.
Then find the common prime factors.
24: 1, 2, 3, 4, 6, 8, 12, 24
32: 1, 2, 4, 8, 16, 32
24: 2 2 2 3
32: 2 2 2 2 2
The common factors are 1, 2, 4, and 8,
so the GCD of 24 and 32 is 8.
The common prime factors are 2, 2, and 2.
The GCD is the product of the factors, so
the GCD of 24 and 32 is 2 2 2 8.
PRACTICE
Find the GCD of each pair of numbers by either method.
1. 9, 15
2. 25, 75
3. 18, 30
4. 4, 10
5. 12, 17
6. 30, 96
7. 54, 72
8. 15, 20
9. 40, 60
10. 40, 50
11. 14, 21
12. 14, 28
Least Common Multiple (LCM)
6NS2.4
The least common multiple (LCM) of two or more numbers is the common
multiple with the least value.
EXAMPLE
Find the least common multiple of 8 and 10.
Method 1: List multiples of both numbers.
Then find the least value that is in both lists.
8: 8, 16, 24, 32, 40, 48, 56
10: 10, 20, 30, 40, 50, 60
The least value that is in both lists is 40, so
the LCM of 8 and 10 is 40.
Method 2: Find the prime factorization.
Then find the most occurrences of each
factor.
8: 2 2 2
10: 2 5
The LCM is the product of the factors, so
the LCM of 8 and 10 is 2 2 2 5 40.
PRACTICE
Find the LCM of each pair of numbers by either method.
1. 2, 4
2. 3, 15
3. 10, 25
7. 12, 21
8. 9, 21
9. 24, 30
SB6
Skills Bank
4. 10, 15
10. 9, 18
5. 3, 7
11. 16, 24
6. 18, 27
12. 8, 36
Multiply and Divide by Powers of Ten
4NS3.2,
5NS2.2
When you multiply by powers of ten, move the decimal point one place to
the right for each zero in the power of ten. When you divide by powers of ten,
move the decimal point one place to the left for each zero in the power of ten.
EXAMPLE
Find each product or quotient.
A 0.37 100
0.37 100 0.37
B 43 1000
43 1000 43.000
37
43,000
C 0.24 10
0.24 10 0.24
0.024
D 1467 100
1467 100 14 6 7.
14.67
PRACTICE
Find each product or quotient.
1. 10 8.53
2. 0.55 104
3. 48.6 1000
4. 2.487 1000
6. 103 12.1
7. 3.75 10
8. 8.5 10
9. 6420 103
5. 6.03 103
10. 1.9 10
Dividing Whole Numbers
5NS2.2
Division is used to separate a quantity into equal groups. The number to be
divided is the dividend , and the number you are dividing by is the divisor .
The answer to a division problem is known as the quotient .
EXAMPLE
Divide 8208 by 72.
114
728
2
0
8
72
100
72
288
288
0
Write the dividend under the long division symbol.
Subtract.
Bring down the next digit.
Subtract.
Bring down the next digit.
Subtract.
PRACTICE
Divide.
1
2
5
1. 1254
2. 1582
0
,6
9
8
3. 2684
5
5
6
4. 393
4
7
1
5. 994
6
5
3
6. 3213
8
,8
4
1
7. 1205
0
4
0
8. 1081
0
,4
7
6
9. 7411
0
7
,4
4
5
Skills Bank
SB7
Plot Numbers on a Number Line
5NS1.5,
6NS1.1
You can order rational numbers by graphing them on a number line.
EXAMPLE
3
4
Put the numbers 0.25, 4, 0.1, and 5 on a number line. Then order the
numbers from least to greatest.
3 __
4
__
0.1 0.25
4 5
0
0.5
1
3
0.75
4
4
0.8
5
The values increase from left to right: 0.1, 0.25, 34, 45.
PRACTICE
Plot each set of numbers on a number line. Then order the numbers from
least to greatest.
2
1
3 4
1. 2.6, 25, 22
2
2. 0.45, 8, 9
3. 0.55, 3, 0.6
4. 5.25, 53, 5.05, 5.5
1
5. 0.4, 5, 4, 0.42
5 4
6
6. 8, 9, 0.6, 7
1 1
8. 0.3, 7, 0.4, 8
2
7 5 4
9. 8, 6, 7, 0.65
7. 0.18, 7, 6, 0.12
3 1
3
Simplest Form of Fractions
6NS2.4
A fraction is in simplest form when the greatest common divisor of its
numerator and denominator is 1.
EXAMPLE
Simplify.
24
A 30
24: 1, 2, 3, 4, 6, 8, 12, 24
Find the greatest
common
divisor
30: 1, 2, 3, 5, 6, 10, 15, 30
of 24 and 30.
24 6
4
Divide both the numerator and
30 6
5
the denominator by 6.
18
B 28
18: 1, 2, 3, 6, 9, 18 Find the greatest
28: 1, 2, 4, 7, 14, 28 common divisor
of 18 and 28.
18 2
9
Divide both the
28 2
14
numerator and the
denominator by 2.
PRACTICE
Simplify.
15
1. 2
0
32
2. 4
0
14
3. 3
5
30
4. 7
5
17
5. 5
1
18
6. 4
2
19
7. 3
8
22
8. 121
10
9. 3
2
39
10. 9
1
SB8
Skills Bank
Mixed Numbers and Improper Fractions
6NS1.0
Mixed numbers can be written as fractions greater than 1, and fractions
greater than 1 can be written as mixed numbers.
EXAMPLE
3
A Write 2
as a mixed number.
5
2
B Write 6 7 as a fraction.
23 Divide the numerator
5 by the denominator.
4
52
3
20
3
3
45
Multiply the
denominator by
the whole number.
Write the remainder
as the numerator of
a fraction.
2
67
Add the product to
the numerator.
7 6 42
42 2 44
44
7
Write the sum over
the denominator.
PRACTICE
Write each mixed number as a fraction. Write each fraction as a mixed number.
22
1. 5
2. 97
1
41
3. 8
4. 59
7
5. 3
6. 41
1
9
47
7. 1
6
8. 38
2
33
11. 5
31
9. 9
10. 83
7
3
1
12. 129
Finding a Common Denominator
6NS2.4
You must often rewrite two or more fractions so that they have the same
denominator, or a common denominator . One way to find a common
denominator is to multiply the denominators. Or you can use the
least common denominator (LCD), which is the LCM of the denominators.
EXAMPLE
3
1
Rewrite 4 and 6 so that they have a common denominator.
Method 1: Multiply the denominators: 4 6 24
18
3
36
24
4
46
4
1
14
24
6
64
For each fraction, multiply the denominator by a
number to get the common denominator. Then
multiply the numerator by the same number.
Method 2: Find the LCD. The LCM of the denominators, 4 and 6, is 12. So the LCD is 12.
9
3
33
12
4
43
2
1
12
12
6
62
PRACTICE
Rewrite each pair of fractions so that they have a common denominator.
5 4
1. 6, 9
1 5
2. 6, 8
3 1
3. 1
, 0 8
1 3
4. 4, 1
4
2 5
5. 9, 1
2
Skills Bank
SB9
Adding Fractions
5NS2.3
To add fractions, first make sure they have a common denominator. Then
add the numerators and keep the common denominator.
EXAMPLE
Add. Write your answer in simplest form.
7
3
A 8 8
7
3
73
10
5
8
8
8
8
4
Add the numerators. Keep the denominator.
B 5 3
6
5
Step 1 Find the LCD. The LCD is 30.
5
55
25
Step 2 Rewrite the fractions using the LCD: 6 6 5
30
25
18
43
Step 3 Add: 3
30 3
0
0
3
36
18
5
56
30
Add the numerators. Keep the denominator.
PRACTICE
Add. Write your answer in simplest form.
3
1
6
3
3
1
1. 5 5
2. 7 7
3. 8 4
2
5
4. 3 9
3
2
5. 4 5
Subtracting Fractions
5NS2.3
To subtract fractions, first make sure they have a common denominator.
Then subtract the numerators and keep the common denominator.
EXAMPLE
Subtract. Write your answer in simplest form.
7
3
1
A 1
0
0
7
3
4
73
2
10
10
10
10
5
Subtract the numerators. Keep the denominator.
B 3 1
8
6
Step 1 Find the LCD. The LCD is 24.
3
33
9
Step 2 Rewrite the fractions using the LCD: 8 24
8 3
9
4
5
Step 3 Subtract: 2
24 2
4
4
4
1
14
24
6
64
Subtract the numerators. Keep the denominator.
PRACTICE
Subtract. Write your answer in simplest form.
9
5
8
5
11
2
1. 7 7
2. 9 9
3. 1
3
2
SB10
Skills Bank
8
4
4. 9 5
7
3
5. 1
8
0
Multiplying Fractions
5NS2.4, 5NS2.5
To multiply fractions, you do not need a common denominator. Multiply
the numerators, and then multiply the denominators.
EXAMPLE
5
2
Multiply 7 5. Write your answer in simplest form.
5 2
52
7 5
75
10
3
5
2
7
Multiply numerators and denominators.
Write in simplest form.
PRACTICE
Multiply. Write your answer in simplest form.
1 4
1. 2 7
3 4
2. 8 5
1 3
3. 5 5
6
7
4. 1
4 12
1 3
5. 3 8
2 14
6. 7 4
3 5
7. 5 7
6 1
8. 9 2
5 7
9. 8 1
0
10 1
10. 1
35
Dividing Fractions
5NS2.4, 5NS2.5
Two numbers are reciprocals if their product is 1. To find the reciprocal of a
fraction, switch the numerator and denominator. Dividing by a fraction is
the same as multiplying by its reciprocal. So, to divide fractions, multiply
the first fraction by the reciprocal of the second fraction.
EXAMPLE
2
3
Divide 5 10. Write your answer in simplest form.
3
2
2 10
10
5
5 3
2 10
53
20
1
5
4
3
Change the division to multiplication by the reciprocal.
Multiply numerators and denominators.
Write in simplest form.
PRACTICE
Divide. Write your answer in simplest form.
3
5
1. 8 6
5
3
2. 8 4
7
3
3. 1
4
2
2
6
4. 9 7
3
4
5. 5 5
3
3
6. 1
4
2
1
2
7. 6 3
9
3
8. 1
2
1
2
5
5
9. 6 9
7
3
10. 8 4
Skills Bank
SB11
Adding Decimals
5NS2.1
When adding decimals, first align the numbers at their decimal points. You
may need to add zeros to one or more of the numbers so that they all have
the same number of decimal places. Then add the same way you would
with whole numbers.
EXAMPLE
Add 23.7 1.426.
23.700
1.426
25.126
Align the numbers at their decimal points. Place two zeros after 23.7.
Add and bring the decimal point straight down.
You can estimate the sum to check that your answer is reasonable: 24 1 25 ✔
PRACTICE
Add.
1. 4.761 3.41
2. 14.2 16.9
3. 5.785 0.215
4. 32 1.75
Subtracting Decimals
5NS2.1
When subtracting decimals, first align the numbers at their decimal points.
You may need to add zeros to one or more of the numbers so that they all
have the same number of decimal places. Then subtract the same way you
would with whole numbers.
EXAMPLE
Subtract.
A 42.543 6.7
42.543
6.700
35.843
Align the numbers at their decimal points.
Place two zeros after 6.7.
Subtract and bring the decimal point straight down.
Estimate to check that your answer is reasonable: 43 7 36 ✔
B 5.0 0.003
5.000
0.003
4.997
Place two zeros after 5.0.
Align the numbers at their decimal points.
Subtract and bring the decimal point straight down.
PRACTICE
Subtract.
1. 4.761 3.41
SB12
Skills Bank
2. 30.79 28.18
3. 24.912 22.98
4. 20.11 8.284
Multiplying Decimals
5NS2.1
When multiplying decimals, multiply as you would with whole numbers.
The sum of the number of decimal places in the factors equals the number
of decimal places in the product.
EXAMPLE
Find each product.
A 81.2 6.547
6.547
81.2
1.3094
6.5470
523.7600
531.6164
B 0.376 0.12
3 decimal places
1 decimal place
0.376
0.12
752
3760
0.04512
3 decimal places
2 decimal places
5 decimal places
4 decimal places
PRACTICE
Find each product.
1. 0.97 0.76
2. 0.5 3.761
3. 42 17.654
4. 7.005 32.1
5. 9.76 16.254
6. 296.5 2.4
7. 7.7 6.5
8. 8.92 2.8
9. 3.65 4.2
10. 0.002 8.1
11. 0.03 0.204
12. 98.6 4.9
Dividing Decimals
5NS2.1
When dividing with decimals, set up the division as you would with whole
numbers. Pay attention to the decimal places, as shown below.
EXAMPLE
Find each quotient.
A 89.6 16
B 3.4 4
0.85
43
.4
0
32
20
20
0
5.6
168
9
.6
80
96
96
0
Place decimal point.
Insert zeros if necessary.
PRACTICE
Find each quotient.
1. 242.76 68
2. 40.5 18
3. 121.03 98
4. 3.6 4
5. 1.58 5
6. 0.2835 2.7
7. 8.1 0.09
8. 0.42 0.28
10. 36.9 0.003
11. 0.784 0.04
9. 480.48 7.7
12. 15.12 0.063
Skills Bank SB13
Order of Operations
6AF1.3, 6AF1.4
When simplifying expressions, follow the order of operations.
1. Simplify within parentheses.
2. Simplify exponents.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.
EXAMPLE
Simplify each expression.
A 32 (11 4)
32 (11 4)
32 7
Simplify within parentheses.
97
Simplify the exponent.
63
Multiply.
2
22 2
B 53
22 22
53
(22 22)
(5 3)
The fraction bar acts as a grouping symbol. Simplify
the numerator and the denominator before dividing.
22 4
53
Simplify the power in the numerator.
26
53
Subtract to simplify the numerator.
26
2
Subtract to simplify the denominator.
13
Divide.
PRACTICE
Simplify each expression.
2
1. 45 15 3
4
2. 3. 35 (15 8)
0 24
4. 62
5. 24 3 6 12
6. 6 8 22
8. 32 10 2 4 2
9. 27 (3 6) 62
49 4
7. 20 3 4
10. 4 2 8 23 4
2
7
13. 42
53
2 3(6)
2
11. 2
12. 82 4 12 13 5
14. 37 21 7
15. 92 32 8
3
16. 10 2 8 2
2 8
17. 18. 4 12 4 8 2
19. 28 32 27 3
20. 9 (50 16) 2
18 6
21. SB14
Skills Bank
21
2
9
Measurement
6AF2.1
1 min 60 s
1 h 60 min
1 day 24 h
The measurements for time
are the same worldwide.
The customary system of
measurement is used in the
United States.
1 wk 7 days
1 yr 12 mo
1 yr 365 days
Length
12 in. 1 ft
3 ft 1 yd
5280 ft 1 mi
The metric system is used
elsewhere and in science
worldwide.
Capacity
8 oz 1 c
2 c 1 pt
2 pt 1 qt
Length
1 mm 0.001 m
1 cm 0.01 m
1 km 1000 m
1 leap yr 366 days
Weight
16 oz 1 lb
2000 lb 1 ton
Capacity
1 mL 0.001 L
1 kL 1000 L
Mass
1 mg 0.001 g
1 kg 1000 g
Use the table below to convert from metric to customary measurements.
Length
Capacity
Mass/Weight
Temperature
1 cm 0.394 in.
1 L 1.057 qt
1 g 0.0353 oz
1 m 3.281 ft
1 L 0.264 gal
1 kg 2.205 lb
1 m 1.094 yd
1 L 4.227 c
1 kg 0.001 ton
1 km 0.621 mi
1 mL 0.338 fl oz
1 metric T 1.102 ton
C 32
F 9
5
Use the table below to convert from customary to metric measurements.
Length
Capacity
Weight/Mass
Temperature
1 in. 2.540 cm.
1 qt 0.946 L
1 oz 28.350 g
1 ft 0.305 m
1 gal 3.785 L
1 lb 0.454 kg
1 yd 0.914 m
1 c 0.237 L
1 ton 907.185 kg
1 mi 1.609 km
1 fl oz 29.574 mL
1 ton 0.907 metric ton
(F 32)
C 5
9
EXAMPLE
A Write , , or .
35 in.
1 yd
35 in.
3 ft
35 in. 36 in.
35 in. 1 yd
B
Convert 32 km to mi.
C
Convert 25°C to °F.
9
F 5 25 32
1 km 0.621 mi
1 yd 3 ft
3 ft 36 in. 32 km 32 0.621 mi
F 45 32
F 77°F
32 km 19.872 mi
PRACTICE
Write , , or .
1. 3 lb
40 oz
Convert.
4. 15 mi to km
2. 200 cm
5. 2 weeks to hours
2m
6. 32 fl oz to mL
3. 6 c
2 qt
7. 95°F to °C
8. 14 tons to kg
Skills Bank
SB15
Polygons
3MG2.1
A polygon is a closed figure with three
or more sides. The name of a polygon
is determined by its number of sides.
If all the sides are the same length, and all
the angles have the same measure, the
polygon is a regular polygon . Sides and
angles with the same measures are
marked with the same symbol.
Number
of Sides
Name
Number
of Sides
Name
3
Triangle
8
Octagon
4
Quadrilateral
9
Nonagon
5
Pentagon
10
Decagon
6
Hexagon
12
Dodecagon
7
Heptagon
n
n-gon
EXAMPLE
Identify each polygon.
The mark on each side indicates that the sides are
all the same length. The arch inside each angle
indicates that the angles all have the same measure.
A
regular hexagon
B
pentagon
PRACTICE
Identify each polygon.
1.
2.
3.
Geometric Patterns
3MG2.0
Patterns involving polygons may deal with size, color, position, or shape.
EXAMPLE
Predict the next term:
,
,
, ...
Each term has one more side than the previous
term. The next term will have six sides.
hexagon
PRACTICE
1. Predict the next term.
,
SB16
,
,...
Skills Bank
2.
Describe the missing term.
,
,
,
,...
Classify Triangles and Quadrilaterals
A triangle can be
classified according
to its angle measurements
or according to the number
of congruent sides it has.
Classifying by Angles
4MG3.7, 4MG3.8
Classifying by Sides
Acute
Three acute angles
Scalene
No sides congruent
Right
One right angle
Isosceles
At least 2 sides congruent
Obtuse
One obtuse angle
Equilateral
All sides congruent
EXAMPLE 1
Classify each triangle according to its angles and sides.
A
B
C
12 cm
4 cm
9 cm
acute isosceles
obtuse scalene
acute equilateral
Quadrilaterals can also be classified according to their sides and angles.
Parallelograms
Parallelogram
2 pairs of parallel,
congruent sides
Rectangle
4 right angles
Rhombus
4 congruent sides
Other Quadrilaterals
Trapezoid
exactly 1 pair of parallel sides
Isosceles Trapezoid
congruent, nonparallel legs
Kite
2 pairs of adjacent,
congruent sides
Square
4 right angles and
4 congruent sides
EXAMPLE 2
Tell whether the following statement is always, sometimes, or never true:
A square is a rectangle.
always
A rectangle must have four right angles, and a square always has four right angles.
PRACTICE
Classify each triangle according to its angles and sides.
1.
2.
35º
35º 110º
3.
4 in.
2 in.
4 in.
Tell whether each statement is always, sometimes, or never true.
4. A rectangle is a square.
5. A trapezoid is a parallelogram.
Name the quadrilaterals that always meet the given conditions.
6. All sides are congruent.
7. Two pairs of sides are congruent.
Skills Bank
SB17
Bar Graphs
5SDAP1.2
A bar graph displays data using vertical or horizontal bars that do not
touch. Bar graphs are often a good way to display and compare data that
can be organized into categories.
EXAMPLE 1
Use the bar graph to answer each question.
Most Widely Spoken Languages
A Which language has the most native speakers?
The bar for Mandarin is the longest, so
Mandarin has the most native speakers.
B About how many more people speak
Mandarin than speak Hindi?
About 500 million more people speak
Mandarin than speak Hindi.
English
Hindi
Mandarin
Spanish
0
200
400
600
800
1,000
Number of speakers (millions)
You can use a double-bar graph to compare two
related sets of data.
EXAMPLE 2
The table shows the life expectancies of people in three
Central American countries. Make a double-bar graph of
the data.
Country
Male
Female
El Salvador
67
74
Honduras
63
66
Nicaragua
65
70
Step 1 Choose a scale and interval for the vertical axis.
Life Expectancies in
Central America
Step 2 Draw a pair of bars for each country’s data. Use
different colors to show males and females.
80
Step 3 Label the axes and give the graph a title.
Age
60
Step 4 Make a key to show what each bar represents.
40
20
0
El Salvador
Male
SB18
Skills Bank
15
10
5
es
ge
s
an
Or
ap
na
s
s
0
Gr
3. About how many more pounds of bananas
than pounds of oranges were eaten per person?
20
na
2. About how many pounds of apples were
eaten per person?
25
Ba
1. Which fruit was eaten the least?
30
Ap
ple
The bar graph shows the average amount of fresh
fruit consumed per person in the United States in
1997. Use the graph for Exercises 1–3.
Nicaragua
Fresh Fruit Consumption
Average per
person (lb)
PRACTICE
Honduras
Female
Line Graphs
5SDAP1.2
You can use a line graph to show how data changes over a period of time.
In a line graph , line segments are used to connect data points on a
coordinate grid. The result is a visual record of change.
EXAMPLE
Make a line graph of the data in the table. Use the
graph to determine during which 2-month period
the kitten’s weight increased the most.
Age (mo)
Weight (lb)
0
0.2
2
1.7
4
3.8
6
5.1
8
6.0
10
6.7
12
7.2
Step 1 Determine the scale and interval for each
axis. Place units of time on the horizontal axis.
Step 2 Plot a point for each pair of values. Connect the
points using line segments.
Step 3 Label the axes and give the graph a title.
Growth Rate of a Kitten
Weight (lb)
8
6
4
2
0
0
2
4
6
8
10
12
Age (mo)
The graph shows the steepest line segment between 2 and 4 months. This
means the kitten’s weight increased most between 2 and 4 months.
PRACTICE
1. The table shows average movie theater ticket prices in the United States. Make a line
graph of the data. Use the graph to determine during which 5-year period the average
ticket price increased the least.
Year
1965
1970
1975
1980
1985
1990
1995
2000
2005
Price ($)
1.01
1.55
2.05
2.69
3.55
4.23
4.35
5.39
6.41
2. The table shows the number of teams in the National Basketball Association (NBA).
Make a line graph of the data. Use the graph to determine during which 5-year period
the number of NBA teams increased the most.
Year
Teams
1965
1970
1975
1980
1985
1990
1995
2000
2005
9
14
18
22
23
27
27
29
30
Skills Bank
SB19
Histograms
5SDAP1.2
A histogram is a bar graph that shows the frequency of data within equal
intervals. The bars must be of equal width and should touch, but not
overlap.
EXAMPLE
The table shows survey results about the number of CDs students own.
Make a histogram of the data.
Number of CDs
1
2
3
4
lll
ll
llll
llll l
5
6
7
8
llll l
lll
llll lll
llll ll
9
10
11
12
llll
llll
llll
llll
l
llll
llll l
llll
13
14
15
16
llll
llll
llll
llll
llll
llll l
llll l
llll l
17
18
19
20
llll llll
llll ll
ll
llll l
Step 1 Make a frequency table of the data. Be sure to use a scale that includes
all of the data values and separate the scale into equal intervals. Use
these intervals on the horizontal axis of your histogram.
Frequency
1–5
22
6–10
34
11–15
52
16–20
35
Step 2 Choose an appropriate scale and interval for
the vertical axis. The greatest value on the scale
should be at least as great as the greatest frequency.
Step 3 Draw a bar for each interval. The height of the bar is the
frequency for that interval. Bars must touch but not
overlap.
Step 4 Label the axes and give the graph a title.
CD Survey Results
60
50
Frequency
Number of CDs
40
30
20
10
0
PRACTICE
1. The list below shows the ages of musicians in a local
orchestra. Make a histogram of the data.
14, 35, 22, 18, 49, 38, 30, 27, 45, 19, 35, 46, 27, 21, 32, 30
2. The list below shows the results of a typing test in words
per minute. Make a histogram of the data.
62, 55, 68, 47, 50, 41, 62, 39, 54, 70, 56, 47, 71, 55, 60, 42
SB20
Skills Bank
1–
5
6–
10
0
5
–1 6 – 2
1
11
Number of CDs
Circle Graphs
5SDAP1.2
A circle graph shows parts of a whole. The entire circle represents 100% of
the data and each sector represents a percent of the total.
EXAMPLE
Type of Program
Number of Students
At Mazel Middle School, students were surveyed
about their favorite types of TV programs. Use
the given data to make a circle graph.
Science
25
Cooking
15
Sports
50
Step 1 Find the total number of students
surveyed.
Sitcoms
150
Movies
60
Cartoons
200
25 15 50 150 60 200 500
Step 2 Find the percent of the total students
who like each type of program.
Percent
25
500
15
500
50
500
150
500
60
500
200
500
Step 3 Find the angle measure of each sector of
the graph. There are 360° in a circle, so
multiply each percent by 360°.
5%
0.05
360° 18°
3%
0.03
360° 10.8°
10%
0.1
360° 36°
30%
0.3
360° 108°
12%
0.12
360° 43.2°
40%
0.4
360° 144°
Step 4 Use a compass to draw a large circle. Use a
straightedge to draw a radius.
Step 5 Use a protractor to measure the angle of the
first sector. Draw the angle.
Step 6 Use the protractor to measure and draw each
of the other angles.
Step 7 Give the graph a title, and label each sector
with its name and percent. Color the sectors.
Angle of Sector
Favorite TV Programs
Cooking
3%
Science
5%
Sports
10%
Cartoons
40%
Sitcoms
30%
Movies
12%
PRACTICE
1. Use the given data to make a circle graph.
Favorite Pets
Type of Pet
Dog
Fish
Bird
Cat
Other
Number of People
225
150
112
198
65
Skills Bank
SB21
Sampling
6SDAP2.2
A population is a group that someone is gathering information about.
A sample is part of a population. For example, if 5 students are chosen to represent a class
of 20 students, the 5 chosen students are a sample of the population of 20 students.
The sample is a random sample if every member of the population had an equal chance of
being chosen.
EXAMPLE
Jamal telephoned people on a list of 100 names in the order in which they appeared. He
surveyed the first 20 people who answered their phone. Explain whether the sample is
random.
Names at the beginning of the list have a greater chance of being selected than those at the
end of the list, so the sample is not random.
PRACTICE
Explain whether each sample is random.
1. Rebecca surveyed every person in a theater who was sitting in a seat along the aisle.
2. Inez assigned 50 people a number from 1 to 50. Then she used a calculator to generate
10 random numbers from 1 to 50 and surveyed those with matching numbers.
Bias
6SDAP2.4
Bias is error that favors part of a population and/or does not accurately represent the
population. Bias can occur from using sampling methods that are not random or from
asking confusing or leading questions.
EXAMPLE
Jenn went to a movie theater and asked people who exited if they agree that the theater
should be torn down to build office space. Explain why the survey is biased.
People usually only go to movies if they enjoy them, so those exiting a movie theater would not
want it torn down. People who do not use the theater did not have a chance to answer.
PRACTICE
Explain why each survey is biased.
1. A surveyor asked, “Is it not true that you do not oppose the candidate’s views?”
2. Brendan asked everyone on his track team how they thought the money from
the athletic department fund-raiser should be spent.
SB22
Skills Bank
Compound Events
6SDAP2.2
A compound event consists of two or more single events.
EXAMPLE
Marilyn randomly draws 1 of 6 cards, numbered from 1 to 6, from a box and then
randomly selects 1 of 2 marbles, 1 red (R) and 1 blue (B), from a jar. Find the probability
that the card will show an even number and that the marble will be red.
1
2
3
4
5
6
R
1, R
2, R
3, R
4, R
5, R
6, R
B
1, B
2, B
3, B
4, B
5, B
6, B
Use a table to list all possible outcomes.
Circle or highlight the outcomes with an
even number and “red.”
3
1
3 ways outcome can occur
P(even, red) 1
4
2
12 equally likely outcomes
In the Example, a table was used to list the possible outcomes. Another
way to list outcomes of a compound event is to use a tree diagram .
Card Number
Marble
R
B
List all possible outcomes
for the six cards: 1, 2, 3, 4,
5, 6.
1
R
2
B
R
3
B
R
4
5
Then, for each outcome of
the six cards, list all possible
outcomes for the marbles:
red and blue for each card.
B
R
B
6
R
B
PRACTICE
1. If you spin the spinner twice, what is the
probability that it will land on blue on the
first spin and on green on the second spin?
2. What is the probability that the spinner will
land on either red or yellow on the first spin
and blue on the second spin?
3. What is the probability that the spinner will
land on the same color twice in a row?
Skills Bank
SB23
Inductive and Deductive Reasoning
6AF2.0, 7MR2.4
Inductive reasoning involves examining a set of data to determine a
pattern and then making a conjecture about the data. In deductive
reasoning , you reach a conclusion by using logical reasoning based on
given statements, properties, or premises that you assume to be true.
EXAMPLE
A Use inductive reasoning to determine the 30th number of the sequence.
3, 5, 7, 9, 11, . . .
Examine the pattern to determine the relationship between each term in
the sequence and its value.
Term
1st
2nd
3rd
4th
5th
Value
3
5
7
9
11
121213
421819
221415
5 2 1 10 1 11
321617
To obtain each value, multiply the term by 2 and add 1. So the 30th term is
30 2 1 60 1 61.
B Use deductive reasoning to make a conclusion from the given premises.
Premise: Makayla needs at least an 89 on her exam to get a B for the
quarter in math class.
Premise: Makayla got a B for the quarter in math class.
Conclusion: Makayla got at least an 89 on her exam.
PRACTICE
Use inductive reasoning to determine the 100th number in each pattern.
1
1
1
1. 2, 1, 12, 2, 22, . . .
2. 1, 4, 9, 16, 25, . . .
3. 4, 6, 8, 10, 12, . . .
4. 0, 3, 6, 9, 12, 15, . . .
Use deductive reasoning to make a conclusion from the given premises.
5. Premise: If it is raining, then there must be a cloud in the sky.
Premise: It is raining.
6. Premise: A quadrilateral with four congruent sides and four right
angles is a square.
Premise: Quadrilateral ABCD has four right angles.
Premise: Quadrilateral ABCD has four congruent sides.
7. Premise: Darnell is 3 years younger than half his father’s age.
Premise: Darnell’s father is 40 years old.
SB24
Skills Bank
Selected Answers
37. 43 39. 8 41. 30 43. 15
Chapter 1
1-1
Exercises
45a. $1,146,137,000,000
m; m $39 57. C 59. 16
b. $1,763,863,000,000 c. about
61. 12 63. x 9 65. x 26
$618,000,000,000 or $618 billion
1
1. 15 3. 3 5. 18 7. 2 c 9. 22 c
11. 37 13. 57 15. 13 pt 17. 10 pt
49. C 51. 4 53. 12 55. 13
1-5
19. 22 21. 10 23. 20 25. 16
q 4 51. 74 mi 53. $195 $156
Exercises
1-9
Exercises
1. 9x 6 12 3. 2 5. 8
7. 5 9. 24 11. 42 13. 88 15. 18
27. 45 29. 138 31. 20.7 33. 36
1. 14 3. 12 5. 17 7. 18 9. 10
DVDs 17. 4z 18 54 19. 1
35. 105 37. 11 39. 32 41. 21
11. 17 13. 17 15. 10 17. 6 23. 5 25. 2 27. 9 29. 4
43. 19 45. $110 47. B 49. yes
(4) 2 19. 3 21. 56
31. 40 33. 55 35. 30 37. 5 h
51. A 53. 15, 21, 61, 71 55. 49, 81
23. 26 25. 20 27. 24
39. Nine less than 4 times a
57. 202 59. 400 61. 200.2 63. 40
29. 13 31. 190 ft above the
number is 3; 3 41. 21 43. 3
starting point 33. Great Pyramid
x
to Cleopatra; about 500 years
1. 3p 5 3. 16 7 5. 18 plus
45. 0 47. 9 3 8; x 99
49. 5 3m 4; m 3 51. 16m
35. Cleopatra takes the throne and
42,000; m 2625 miles per year
the product of 43 and s 7. 10 plus
Napoleon invades Egypt.
the quotient of y and 31 9. 5n;
39. 8 41. 3 43. 12
53. 6m 22; m 132 miles 55. A
1-2
Exercises
d
5
$75; $125; $175; $225 11. 1 n
13. 78j 45 15. 14 59q 17. 12
1-6
Exercises
more than the product of 16 and g
1. 32 3. 84 5. 49 7. 24
19. 51 less than the quotient of w
9. gains $15 11. 21 13. 84
1
and 182 23. 6y 9 25. 3g
m
2
27. 13y 6 29. 23
31. 83 x
5
33. 8 times the sum of m and 5
15. 3 17. 140 19. 60 21. 39
15
6
9
23. $100 25. 3, 5; 3, 2; 3 , 3;
15
, 5 27. 12 29. 4 31. 8
3
1
57. 44 59. 30 60. 6 61. 72
62. 3 63. 147 64. 9
Chapter 1 Study Guide:
Review
1. equation 2. opposite
3. absolute value 4. 147 5. 152
6. 278 7. 2(k 4) 8. 4t 5
35. 17 times the quotient of 16
33. 36 35. 11 37. –8 39. –6
9. 10 less than the product of 5
45. D 47. j 18 49. y 22
and b 10. 32 plus the product of
43. 9n; $9450 45. 24 47. 7
51. 9 53. 254
23 and s 11. 12 less than the
1
x7
and w 37. 4(x 7) or 4 41. C
quotient of 10 and r
1-3
Exercises
1-7
Exercises
12. 16 more than the quotient of y
1. 4 2 3. 17, 8, 6 5. 7,
1. 12 3. 14 5. 23 7. 39
and 8 13. 1 14. 15 15. 34
0, 3 7. 15 9. 5 11. 21 13. 14
9. 15,635 ft 11. 32 13. 44
16. 21 17. 14 18. 1 19. 2
15. 6, 2, 5 17. 30, 27, 25
15. 74 17. 35 19. 5 21. 24
20. 12 21. 3 22. 1 23. 24
19. 9 21. 11 23. 5 25. 0 27. 23. 3 25. 949 27. 110 29. 17
24. 8 25. 8 26. 16 27. 17
29. 31. 33. 35. 16,
31. 138 33. 1784
28. 3 29. 15 30. 22 31. 4
12, 24 37. 45, 25, 35 39. 50
35. t 600 173; 427°C 37. 40
32. 16 33. 5 34. 35 35. 18
41. 1 43. 72 45. 6 47. 9 49. 38
39. 1 41. 59 47. B 49. 14
36. 52 37. 25 38. 120 39. 2
51. 16 53. Antarctica, Asia, North
51. 13 53. 56 55. 2
40. z 23 41. t 8 42. k 15
43. x 15 44. 1300 lb
America, Europe, South America,
Africa, Australia 57. 7, 6, 5
59. A 61. 9 62. 64 64. 7t 8
1- 4
Exercises
1-8
Exercises
45. 3300 mi2 46. g 8 47. k 9
1. 7 3. 2 5. 60 7. 6 9. 54
48. p 80 49. w 48
people 11. 15 13. 7 15. 2
50. y 40 51. z 192
17. 4 19. 54 21. 96 23. 161
52. 705 mi 53. 24 months
1. 6 3. 2 5. 7 7. 6 9. 11
25. 252 27. 7 29. 2 31. 56
54. x 6 55. y 96
11. 10 13. 2 15. 5 17. 22
33. 72 35. 17 37. 207 39. 48
56. n 49 57. x 4
19. 16 21. 7 23. 32 25. 23
41. 15 43. 8n 32; n 4
58. n 24 59. y 11
27. 9 29. 3 (4) 7
servings 45. 16 h; $160 47. 7 n
60. 3 hours
31. 12 33. 17 35. 22
15; n 8 49. 12 q (8);
Selected Answers
SA1
Chapter 2
2-4
5
5
1
1. 3
3. 58 5. 42 miles 7. 0.162
2
7
7
1
13. 2
15. 12
9. 0.42 11. 3
6
4
Exercises
2-1
1. 0.625 3. 0.416 5. 0.1 7. 0.375
3
2
1
9. 1.25 11. 4 13. 5 15. 25
21
9
115
73
19. 21. 23. 17. 3
100
11
333
99
58
25. 9
27. 0.375 29. 1.8
9
3
31. 1.6 33. 4.6 35. 1.3 37. 377
18
1
31. Cullinan III 33. z 3
Exercises
5
2
5
43. 1 45. 39. 2
41. 1
1000
33
5
5
4
3
151
51. 53. yes
47. 1
49.
1
11
333
21
17. 4
19. 27 boys 21. 0.235
0
b. 3 3; 2 3; 2 2; 3 5; 2 2
2 2; 5 5; 2 2 2 c. 0.4,
repeating; 0.16, repeating; 0.25,
terminating; 0.46, repeating;
47. y 54.2 49. m 1.4
53. 60 carats 55. 3v 64;
1
1
minutes 56. p 15
21
2
2-5
2
1. 7 hours 3. y 11 5. x 5
11
2
1. 3 3. 7 5. 18
7. 15 9. 12.4
0
15. 490
11. 15.3 13. 4.23
1
17. 19.4 19. 45 21. 18 23. 6
9
8
3
serving 25. 13
27. 15 29. 2
5
1
39. 13.6 41. 12 43. 11 45. 370
0.375, terminating 65. GCD 2;
in.
47. 11 glasses 49. 34
8
1
13
53. about 3 55. B 57. 11 59. 2
0
723
4
63. 61. 1000
5
1. 3. 5. 7. 5
1
in., 7.5 in., 88 in., 8.25 in.
9. 71
6
11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 37a. apricot,
sulphur, large orange sulphur,
white-angled sulphur, great white
b. between the apricot sulphur
and the large orange sulphur
2
31
2-6
Exercises
2-2
5
41. ⏐0.62⏐, ⏐3⏐, ⏐0.75⏐, ⏐6⏐
Exercises
43. D 45. 10 47. 47 49. 0.75
meters 55. The company did not
51. 2.5 53. 0.95
find a common denominator
1
when adding 2 and 4. 57. 28
Exercises
2-3
3
5
61. 6
59. 11
1
1
1
4
8
1
21. 3
23. 3 25. 7.9375
3
69
6
1
29. in. 31. 27. 4
200
11
4
5
1
33. 29 35. 1 37. 12
39. 0.186 quadrillion Btu 43. D
11
47. b 1 49. a 5
45. 1
5
51. 53. SA2
Selected Answers
2-7
1. y 82.3 3. m 19.2
5
5. s 97.146 7. x 9
7
9. w 1
11. y 8 13. 8 days
5
15. m 7 17. k 3.6
6
19. c 3.12 21. d 2
5
5
23. x 2
25. r 7
4
1
1
5
45. y 4.4
41. 8 43. 1
2
47. m 25.6
Chapter 2 Study Guide:
Review
1. rational number
2. terminating decimal
3
1
21
5
7. 1
inverse 4. 5 5. 4 6. 4
0
1
1
212
10. 1.75 11. 0.26
8. 3 9. 999
12. 0.7 13. 14. 2
1
15. 0.9, 3, 0.25, 2 16. 0.11, 0,
9
6
7
5
17. 1
18. 5 19. 9
0.67, 1
0
3
1
1
12
1
20. 6 21. 1
22. 1
23. 15
1
3
3
8
1
5
1
24. 75 25. 1
26. 4 27. 24
5
1
7
28. 34 29. 13 30. 1
31. 6
8
3
2
5
32. 8 33. 9 34. 16 35. 4 36. 2
3
7
39. 111
40. 42
37. 16 38. 1
8
0
0
17
11
43. 21.8
41. 36
42.
9
0
36
5
95
44. 18 45. 8 46. 2 47. 9
9
48. 2 49. 44.6 50. 6
54. c 16 55. r 3 56. t 16
Exercises
1
72 35. 110,000 37. 25 in. 39. B
51. $108 52. m 10 53. y 8
1. 30.01 3. 24.125 5. 0.56 s
7. 15 9. 5 11. 9 13. 33.67
14
15. 12.902 17. 10.816 s 19. 1
7
3
13. r 64 15. 2.02 17. 17.5
1
1
21. 1
23. 10 25. 64
19. 1
5
8
11
n7
27. 1.3 29. 5 31. 5 13;
3. reciprocal or multiplicative
3
1
7
19
1. 2
3. 41
5. 4
7. 81
0
1
0
2
69
1
11
13. 4 yd 15. 1
9. 2 11. 130
72
29
13
19
1
21. 1 23. 17. 1
19.
126
4
21
3
4
39
11
29. 25. 14
27. 5
833
120
1
1
19
31. 18 miles 33. 1
35. 4
2
2
7
5
145
67
in. 41. 43. 37. 3
39.
4
8
168
72
1
5
45. 43 47. 28 cups
3
1
1
49a. 168 m b. 118 mi c. 272 mi
73
19
meter 53. 19
51. 100
100
1
3
2
7. a 22 9. y 5 11. m 121
0
terminating; 0.625, terminating;
81. 126
4
Exercises
2-8
Exercises
2
5
1
61. 24
57. 2(m 19) 59. 101
2
5
0.5625, terminating; 0.48,
75. 20 77. 21 79. 180
1
43. y 4.2 45. c 2
0
7
5
31. 159
27. 0.368 29. 81
1
53
33. 1.82 35. 0.558 37. 25
4
55
3
1
41. 43a. 1 tsp
38. 192
8
4
1
b. 12 tsp c. 2 tsp 47. A 49. C
5
2
51. 53. 55. 6 57. 9
1
31. 22
33. 83 35. 9.7 37. 40.55
8
21
69. C 71. 9.875 73. 28; 48
34
1
39. d 2 41. v 30.25
23. 4.125 25. 0.496
3
55. no 57. yes 59. yes 61. 38
4 1 1 7 9 12 5 3
63a. 9; 6; 4; 1
; ; ; ; 5 16 25 8 8
35. j 21.6 37. t 7
4
27. d 12
29. 22581
carats
1
5
57. w 64 58. r 42
59. h 50 60. x 52
61. d 33 62. a 67
63. c 90 64. 11
Chapter 3
3-1
13. k 10 15. w 3 17. y 5
29. The solution is x 4. 33. B
19. h 6 21. m 2 23. x 12
37. 1
39. t 2 8
35. 2
5
8
25. n 2 27. b 13 29. x 17
Exercises
31. y 7 33. $11.80 per hour
1
19
3-7
Exercises
1. Comm. Prop. of Add. 3. 39
35. 31 and 32 37. 212°F 41. C
1. r 18 3. 120 j, or j 120
5. 700 7. 130 9. 168 11. 54
43. n 3 45. x 121
5. 40 a, or a 40
13. 396 15. Comm. Prop. of Mult.
47. 6t 3k 15
7. r 63 9. 104 sandwiches
17. 109 19. 1300 21. 24 23. 133
25. 132 27. 21 29. Distrib. Prop.
3-4
11. 75 x, or x 75 13. 77 p,
Exercises
or p 77 15. h 12
31. Assoc. Prop. of Add.
1. x 1 3. x 2 5. x 20
17. q 4 19. 6 r, or r 6
33. Comm. Prop. of Add. 35. 40
7. x 1 9. d 5
21. w 3 23. t 95
37. 15 39. $53 43. 8; Distrib.
11. 250 min; $8.75 13. x 1
25. a 120 33. A 37. 27 lb,
Prop. 45. y; Assoc. Prop. of Add.
15. all real numbers 17. y 6
135 lb 39. at least $13.34 per
19. x 16.2 21. a 13 23. y 2
43. 83
week 41. 3
3
47. 24 19 26 21 24 26
19 21 (Comm. Prop. of Add.)
(24 26) (19 21) (Assoc.
Prop. of Add.) 50 40 90 in.
25. n 5 27. x 5 29. 22, 23
5
3-8
31. x 25 10 4x; x 7
1
Exercises
33. 350 units 35a. 17 protons
1. k 2 3. y 8 5. y 7
49. The sentence should read,
b. 11 39. C 41. x 3 43. g 12
7. x 3 9. h 1 11. d 1
“You can use the Commutative
45. 47. 13. at least 21 caps 15. x 4
Property of Addition...”
1
1
1
1
51. 12 3 6 4 12 3 12 1
1
12 (Distrib. Prop.) 4 2
6
4
3 (Mult.) (4 2) 3 (Assoc.
Prop. of Add.) 6 3 (Add) 9
2
1
1
59. 21
53. C 55. 15 57. 2
5
0
61. 28
3-2
Exercises
3-5
7. 5x 8y 9. 9x y 11. 7g 5h
12 13. r 12 15. 2t 56
17. 10y 17 19. 13y 21. 6a 15
23. 5x 3 25. 7z b 5
22
23. k 3 25. r 3 27. p 3
1
1. p 60 3. m 7 15
5.
7.
29. w 1 31. a 2 33. q 6
35. b 2.7 37. f 2.7 39. 7
5 4 3 2 1 0 1 2
41. at least 31 beads
2 1 0 1 2 3 4 5
43a. $158 b. 17 mo 47. B
9. s 5 or s ≥ 3 11. s 10
49. Comm. Prop. of Mult.
y
13. x 11 35 15. 7 10
51. Comm. Prop. of Add.
17.
1. 5x 3. 12f 8 5. 6p 9
17. q 2 19. x 7 21. a 3
Exercises
19.
21.
23.
2 1 0 1 2 3 4 5
2 1 0 1 2 3 4 5
2 1
0
1
2
3
4
5
5 4 3 2 1 0 1 2
53. 7r 60
Chapter 3 Study Guide:
Review
1. inequality 2. Comm. Prop.
3. terms 4. Comm. Prop. of Add.
5. Assoc. Prop. of Add. 6. Dist.
35. 3x 48 37. 2(5x x); 12x
1
25. c 2 or c 7 27. 5w 60
2
1
29. m 25 35 31. x 9
33. x 4 35. d 89,000
8. 19m 10 9. 14w 6
39. no; 6r 12m 5m 15 5r
39. B 41. 25, 19, 12
10. 2x 3y 11. 2t2 4t 3t3
7, Distrib. Prop.; 6r 5r 12m
43. 11, 9, 7, 5 45. 1
1
1
47. 13
27. 11x 4y 8 29. 6d 3e 12
31. 4y 10 33. 11x 18
5m 15 7, Comm. Prop.; 6r
5r 12m 5m 15 7; 11r 2
17m 8 41. 7d 1 43. 6r 11r
1
3-6
Exercises
Prop. 7. Assoc. Prop. of Add.
12. y 1 13. h 2 14. t 1
15. r 3 16. z 2 17. a 12
1
18. s 7 19. c 24 20. x 6
2
21. y 3 22. no solution
45. k 13 47. 49g 53s 44b
1. x 7 3. f 24 5. k 9.3
23. z 5 24. Let d distance;
49. y2 2(x y2); y2 2x
d 1 mi 25. Let c cost;
59. 2; Distrib. Prop. 61. 5; Assoc.
1
1
7. 62 x 16; x 92 9. x 56
1
11. x 15 13. c 33
15. 21.75 x 50; x 28.25
students; s 45
Prop. of Mult.
17. z 0 19. y 1.8
27.
5
1
53. 6x 112 55. 16 57. a 80
3-3
Exercises
1. d 3 3. e 6 5. h 7
7. x 1 9. p 1 11. 6 hours
21. k 1 23. {x : x 20}
c 1500 26. Let s number of
3 2 1
0
1
2
3
25. {b : b 3.5} 27a. 98,200 s
201,522; s 103,322
Selected Answers
SA3
28.
6 4 2
29.
1
1
–2 –4
0
0
2
4
6
1
4
1
2
3
4
1
1
t
33. 4|y7| 35. a2|b3| 37. 13|p15|q12
43. 712 45. cannot combine
39. 4 41. 2 43. 8
47. y0 1 49. 262, or 676
1
30. r 4 31. n 2 32. x 0.2
33. y 5 34. n 17.75 20;
n 2.25 35. m 18 36. n 3
37. t 16 38. p 3
39. b 27 40. a 8 41. z 1
42. h 6 43. a 24 44. x 6
1
45. k 3 46. y 8
Chapter 4
4-1
35. 8 37. 44 39. a7 41. x10
51. 122; 121 53. 4 55. 0
100
57a. 10
200
b. 10
61. B 63. 25
1
1
69. 9 71. 1
65. 22.8 67. 11
1
4-4
Exercises
1. 56y7 3. 6a5b5 5. 4xy 7. 3n3
3
9. 2ab3 11. 6c5 13. 125a3
x 8 x4; x10 |x5|;
|x3|; 7
x12 x6 49. C 51. 2
0
9
53. 75
55. 1.97 109
0
57. 3.14 1010 59. 6 103
4-7
Exercises
1. 6 and 7 3. 12 and 13
5. 15 and 16 7. 6.48 9. 12.49
11. 16.58 13. 5.8 15. 13.8
6
1
x 2 |x|; x4 x 2; x6 45. 19. 22z12 21. 2x10 23. 6a2b5
3
1. 121 3. 22b 3 5. 64 7. 8
9. 4096 11. 5 13. 710 15. 56
1
15. 216x6y15 17. 32m15n10
25. 5x2 27. 2q3 29. 2xy5
31. 256y8 33. 256b8 35. 32a15b50
Exercises
9
17. 7 and 8 19. 24 and 25
21. 20 and 21 23. 4.36 25. 11.09
37. 144m4 39. 5a3b5 41. 9
r
43. 3 45. 16m4n5 47. 6x3y2
27. 17.03 29. 9.6 31. 12.2 33. B
49a. The degree of a monomial is
, 53, 7.15, 4, 32
43. 25
35. E 37. F 39. 89.6 in. 41. 40 ft
2
17. 32d 2 19. (4)2c 3 21. 256
the sum of the exponents of the
45. 151 km
1
1
25. 27. 173 29. 1
23. 32,768
36
variables in the monomial. b. 8
47.
31. 36 33. 1 35. 325
53. D 55. 20y 18
57. 21 21k 59. g11 61. 71 or 7
37. 1 39. 426 41. 218 262,144 bacteria 43. (3d)2
45. (7x)4 47. 1728 cm3 51. B
53. 625 55. 83 57. 55
4-5
Exercises
1. 15,000 3. 208,000 5. 5.7 105 7. 6.98 106 9. 4170
59. 0.14 61. 0.375
11. 62,000,000 13. no 15. 80,000
4-2
17. 400,000 19. 5,500,000,000
Exercises
1
1
1. 0.01 3. 0.000001 5. 6
7. 2
4
7
1
1
11. 13. 0.1
9. 13
125
8
1
15. 0.00000001 17. 4
1
3
, or 0.0001 21. 1
19. 10,000
4
4
1
3
4
27. 29. 23. 118
25.
1
32
9
4
3
31. 28 33. 13.02 35. 4
1
37. 114 11 11 11 11
1
14,641
1
1
39. 63 666
216
1
meter 45. 38,340 lb
41. 250,000
1
49. C 51. 8x 21
47. 480
53. 7x 24y 55. 81 57. 125
59. 32
4-3
21. 700,300 23. 6.5 106
25. 5.87 106 27. 0.00067
29. 524,000,000 31. 140,000
33. 78 35. 0.000000053
37. 559,000 39. 7,113,000
41. 0.00029 43a. 1.5 104 g
b. 1.5 1026 g 45. 367,000 47. 4
49. 340 51. 540,000,000
53. 9.8 108 feet per second
55. 8.58 103 57. 5.9 106
59. 7.6 103 61. 4.2 103
63. 6 1010 65. 7 106
67. 5.85 103, 1.5 102, 2.3 102, 1.2 106, 5.5 106 71. C
73. number of students 35
Exercises
1. 515 3. m4 5. 62 7. 120 1
1
4
1 2
15. r 17. 3
19. y3 21. 54
1
23. t13r 25. 3 27. 60 1 29. 50
1 4
1 31. 4 33. (1)9 or 1
3
9. 320 11. 46 or 6 13. 1017
()
SA4
29
Selected Answers
75. 72 77. t3
4-6
Exercises
1. 2 3. 11 5. 16 ft 7. |y3|
9. 7a4 11. 13 13. 19 15. |s3|
17. 6x4 19. 6 21. 15 23. 21
25. 24 29. 104 ft 31. 8x8
49a. about 610 mi/h
b. about 7.8 h 51. B 53. 21
55. 18 57. 8 59. 36
4-8
Exercises
1. irrational, real 3. rational, real
5. rational 7. irrational 9. rational
11. rational 17. rational, real
19. integer, rational, real
21. rational 23. irrational
25. irrational 27. not real
31. whole, integer, rational, real
33. irrational, real 35. rational, real
37. rational, real 39. rational, real
41. integer, rational, real
3
43. 0 is undefined so it is not a
0
real number. 3 is 0 so it is a
rational number. 55. irrational
57. rational 59. irrational
63. C 65. C 67. Dist. Prop.
69. 32,768 71. 625
4-9
Exercises
1. 20 m 3. 24 cm 5. yes 7. yes
9. 15 ft 11. about 21.2 mi 13. no
15. 5 17. 13 19. 9 21. Yes. 62 82 102 23. 22.6 ft 25a. 110 m
b. 155.6 m 27. 208.5 m 31. C
1
33. x 3 35. x 4
notation 3. Pythagorean
2
4
4. real numbers 5. (3)
6. k
9. 625 10. 32
11. 1 12. 256 13. 3 14. 64
1
1
1
27. yes 29. no 31. yes 33. no
5-2
1
16. 17. 15. 125
64
11
1
1
1
19. 1 20. 21. 18. 10,000
36
8
1
22. 1 23. 2 24. 0 25. 47 26. 96
1. 3 mi 3. approximately 40
per serving 7. 38 oz box
35. 4 , or 1 36. y
37. 4
2 cups per batch
13. approximately $4 per lb
15. 16 oz package
minute 23. approximately
41. 7x3z11 42. a7b2 43. 20r6s6
$4.50/lb; 3 lb 27. approximately
50. 216x12y3 51. 10,000m8n20
9
52. 8 10
7
53. 7.3 10
54. 9.6 106 55. 5.64 1010
2
$110 per day 31. width: 20 in.;
height: 15 in. 33. The bunch of 4
has the lower unit price.
59. 0.000091 60. 3.1 105, 1.7
104, 2.3 105, 4.9 104
61. 4 and 4 62. 30 and 30
63. 26 and 26 64. 7m2 65. 2|a3|
1
1. yes 3. no 5. no 7. 53 in.
9. no 11. no 13. yes 15. 2.25 m
81 27
0.5 1
66. x6 67. 9 and 10 68. 3 and 4
19. 3
, 21. 6, 1
17. 4, 1
2
2
9 13
23. $144 25. 64 minutes
69. 11 and 12 70. 6 and 7
27. 12 computers
71. 16 and 17 72. 13 and 14
29. 14 molecules 31a. about 3:2
73. rational 74. irrational
b. about 68 mm Hg
75. rational 76. irrational
33. 154 and 56 35. 16 37. 33
77. rational 78. not a real
39. 6-ounce can
number 79. Possible answer: 3.5
80. 10 81. 10 82. no 83. yes
84. no
5-4
Exercises
Chapter 5
2
1
5-7
Exercises
1
13. 630 ft
7. 7.5 ft 9. 1 11. 2
0
15. 6.25 ft 17. 18 in.
19. 945 in2; 6.6 ft2 23. D
25. 5 and 6 27. 7 and 8
29. 6 and 7 31. $0.17 per apple
Chapter 5 Study Guide:
Review
rate 3. similar; scale factor 4. 4
27
3
2
5. 4
6. 4 7. 1 8. yes 9. no
0
13. unit prices are the same
14. 8-pack 15. x 15 16. h 6
1
17. w 21 18. y 293
19. 72 min 20. 90,000 m/h
1
21. 4500 ft/min 22. 5833 m/min
23. 0.8 mi/min ( 48 mi/h)
24. 12.5 in. 25. 3.125 in. 26. 18 ft
27. 6.2 ft 28. 43.75 miles 29. 3 in.
30. 46 mi 31. 57.5 mi 32. 153 mi
Chapter 6
1. 0.694 km/s 3. 7.5 mi/h
5. 0.075 page/min 7. 1.8 km/h
5-1
1
10. yes 11. no 12. 75 disks
Exercises
8 24
1
19. 6 21. 4
23. 12
9
5
37. t 8.4 39. no 41. no
5-3
9. 85 ft 11. 65 ft 15. C 17. 5
1. ratio; proportion 2. rate; unit
1
35. w 13
56. 1620 57. 0.00162 58. 910,000
1. 128 yd 3. 5.6 ft 5. 4 ft 7. 90 ft
12
4 apples per pound 25. $3.75/lb;
7
47. 6m9n3 48. 16t6 49. 49p10q12
Exercises
1. 300 ft 3. 14 in. 5. 25 mi
17. 14 points per game
39. (10)0 1 40. 5m10n10
44. 9p 45. 6t2 46. 2x3y2
23. 70 25. 3328 quarts
1
9. 3.52 g/cm3 11. approximately
21. approximately 50 beats per
1
38. 10
x
Exercises
1. triangle A and triangle B
5-6
5. approximately 500 Calories
31. 83 32. 92 33. m5 34. 37
12
5-5
15. 18 in. 17. 15 ft 21. 31.5 cm2
Exercises
19. 16 beats per measure
9
41. $249 per monitor
9. similar 11. yes 13. x 6 ft
27. p4 28. 153 29. 64 30. x10
0
39. $0.175 per oz
3. 16.5 cm 5. 2.98 gal 7. similar
49. 1.1 106
students per bus
theorem; legs; hypotenuse
8. 6x
1
45. 0.642 47. 1.2 107
1. irrational number 2. scientific
7. (9)
3
39
Chapter 4 Study Guide:
Review
2
3
35. 1
39. C 41. yes 43. 5.44
8
37. 5 and 6 39. 7 and 8
1
2
17. 5 19. 5 5 21. 3 4 23. no
4 12
2
3 2
4 12
9
; 1; 8 6
25. 4 6; 5 1
0 3
9. 480 cereal boxes 11. 6 fish
13. 5.8 mi 15. 0.88 g
17. 28.75 tons 19. 10.3 m/s
Exercises
10
15
4
2
1. 5 3. 7 5. 1 6. 1
1
1
1
7
7
25
12
8. 4 4 11. yes 13. 1
15.
2
1
21. 2.85 gal 23. C 27. B 29. 32
31. 22 33. 1012 35. 27 37. m13
6-1
Exercises
1
1. 4 3. 87.5% 5. 7. 1
3
1
9. 0.3, 333%, 36%, 8 11. 333%
39
15. 125% 17. 19. 13. 100
2
21. 0.04, 5, 42%, 70% 23. 40%,
30%, 20%, 10% 25. 40%, 30%, 25%,
5% 33. B 35. 37. 39. z 5
Selected Answers
SA5
Exercises
6-2
13. $81,200 15. Deborah should
1. 50 3. 30 5. 13 7. 16 11. 100
choose the salary option that pays
13. 6 15. 32 17. 9 21. B 23. B
$2100 plus 4% of sales.
25. C 27. 150 29. 40 31. 800
17a. $64,208 b. $12,717
33. 30 35. 100 37. 300 cars
39. 475,000 41. 12 hours
43a. no b. yes c. 1 per mi2;
1000 per mi
2
47. B 49. B
51. 9 53. 64 55. 125 57. 8
23
59. 5
61. 0.5 63. 0.525
0
Exercises
6-3
y2
21. x2 23. 2 25. 50% decrease
x
6-7
31. Lena: $11.87, Ana: $12.36,
Joseph: $12.50, George: $12.71
35. B 37. 1000 g/1 kg
39. 1 mi/5280 ft 41. 16 oz/1 lb
43. 100 45. 40
6-4
Exercises
1. 60 3. 166.7 5. 2.4 oz
7. 135 9. 1333.3 11. 400 cards
13a. 250 b. 125 c. 62.5 15a. 30
b. 20 c. 15 17. 657,000 19. 6.7%
21. 98,000 23. C 25. 5 and 6
27. 7 and 8 29. 11 and 12
31. 10 and 11 33. 14 and 15
35. 0.625 37. 0.71 39. 0.75
41. 1.23 43. 3.5
6-5
Exercises
1. 48% increase 3. 100% increase
5. $9773.60 7. 22% increase
9. 8.6% 11. 33% decrease
5. about $2971.89 7. 17 years
9. 5.5% 11. $94.50, $409.50
29. C 31. 25% 33. $7.49; $31.76
35. 50% 37. 311.75
6-6
Exercises
1. $574 3. 11.6% 5. $603.50
7. 3.1% 9. $15.23 11. $38.07
SA6
Selected Answers
2
4
4
21. (4, 4) 23. (5, 4) 25. (5, 6)
27.
13. $446.25, $4696.25
y
6
(3, 6)
4
25. B 27. 1 gal/4 qt 29. 95
(4, 3)
2
(8, 1)
money in the savings account?
x
6 4
2
O
2
2
Chapter 6 Study Guide:
Review
1. percent 2. percent of change
7
1
5. 43.75% 6. 18 7. 112.5% 8. 1
0
9. 0.7 10. 30 11. 62 12. 3.3
31. III 33. (12, 7) 35. a. (68°,
39. B 41. about $22 per hour
43. about 16 students per teacher
1
1
45. 0.14, 7, 15%, 6
13. 18 14. $7.50 15. $16.00
16. 33% 17. 4200 ft 18. 7930 mi
19. 5 lb 7 oz 20. 472,750%
21. 34.4% 22. $21 23. $16,830
24. $3.55 25. $2000 26. $3171.88
7-2
Exercises
5. yes 7. no 13. no 15. no
17. yes 19. a. yes b. input:
{0, 20, 40, 60, 80, 100};
27. $400 28. 7% 29. 0.5 yr
30. $1000 at 3.75% for 3 years;
output: {0, 150, 300, 450, 600, 750}
21. a. $0.20 b. any nonnegative
$7.50 31. about $574.44
number of hours (x 0) c. 550
hours 25. All real numbers 27. D
Chapter 7
7-1
29. triangle; Quadrants I and II
26°) b. (80°, 26°) c. (91°, 32°)
3. commission 4. 0.4375
29. 7 31. 6 33. 100 35. $3
7-3
Exercises
Exercises
1.
1. II 3. III
5, 7.
y
6
y
(2, 5)
4
4
(0, 3)
(1, 2) 2
(2, 1)
x
x
23a. $78 b. $117 c. $39 d. 80%
25. 24,900% 27. decrease; 13%
x
O
2
(5, 5)
1. $2234.38; $9384.38 3. $1430.24
13. 39% decrease 15. 24%
decrease 17. $500 19. 120 21. 50
2
2
21. How long did Alice keep her
23a. 10 b. 20 c. 40 29. 1.0%
4
Exercises
7. 1.6 mi 9. 400% 11. 1%
level 17. 24.4 19. 399 21. 500
(1, 1)
c. 17.8% d. 19.8% 19. $695
15. $9.26, $626.26 17. 5 years
1
y
4
1. 49.5% 3. 75% 5. 23%
13. 296% 15. 54.0 ft above sea
17, 19.
2
O
2
4
2
(3, ⫺4)
4
9. (6, 3) 11. (4, 0) 13. I 15. IV
O
2
2
3. a. y 750x
2
4
b.
Amount of water (gal)
5,000
4,000
21. Simon calculated the
b. 3 s 21. a. $4860, $4940, $5000,
y-coordinates incorrectly.
$5040, $5060 b. 7 23. B
23. 32.3 25. 2.3
25. It has no x-intercepts. 27. 7
29. 7.5 ft 31. 12.75 ft 33. 12,444.4
3,000
Exercises
7-4
2,000
1.
1,000
7-5
y
6
Exercises
1.
y
4
0
2
x
Time (hr)
5.
4
2
1 2 3 4 5 6 7
– 4 –2 O
–2
y
4
2
x
4
–4 –2 O
–2
–4
2
O
2
4
3.
6
4
3.
4
x
4
O
2
–4 –2 O
–4
4
(2, 7)
6
–8
4
5.
x
O
2
4
2
4
–4
9. $550; $975; $1400; $1825; $2250
y
–12
9
8
7
6
5
4
3
2
1
(0, 3)
4
(2, 1)
x
4
2
2
y
5. linear
7.
10
6
4
2
–2 –4
2
x
4
–10 –8 –6 –4 –2 O
–2
Distance (mi)
4
6
8
10
y
–6
–8
–10
2
9.
x
30
4
O
2
y
4
4
2
2
10
1
2
x
4
x
0
–4 –2 O
–2
2
Time (h)
Distance (ft)
2
–4
7.
50
20
y
8
4
13.
4
y
8
2
7.
70
2
y
4
11.
4
–4
x
2
2
9. 15, 6, 15 11. 0, 0, 18
y
13. 37, 7, 31 15. Graph C
2
4
–4
17. Graph B
16
19. a.
8
4
x
0
1
2
Time (s)
15. a. 5 ppm b. about 382 ppm
19. It is not linear.
11.
h
12
40
35
30
25
20
15
10
5
0
16
y
12
8
4
x
t
0.5
1
1.5
2
2.5
3
–4
–2 O
2
4
–4
Selected Answers
SA7
13. quadratic 15. quadratic
17.
Exercises
7-6
y
11.
y
1
1. constant 3. 3 5. 6 7. variable
4
4
9. 0 11. 4 13. constant
2
15. variable 17. 19
2
x
–4 –2 O
–2
2
x
19. a. $0.11/yr; $0.32/yr; $0.19/yr
4
ⴚ4
ⴚ2
b. 1998 to 2001 23. D 25. 12. 5
2
4
2
4
ⴚ2
27. 6.9 29. 20 31. 20
ⴚ4
–4
Exercises
7-7
1
1. 1 3. 4 5. 0 7. The slope of the
1
3
6
line is 5. 9. 2 11. 4 13. 7
1
15. 5 17. The slope of the line
4
is 4. 19. y 5x 350 21. The
2z
roof is flat. 25. w 27. 3
y
19.
4
2
x
–4 –2 O
–2
2
4
9
x
2
4
right.
(2, 5)
linear relationship in which the
y-intercept is always 0. 13. y 4x
y
–4
2
4
(2, 1)
(0, 3)
4
y
14.
4
1
15. y 2x 17. y 8x 19. y 13x
2
23. Each watermelon would need
4
y = x3+3
y = x3+1 2
O
6
9. no 11. A direct variation is a
1
–4 –2 O
–2
2
2
1
the curve rises or falls from left to
x
to be exactly the same weight.
O
25. 28 27. $348.75; $1123.75
2
4
2
4
x
2
4
y = x3– 2
y = x3– 4
Chapter 7 Study Guide:
Review
1. direct variation 2. function
3. linear function 4. J(2, 1), IV
b. 1; 3; 2, 4 c. 15 29. B
5. K(2, 3), II 6. L(1, 0), x-axis
31. 38% increase
7. M(4, 2), III
33. 12% increase
8. Possible answer:
x 1
0
1
y
x
2
4
–4
–6
–8
SA8
x
4
5. y 6x; about 968 kg 7. yes
23. The sign determines whether
y
2
1. yes 3. no direct variation
–4
–4 –2 O
–2
13.
Exercises
7-9
–2
25. a.
ⴚ2
ⴚ4
15. 9 17. 15 19. 5 21. 31
4
1
23. 11
inches
6
2
2
x
ⴚ4
ⴚ2
9. Graph A 10. Graph B 13. B
4
35.
2
1. Graph A 3. Graph B
y
–4
4
Exercises
7-8
–2 O
y
29. 4 miles 31. 20
–4
21.
12.
Selected Answers
y
11
4
3
9. Possible answer:
x 1
0
1
y
2
10. yes
0
15.
y
x
4
2
O
2
4
2
3
10 17
2
6
3
2 8 18
(2, 8)
8
(2, 4)
(0, 6)
16.
22.
31.
y
4
4
2
2
y
4
2
x
–4
–2
2
–4 –2 O
–2
4
–2
–4
2
–4
33.
2
4
y
4
3
27. 4 8. 4 29. 1
2
30.
–2 –1
2
x
Distance (mi)
–4
4
⫺4
25. constant 26. constant
9
8
7
6
5
4
3
2
1
2
⫺2
23. quadratic 24. linear
17.
x
⫺4 ⫺2 O
4
4
⫺4 ⫺2 O
⫺2
18
12
⫺4
6
Time
31. y 5x; $22.50
18.
4
Chapter 8
–4
–2
2
4
8-1
–2
Exercises
3. XY
, YZ
, ZX
5. AEB or
1. XY
–4
DEB 7. AEC 9. AEB and
BED, AEC and CED
4
,
11. plane N or plane JKL 13. KJ
, LK
, MK
15. VWZ,
, KM
KL
2
YWX 17. VWZ, YWX
19.
y
19. false 21. false 23. false
,
, VX
25. false 27. 30°, 60° 29. YV
x
ⴚ4
ⴚ2
O
2
4
ⴚ2
33. A 35. m5 37. 711
, YZ
XY
ⴚ4
39. 2.8 ft
20.
8-2
y
13. none of these 15. skew
, and EH
21. plane
, FG
17. BC
4
2
x
–4
–2
2
4
29. 36m6 31. 27x12y3 33. AEC
–4
35. BEC, CED
37. AEC, CED
y
4
8-3
2
x
–4 –2 O
–2
–4
ABF, plane FBC, plane DAE, and
plane DCG 23. yes 27. B
–2
21.
Exercises
2
4
Exercises
1. 105° 3. 62° 5. 118° 7. 126°
9. 70° 11. 110° 13. 4, 5, and
8 17. 129° 19. 180° x°
8-4
Exercises
1. q 77 3. s 120 5. c 56
7. 60°, 30°, 90° 9. r 86
11. t 115 13. m 72 15. 27°,
135°, 18° 17. y 15 19. w 60
21. 64° 23. C 25. x 30, y 100,
z 50 27. 105° 29. 8 and 9
CD
31. 17 and 18 33. AB
8-5
Exercises
CD
3. Parallelogram,
1. AN
rhombus, rectangle, square
AB
5. C(2, 1) 7. CD
9. Parallelogram, rhombus,
rectangle, square 11. C(4, 1)
13. 3 15. 0 17. 2 21. true
23. false 25. true 27. The slope
is also undefined because
of CD
parallel lines have the same slope.
1
29. D 31. B 37. 3 39. 140
41. 20
8-6
Exercises
1. triangle ABC triangle FED
3. q 5 5. s 7 7. quadrilateral
PQRS quadrilateral ZYXW
9. n 7 11. x 19, y 27, z 18.1 13. r 24, s 120, t 48
15. 62° 19. C 21. 3 23. P(4, 1)
29. The measures of the remaining
angles are 90°.
Selected Answers
SA9
Exercises
8-7
17.
y
1. rotation
4
y
2
3.
4
D
Aʹ
A
2
Cʹ
Bʹ
O
ⴚ4
ⴚ2
ⴚ4
2
O(3, 1)
7.
y
N
4
M′
x
O
ⴚ2
C′
4
x
D′
A′
4. LKM 5. LKM and JKM
and SV
7. plane SVR ⊥
6. PQ
plane RVT 8. plane PQR plane
STV 9. 66° 10. 114° 11. 66°
23. (5, 2) 29. A(0, 4), B(0, 1),
12. 66° 13. 114° 14. m 26
C(5, 1) 31. constant 33. 7 in.
15. 13 cm 16. trapezoid
y
17.
Exercises
4
1.
O
ⴚ2
x
L
N
N′
4
ⴚ2
M
ⴚ4
3.
11.
K
2
ⴚ4
9. translation
y
J′
lines 2. rectangle; square;
rhombus; square 3. KM
4
2
ⴚ2
1. parallel lines; perpendicular
19. (3, 2) 21. (m, n)
8-8
L
M
B′
O
ⴚ2
x
5. L(2, 3) M(4, 6), N(7, 3),
ⴚ4
Chapter 8 Study Guide:
Review
C
B
18.
H′
y
4
J
F′
ⴚ4
ⴚ2
W
H
G′
Z
x
x
F
O
5.
O
G
ⴚ2
X
Y
13. A(1, 3), B(5, 1), C(7, 5), D(3, 7)
8
19. x 19 20. t 2.4 21. q 7
7.
y
D′
y
22.
C′
A′
⫺4
O
4
B′
B
2
x
8
A
ⴚ4
⫺4
D
15.
ⴚ4
y
B′
B
4
A′
C′
C
11. yes 15. hexagon 17. D
9
19. 3.4 10
D′
2
x
D
A ⴚ2
O
2
B′
21. 2.8 10
y
A′
ⴚ4
2
ⴚ4
x
⫺4 ⫺2
O
⫺2
⫺4
B′
4
B
2
4
4
Selected Answers
x
4
C′
y
23.
4
23.
ⴚ2
SA10
ⴚ2
C
A
O A′
ⴚ2
9.
C
⫺8
B
4
4
2
4
C′
A
ⴚ2 O
ⴚ2
ⴚ4
C
x
2
4
y
24.
4
2
C
x
A
ⴚ4
C′
dimensions are multiplied by 4,
Chapter 9 Study Guide:
Review
the area will be 42 times as great
1. perimeter, area 2. chord
and the perimeter will be 4 times
3. about 79 in2, 12 in. 4. 198 m2,
27. 9.1 ft 29. When the
B
A′ O
2
as great. 31. 153.8 cm2
4
1
11 yd2 7. 9 cm2, 14.2 cm
37. 874.6 ft2; 160.4 ft 39. C
41. 3.7 mi 43. 14 units
25. Possible answer:
8. 16 in2, 26.3 in. 9. 36 ft
, FG
11. GI
12. HI
, GI
,
, FI
10. HF
2
13. A 144π 452.2 in2;
, JI
GJ
Exercises
9-3
5
80 m 5. 112 ft; 58 ft2 6. 20 yd;
33. 466.6 ft 35. 49.8 ft
B′
2
, OR
, OS
, OT
3. RT
, RS
,
1. OQ
ST , TQ 5. CA , CB , CD , CE , CF
, DE
, FE
, AE
9. 10 cm
, BF
7. GB
C 24π 75.4 in 14. A 17.6π 55.4 cm2; C 8.4π 26.4 cm
15. A 9π 28.3 m2; C 6π 18.8 m 16. A 0.36π 1.1 ft2;
11. 100.8° 13. 252° 15. 133.2°
C 1.2π 3.8 ft 17. 57 m2
19. 120° 21. 90° 23. 18 25. 35
18. 40.57 ft2 19. 73.5 cm2
20. 14 units2 21. 15 units2
Exercises
9- 4
2
22. 12 units2 23. 10 units2
1. 6π cm; 18.8 cm 3. 16.8π ft ;
26. Possible answer:
52.8 ft2 5. A 4π units2;
Chapter 10
12.6 units2; C 4π units;
12.6 units 7. 18π in.; 56.5 in.
10-1 Exercises
9. 256π cm2; 803.8 cm2
2
2
11. A 16π units ; 50.2 units ;
1. pentagon; triangles; pentagonal
C 8π units; 25.1 units
pyramid 3. triangles; rectangles;
13. C 10.7 m; A 9.1 m2
triangular prism 5. polyhedron;
2
Chapter 9
9-1
15. C 56.5 in.; A 254.3 in.
hexagonal pyramid 7. triangle;
17. 6.4 cm 19. 6 cm 21. 11.7 m
triangles; triangular pyramid
2
23. 38.5 m
25. C 30π ft 94.2 ft;
A 225π ft2 706.5 ft2
Exercises
27.a. 9.6 in.
1. 28 cm 3. 12.2x ft 5. 18 units2
7. 14 units2 9. 42 cm 11. 26x m
2
b. 28.3 in.
pyramid 11. not a polyhedron;
2
c. three
regular pancakes 31. C 33. m4
7
35. 8
37. 27 units
2
17. 33 ft; 54 ft
19. 18 ft; 10.5 ft
cylinder 13. square prism
15. triangular pyramid
19. rectangular pyramid
13. 24 units2 15. 12 units2
2
9. hexagon; triangles; hexagonal
31
2
2
Exercises
9-5
21. $3375 23. 42,000 mi
1. 48 m
27. B 29. x 4 31. a 37
7. 88.1 ft2 9. 54 cm2 11. 23.4 in2
2
3. 109.5 cm2 5. 59.6 in2
21. cylinder 23. A 25. 4
0
25
27. 13
29. 100 oz for $6.99
6
10-2 Exercises
33. rational 35. rational 37. not
13. 63,800 mi
a real number
21. y 5x 23. 10π in.; 31.4 in.
5. 1500 ft3 7. 100 in3 9. 351 m3
25. 8.2π cm; 25.7 cm
11. 60 cm3 13. a. 800 in3
9-2
Exercises
1. 9 units 3. 3 units 5. 21 units
7. 15 units2 9. 5 units
11. 21 units 13. 20 units
19. 33 cm
9-6
2
17. 80 in
19. C
Exercises
13. no 17. Approximate the area
2
15. 12 units2 17. 23.2 m2
2
2
2
2
21. 37 m
23. 60 units2 25. 25x units2
1. 463.1 cm3 3. 1256 m3
15. a. 4.62 107 in3 b. about
18.8 ft 19. 180 in3 21. D
23. (5, 9) 25. 4 in.; 12 in2
of the glacier with a trapezoid
(b1 2, b2 3, h 1) that has
5
area 2 and a triangle (b 3,
3
h 1) that has area 2. 19. D
21. rational 23. rational
10-3 Exercises
1. 20 cm3 3. 99.7 ft3 5. 9.1 cm3
7. 6,255,000 ft3 9. 35.0 m3
11. 66.2 ft3 13. 5494.5 units3
15. 6 in 17. 11 ft 19. 736 cm3
Selected Answers
SA11
21. 600 in3 23. 301,056 ft3 25. 8
27. B 29. x 15 31. x 9
2
33. 56.25π ft ; 176 ft
27. D 29. x 8 31. w 2
2
33. 314 mm
2
5. The medians are equal, but data
set B has a much greater range.
35. 50.2 in
7. 45.5; 62.5
2
9.
10-4 Exercises
Chapter 10 Study Guide:
Review
1. 28 cm2 3. 52 cm2 5. 61.8 m2
1. cylinder 2. surface area
7. 401.9 in2 9. 791.3 cm2
3. cone 4. cylinder
50 54
68
80 85
11. Data set Y has a greater median.
11. 94 cm2 13. 38 cm2
5. rectangular pyramid 6. 364 cm3
3
15. 1160 mm2 17. 791.3 cm2
7. 24 mm
19. 747.3 yd2 21. 1920π 9. 111.9 ft3 10. 60 in3 11. 210 ft3
6028.8 mm2 23. 4 m 25. $34.56
12. 471 cm
27. C 31. 232 33. 4.25
8. 415.4 mm
3
Data set Y has a greater range.
13. 68; 85 15. 35; 57.5
3
17.
3
13. 314 m
2
14. 680 mm
67
15. 944 in2
35. 1.77 37. 110 units2
16. 150.7 in2 17. 180.6 cm2
10-5 Exercises
20. 288π 904.32 in3
1. 105 m2 3. 144 m2 5. 702.5 ft2
21. 7776π 24,416.6 m3 22. 3:1
7. 125.6 mm2 9. no 11. 0.18 km2
23. 9:1 24. 27:1
75
85
93
19.
18. 132 cm2 19. 804.9 in2
0
2
21.
3
34
9
16
c. Khufu; 91,636,272 ft3 19. B
21. 56 23. 17 25. 120 ft3
5 7 10
1. 15
31. 10 and 10 33. 4.8; 5; 5
7. 256π cm2; 803.8 cm2
35. 64.9; 63; 48 and 75
Republicans
3
66 4
8764 5
8411 6
20.7 m3 5. 4π in2; 12.6 in2
2678
1234
34
11- 4 Exercises
Key: 冨4冨1 means 41
6冨4冨 means 46
9. The volume of the sphere and
5. 3 7. 4; 31 9. B 11. 61 13. 27
the cube are about equal
23. 1
19. line plot 21. 4
0
0
2
25. 72 units
1
1.
9
775.3 cm3 13. 1.3π in3; 4.2 in3
15. 207.4π m2; 651.2 m2
2
17. 400π cm ; 1256 cm
2
11-2 Exercises
14
12
10
8
6
4
2
0
0 10,000 30,000 50,000
Area (mi2)
1. 20; 20; 5 and 20; 30
3. Mean: 352.5; median: 350
3. positive correlation
21. V 52.41π 164.55 yd3;
5. 83.3; 88; 88; 28 7. 4.3; 4.4; 4.4
5.
S 46.24π 145.19 yd2
and 6.2; 4.2 9. mean 6.2;
25. 1767.15 cm3 27. 6.33 in3
median 6.5 11. 151 13. 9; 8; 12
29. 113.04 31. 8 33. 15
21. D
35. 364 m2
23.
Stems
4
5
6
10-7 Exercises
1. 4:1 3. 64:1 5. 8.2 cm3 7. 2:1
Leaves
358
17
022
11-3 Exercises
17. 7 cm; 343 cubes
1. 52; 70
19. 1,000,000 cm3 21a. 2508.8 in3
3.
11. positive correlation
13. negative correlation 17. A
19. 78.5 cm2 21. 9 to 1
11-5 Exercises
b. about 10.9 gal 23. No; the
Selected Answers
5 10 15 20 25 30 35
Price ($1000)
1 cube 15. 9 cm; 729 cubes
SA12
35
30
25
20
15
10
5
0
7. positive correlation 9. 73°F
9. 8:1 11. 33,750 in3 13. 1 cm;
the volume increases by 8 times.
Miles peer gallon
19. 366.17π in3; 1149.76 in3
surface area increases by 4 times;
26
27. B 29. 4 and 4
1. 36π cm3; 113.0 cm3 3. 6.6π m3;
( 268 in3). 11. 246.9π cm3;
17
11-1 Exercises
3. Democrats
10-6 Exercises
Tropical storms
Chapter 11
Population (millions)
b. Menkaure; 191,684 ft2
4.5 5
Hurricanes
13. 279,221,850π mi2
15. a. 481; 277
99
19
26
33
44.5
59
1. 0.6, or 60%; 0.4, or 40%
3. 0.709, or 70.9% 5. 0.49, or 49%
7. 0.885 9. 0.784 11. sample
correlation 12. 0.85, or 85%;
space: blue, green, red, yellow;
0.15, or 15% 13. 0.15, or 15%
outcome shown: yellow
16. 15. 14. 1
5
1296
51
4
1
4
21. 2
23. 0.1 25. 0.0000001
5
27. 5 29. 0
6
13
12- 4 Exercises
13. sample space: 1, 2, 3, 4, 5, 6;
outcome shown: 4 15. 0.545
1
11
or 11
31. 2
27. C 29. 1
0
5
0
33. 84 ft 35. 42 ft
Chapter 12
1. 4x2y 3. 3x 2 8x 5
5. 8x 3 5x 6
7. 2b 3 5b 2 b 4
12-1 Exercises
9. 8m2n 3mn2 2mn
11-6 Exercises
1. yes 3. no 5. binomial 7. not a
11. 2x2y 5xy 10x 8
1. 0.34, or 34% 3. 0.136;
polynomial 9. 8 11. 0 13. yes
13. 4x3 9x2 12x 21 in3;
0.113 5. 0.319, or 31.9%
15. no 17. yes 19. monomial
30 in3 15. 3v 5v2
7. 0.398; 0.239 9. 0.25
21. trinomial 23. not a
17. 4xy2 2xy 19. 9b2 2b 9
11. 0.025 13. 0.35 15. 0.3
polynomial 25. 2 27. 4 29. 1
3
1
19. 51 21. 4.4 23. 8 25. 8
31. 8 in3 33. monomial; 3
21. 5a 8 23. x2 3x 4
25. 6p3 5p2 2p2t2 10pt2
35. binomial; 2 37. trinomial; 5
27. 2b 2ab
39. not a polynomial
29. 6y2 12x2y 5x2 31. 2x2 41. trinomial; 3 43. not a
6x 1 in2 37. 10x 29; 109
Exercises
11-7
1
1
1
1. 2 3. 1
5. 4 7. red 9. 0
2
1
2
1
15. 1 17. 30 19. 8
11. 3 13. 1
8
1
1
1
5
21. 2 23. 8 25. 2 29. 6
polynomial 51. 9 53. 3.5 105
39. 63m5 41. 8r10s10
55. 7 57. 9
43. zy3 5zy
31. yes 33. no
12-2 Exercises
12-5 Exercises
11-8 Exercises
1. 3b2 and 4b2, 5b and b
1. 15s 3t 5 3. 35h6j 10 5. 35p 4r 5
1
10
1. dependent 3. 3
5. 2
253
5
1
7. independent 9. 2 11. 2
4
4
1
13. 2
15. 3
0.03125 21. D
7
2
23. 11; 21 25. 0
Chapter 11 Study Guide:
Review
1. median; mode 2. probablilty
3. line of best fit; scatter plot;
correlation
4.
x
x
x
x
x
x
x
x
x
2
3. 7x 4x 5 5. 12x 32
7. 17a2 21a 9. t and 5t, 4t 2
and 5t
2
2
11. 9p 7p
21. 6c4d3 12c 2d 3
19. 2x 2 13x 15
23. 12s 4t 3 15s3t3 6s4t4
21. 9m2 20m 23. 17mn
25. 40 1000d 2 27. 82xy 82y in2
29. C 31. 51.2%
35. 20m4p8 12m3p7 24m4p5
43. 15c 3d 4 20c2d 4
x
x
x
x
6. 43; 46; none; 25
7.
ⴚ5
O
70
75
12-6 Exercises
ⴚ5
1. 5x 3 3x 6 3. 11r 2s 9rs
5. 15ab 2 3ab a2b 8
8.
7. 128 32w in. 9. 7g 2 g 1
50 55 60 65 70 75 80 85 90
11. 3h6 12h 4 h
13. 13t 2 4t 12
9.
15. w 2 4w 2
80 82 84 86 88 90 92 94
10. no correlation 11. positive
45. 4m 3n 2 47. 59 in2
5
12-3 Exercises
65
29. 3m5 15m3 31. x5 x 7y 5
37. V πr 2x3 πr 2y 3; 63π
5. 302; 311.5; 233 and 324; 166
60
25. 24b6 27. 6a3b6
33. 3f 2g2 f 3g2 f 2g 5
y
10 11 12 13 14 15
55
1
19. 15z3 12z2
17. 12s 2 2s 3
5
1
30x 11. A 2b1h 2b2h
13. 2g3h8 15. 2s5t4 17. 7.5h5j10
13. 9x 2 32x 15. 6y 3 4
33.
7. 6hm 8h2 9. 3x3 15x2 17. 7w 2y 2wy 2 4wy
19. 6.19r 3 4r 2 5r 2
1. xy 4x 5y 20
3. 12m2 7m 45
5. m2 9m 14
7. 4x2 100x ft2 9. b2 9
11. 9x2 30x 25
13. v 2 4v 5
15. 3x2 13x 30
17. 12b2 11bc 5c2
19. 12r 2 11rs 5s2
21. 4x 2 60x 125 yd2
23. b2 6b 9 25. 4x2 9
27. a2 14a 49 29. b 2 7b 60
Selected Answers
SA13
31. t2 13t 36 33. 3b 2 5b 28
6. not a polynomial 7. monomial
31. 12a4b3 30a3b3 36a3b 35. 4m2 11mn 3n2 37. r 2 25
8. not a polynomial 9. binomial
24a2b2 32. 2m3 16m3 2m
10. 8 11. 4 12. 3 13. 5 14. 6
33. 10g3h3 15gh5 20gh 30h2
2
2
39. 15r 22rs 8s
41. PV bP aV ab c 45. B
47. 25.1 49. 18.7
51. 4m2 12m 24
2
2
53. 11x y 4xy 16xy
2
2
15. 7t 3t 1 16. 11gh 9g h
2
17. 20mn 12m 18. 8a 10b
2
2
19. 36st 23t 20. 6x 2x 5
21. 5x4 x2 x 7 22. 2h2 2
2
8h 7 23. 2xy 2x y 2xy
26. w 12w 14 27. 4x 1. polynomial; degree 2. FOIL;
16x 14 28. 4ab2 11ab 4a2b
24. 13n2 12 25. 6x2 8
3 2
2
2 2
2
binomials 3. binomial; trinomial
29. p q 4p q 2pq
4. trinomial 5. not a polynomial
30. 12s2t4 4s2t3 32st3
SA14
Selected Answers
35. 18x7y14 15x6y12 12x3y7 24x3y6 36. p2 8p 12 37. b2 10b 24 38. 3r2 11r 4
39. 3a2 11ab 20b2
Chapter 12 Study Guide:
Review
2
3
34. 2j5k3 2j4k4 j6k5
40. m2 14m 49 41. 9t2 36
42. 6b2 2bt 28t2
43. 3x2 2x 40
44. y2 22y 121
Glossary/Glosario
KEYWORD: MT8CA Glossary
ENGLISH
absolute value The distance of a
number from zero on a number
line; shown by ⏐⏐. (p. 15)
SPANISH
valor absoluto Distancia a la que
está un número de 0 en una recta
numérica. El símbolo del valor
absoluto es ⏐⏐.
acute angle An angle that
ángulo agudo Ángulo que mide
measures less than 90°. (p. 379)
menos de 90°.
acute triangle A triangle with all
triángulo acutángulo Triángulo
angles measuring less than 90°.
(p. 392)
en el que todos los ángulos miden
menos de 90°.
Addition Property of Equality
Propiedad de igualdad de la
suma Propiedad que establece que
The property that states that if
you add the same number to both
sides of an equation, the new
equation will have the same
solution. (p. 33)
Addition Property of Opposites
The property that states that the
sum of a number and its opposite
equals zero. (p. 18)
puedes sumar el mismo número a
ambos lados de una ecuación y la
nueva ecuación tendrá la misma
solución.
Propiedad de la suma de los
opuestos Propiedad que establece
EXAMPLES
⏐5⏐ 5
⏐5⏐ 5
14 6 8
6 6
14
14
12 (12) 0
que la suma de un número y su
opuesto es cero.
additive inverse The opposite of
inverso aditivo El opuesto de
a number. (p. 8)
un número.
adjacent angles Angles in
the same plane that are side by
side and have a common vertex
and a common side. (p. 388)
ángulos adyacentes Ángulos en
el mismo plano que comparten un
vértice y un lado.
algebraic expression An
expression that contains at least
one variable. (p. 6)
expresión algebraica Expresión
que contiene al menos una variable.
x8
4(m b)
algebraic inequality An
desigualdad algebraica
inequality that contains at least
one variable. (p. 136)
Desigualdad que contiene al menos
una variable.
x 3 10
5a b 3
alternate exterior angles
ángulos alternos externos Par de
A pair of angles on the
outer sides of two lines cut
by a transversal that are on
opposite sides of the transversal.
(p. 389)
ángulos en los lados externos de dos
líneas intersecadas por una
transversal, que están en lados
opuestos de la transversal.
The additive inverse of 5 is 5.
b
a
a
c
b
d
a and d are alternate
exterior angles.
Glossary/Glosario
G1
ENGLISH
SPANISH
alternate interior angles
ángulos alternos internos Par de
A pair of angles on the
inner sides of two lines
cut by a transversal that
are on opposite sides of
the transversal. (p. 389)
ángulos en los lados internos de dos
líneas intersecadas por una
transversal, que están en lados
opuestos de la transversal.
altitude (of a triangle) A
perpendicular segment from a
vertex to the line containing the
opposite side. (p. 393)
altura (de un triángulo) Segmento
perpendicular que se extiende desde
un vértice hasta la recta que forma el
lado opuesto.
angle A figure formed by two rays
ángulo Figura formada por dos
with a common endpoint called
the vertex. (p. 379)
rayos con un extremo común
llamado vértice.
angle bisector A line, segment,
or ray that divides an angle into
two congruent angles. (p. 382)
bisectriz de un ángulo Línea,
EXAMPLES
r
t
s
v
r and v are alternate
interior angles.
…
N
segmento o rayo que divide un
ángulo en dos ángulos congruentes.
P
O
M
arc An unbroken part of a circle.
arco Parte continua de un círculo.
,
-
(p. 446)
area The number of non-
área El número de unidades
overlapping unit squares needed
to cover a given surface. (p. 435)
cuadradas que se necesitan para
cubrir una superficie dada.
x
Ó
The area is 10 square units.
Associative Property of
Addition The property that states
that for all real numbers a, b, and
c, the sum is always the same,
regardless of their grouping.
(p. 116)
Associative Property of
Multiplication The property that
states that for all real numbers a,
b, and c, their product is always
Propiedad asociativa de la suma
Propiedad que establece que para
todos los números reales a, b y c, la
suma siempre es la misma sin
importar cómo se agrupen.
Propiedad asociativa de la
multiplicación Propiedad que
the same, regardless of their
grouping. (p. 116)
establece que para todos los
números reales a, b y c, el producto
siempre es el mismo, sin importar
cómo se agrupen.
average The sum of a set of data
promedio La suma de los
divided by the number of items in
the data set; also called mean.
(p. 537)
elementos de un conjunto de datos
dividida entre el número de
elementos del conjunto. También se
llama media.
G2
Glossary/Glosario
a b c (a b) c a (b c)
a
b c (a b) c a (b c)
Data set: 4, 6, 7, 8, 10
Average:
4 6 7 8 10
35
7
5
5
ENGLISH
back-to-back stem-and-leaf
plot A stem-and-leaf plot that
compares two sets of data by
displaying one set of data to the
left of the stem and the other to
the right. (p. 533)
SPANISH
diagrama doble de tallo y hojas
Diagrama de tallo y hojas que
compara dos conjuntos de datos
presentando uno de ellos a la
izquierda del tallo y el otro a la
derecha.
EXAMPLES
Data set A: 9, 12, 14, 16, 23, 27
Data set B: 6, 8, 10, 13, 15, 16, 21
Set A
Set B
9 0 68
642 1 0356
73 2 1
Key: 2 1 means 21
3 2 means 23
gráfica de barras Gráfica en la que
se usan barras verticales u
horizontales para presentar datos.
Sunlight’s Travel Time
to Planets
Time (s)
bar graph A graph that uses
vertical or horizontal bars to
display data. (p. SB17)
4800
5000
4000
2600
3000
2000
760
M
ar
s
Ju
pi
te
r
Sa
tu
rn
Ea
rt
h
1000 500
Planet
base (in numeration) When a
base Cuando un número es elevado
number is raised to a power, the
number that is used as a factor is
the base. (p. 166)
a una potencia, el número que se
usa como factor es la base.
base (of a polygon) A side of
a polygon, or the length of that
side. (p. 435)
base (de un polígono) Lado de un
polígono; cara de una figura
tridimensional según la cual se mide
o se clasifica la figura.
base (of a three-dimensional
figure) A face of a three-
base (de una figura
tridimensional) Cara de una figura
dimensional figure by which
the figure is measured or
classified. (p. 480)
tridimensional a partir de la cual se
mide o se clasifica la figura.
base (of a trapezoid) One of the
two parallel sides of a trapezoid.
(p. 440)
35 3 3
3 3 3; 3 is the base.
…
L
Bases of
a cylinder
Bases of
a prism
Base of
a cone
Base of
a pyramid
base (de un trapecio) Uno de los
dos lados paralelos del trapecio.
ÊLÊ£
ÊLÊÓ
binomial A polynomial with two
terms. (p. 590)
binomio Polinomio con dos
términos.
xy
2a2 3
4m3n2 6mn4
Glossary/Glosario
G3
ENGLISH
SPANISH
bisect To divide into two
trazar una bisectriz Dividir en dos
congruent parts. (p. 382)
partes congruentes.
EXAMPLES
JK bisects LJM
box-and-whisker plot A graph
gráfica de mediana y rango
that displays the highest and
lowest quarters of data as
whiskers, the middle two quarters
of the data as a box, and the
median. (p. 543)
Gráfica que muestra los valores
máximo y mínimo, los cuartiles
superior e inferior, así como la
mediana de los datos.
capacity The amount a container
can hold when filled. (p. 512)
capacidad Cantidad que cabe en
un recipiente cuando se llena.
Celsius A metric scale for
Celsius Escala métrica para medir
measuring temperature in which
0°C is the freezing point of water
and 100°C is the boiling point
of water; also called centigrade.
(p. SB15)
la temperatura, en la que 0 °C es el
punto de congelación del agua y
100 °C es el punto de ebullición.
También se llama centígrado.
center (of a circle) The point
inside a circle that is the same
distance from all the points on
the circle. (p. 446)
centro (de un círculo) Punto
interior de un círculo que se
encuentra a la misma distancia de
todos los puntos de la
circunferencia.
center of rotation The point
about which a figure is rotated.
(p. 410)
centro de una rotación Punto
90˚
Lower quartile
Upper quartile
Minimum
Median
Maximum
0
alrededor del cual se hace girar una
figura.
2
4
6
8
10
12
14
A large milk container has
a capacity of 1 gallon.
90˚
Center
90˚
90˚
central angle An angle formed
ángulo central de un círculo
by two radii with its vertex at the
center of a circle. (p. 447)
Ángulo formado por dos radios cuyo
vértice se encuentra en el centro de
un círculo.
certain (probability) Sure to
happen; an event that is certain
has a probability of 1. (p. 556)
seguro (probabilidad) Que con
seguridad sucederá. Representa una
probabilidad de 1.
chord A segment with its
cuerda Segmento de recta cuyos
endpoints on a circle. (p. 446)
extremos forman parte de un círculo.
G4
Glossary/Glosario
When rolling a number cube, it is
certain that you will roll a number
less than 7.
…œÀ`
ENGLISH
circle The set of all points in a
SPANISH
plane that are the same distance
from a given point called the
center. (p. 446)
círculo Conjunto de todos los
puntos en un plano que se
encuentran a la misma distancia de
un punto dado llamado centro.
circle graph A graph that uses
sectors of a circle to compare
parts to the whole and parts to
other parts. (p. SB21)
gráfica circular Gráfica que usa
secciones de un círculo para
comparar partes con el todo y con
otras partes.
EXAMPLES
Residents of Mesa, AZ
65+
13%
45–64
27%
Under
18
19%
11%
30%
18–24
25–44
circumference The distance
circunferencia Distancia alrededor
around a circle. (p. 450)
de un círculo.
Circumference
clockwise A circular movement
to the right in the direction
shown. (p. 412)
coefficient The number that is
multiplied by a variable in an
algebraic expression. (p. 120)
commission A fee paid to a
en el sentido de las manecillas
del reloj Movimiento circular en la
dirección que se indica.
coeficiente Número que se
multiplica por una variable en una
expresión algebraica.
5 is the coefficient in 5b.
person for making a sale. (p. 298)
comisión Pago que recibe una
persona por realizar una venta.
commission rate The fee paid to
a person who makes a sale
expressed as a percent of the
selling price. (p. 298)
tasa de comisión Pago que recibe
una persona por hacer una venta,
expresado como un porcentaje del
precio de venta.
A commission rate of 5% and a
sale of $10,000 results in a
commission of $500.
common denominator A
común denominador
denominator that is the same in
two or more fractions. (p. 70)
Denominador que es común a dos o
más fracciones.
The common denominator of 8
2
and 8 is 8.
common factor A number that is
factor común Número que es
a factor of two or more numbers.
(p. SB6)
factor de dos o más números.
common multiple A number
that is a multiple of each of two or
more numbers. (p. SB6)
común múltiplo Número que es
Commutative Property of
Addition The property that states
Propiedad conmutativa de la
suma Propiedad que establece que
that two or more numbers can be
added in any order without
changing the sum. (p. 116)
sumar dos o más números en
cualquier orden no altera la suma.
múltiplo de dos o más números.
5
8 is a common factor of 16 and 40.
15 is a common multiple of
3 and 5.
8 20 20 8; a b b a
Glossary/Glosario
G5
ENGLISH
SPANISH
Commutative Property of
Multiplication The property that
Propiedad conmutativa de la
multiplicación Propiedad que
states that two or more numbers
can be multiplied in any order
without changing the product.
(p. 116)
establece que multiplicar dos o más
números en cualquier orden no
altera el producto.
compatible numbers Numbers
números compatibles Números
that are close to the given
numbers that make estimation
or mental calculation easier.
(p. 278)
que están cerca de los números
dados y hacen más fácil la
estimación o el cálculo mental.
complementary angles Two
ángulos complementarios Dos
ángulos cuyas medidas suman 90°.
angles whose measures add to
90°. (p. 379)
EXAMPLES
6 12 12
6; a b b a
To estimate 7957 5009, use
the compatible numbers 8000
and 5000:
8000 5000 13,000.
37˚
A
53˚
B
The complement of a 53° angle is
a 37° angle.
composite figure A figure made
up of simple geometric shapes.
(p. 436)
figura compuesta Figura formada
por figuras geométricas simples.
2 cm
5 cm
4 cm
4 cm
4 cm
5 cm
3 cm
composite number A whole
number greater than 1 that has
more than two positive factors.
(p. SB5)
número compuesto Número
mayor que 1 que tiene más de dos
factores que son números cabales.
4, 6, 8, and 9 are composite
numbers.
compound event An event
suceso compuesto Suceso
made up of two or more simple
events. (p. 569)
formado por dos o más sucesos
simples.
Rolling a 3 on a number cube
and spinning a 2 on a spinner is
a compound event.
compound inequality A
combination of more than one
inequality. (p. 137)
desigualdad compuesta
x 2 or x 10; 2 x 10
compound interest Interest
earned or paid on principal and
previously earned or paid interest.
(p. 304)
interés compuesto Interés que se
gana o se paga sobre el capital y los
intereses previamente ganados o
pagados.
cone A three-dimensional figure
with a circular base lying in one
plane plus a vertex not lying on
that plane. The remaining surface
of the cone is formed by joining
the vertex to points on the circle
by line segments. (p. 481)
cono Figura tridimensional con una
base circular que está en un plano
más un vértice que no está en ese
plano. El resto de la superficie del
cono se forma uniendo el vértice con
puntos del círculo por medio de
segmentos de recta.
G6
Glossary/Glosario
Combinación de dos o más
desigualdades.
If $100 is put into an account
with an interest rate of 5%
compounded monthly, then
after 2 years, the account will
12 2 $110.49.
have 100 1 12 0.05
ENGLISH
congruent Having the same size
and shape. (p. 406)
SPANISH
EXAMPLES
congruentes Que tienen la misma
Q
R
forma y el mismo tamaño.
P
S
PQ
RS
congruent angles Angles that
have the same measure. (p. 382)
ángulos congruentes Ángulos que
D
tienen la misma medida.
C
F
E
A
B
ABC DEF
congruent segments Segments
segmentos congruentes
that have the same length. (p. 382)
Segmentos que tienen la misma
longitud.
Q
R
P
S
PQ
S
R
constant A value that does not
constante Valor que no cambia.
3, 0, π
constante de variación La
constante k en ecuaciones de
variación directa e inversa.
y 5x
change. (p. 120)
constant of variation The
constant k in direct and inverse
variation equations. (p. 357)
conversion factor A fraction
whose numerator and
denominator represent the same
quantity but use different units;
the fraction is equal to 1 because
the numerator and denominator
are equal. (p. 237)
coordinate One of the numbers
of an ordered pair that locate a
point on a coordinate graph.
(p. 322)
factor de conversión Fracción
cuyo numerador y denominador
representan la misma cantidad pero
con unidades distintas; la fracción es
igual a 1 porque el numerador y el
denominador son iguales.
coordenada Uno de los números
de un par ordenado que ubica un
punto en una gráfica de
coordenadas.
constant of variation
1 day
24 hours
and 24 hours
1 day
B
4
y
2
x
–4
–2
O
2
4
The coordinates of B are (2, 3)
coordinate plane (coordinate
grid) A plane formed by the
plano cartesiano (cuadrícula de
coordenadas) Plano formado por la
intersection of a horizontal
number line called the x-axis and
a vertical number line called the
y-axis. (p. 322)
intersección de una recta numérica
horizontal llamada eje x y otra
vertical llamada eje y.
y-axis
O
x-axis
Glossary/Glosario
G7
ENGLISH
correlation The description of
the relationship between two data
sets. (p. 548)
SPANISH
correlación Descripción de la
relación entre dos conjuntos de
datos.
EXAMPLES
*œÃˆÌˆÛiÊVœÀÀi>̈œ˜
Þ
œÊVœÀÀi>̈œ˜
Þ
Ý
i}>̈ÛiÊVœÀÀi>̈œ˜
Þ
Ý
Ý
correspondence The
relationship between two or more
objects that are matched. (p. 406)
correspondencia La relación entre
dos o más objetos que coinciden.
A and D are
corresponding
angles.
A
B
C
D
A
B and D
E are
corresponding
sides.
E
F
corresponding angles (for
lines) For two lines intersected
ángulos correspondientes
(en líneas) Dadas dos líneas
by a transversal, a pair of angles
that lie on the same side of the
transversal and on the same sides
of the other two lines. (p. 389)
cortadas por una transversal, el par
de ángulos ubicados en el mismo
lado de la transversal y en los
mismos lados de las otras dos líneas.
corresponding angles (in
polygons) Matching angles of
ángulos correspondientes (en
polígonos) Ángulos que están en la
two or more polygons. (p. 244)
misma posición relativa en dos o
más polígonos.
m n
o p
q
s
r
t
m and q are
corresponding angles.
A and D are
corresponding angles.
corresponding sides Matching
sides of two or more polygons.
(p. 244)
lados correspondientes Lados que
se ubican en la misma posición
relativa en dos o más polígonos.
AB
and DE
are
corresponding sides.
counterclockwise A circular
movement to the left in the
direction shown. (p. 412)
en sentido contrario a las
manecillas del reloj Movimiento
cross products In the statement
productos cruzados En el
bc and ad are the cross
products. (p. 232)
enunciado bc y ad son
productos cruzados.
a
b
c
,
d
G8
Glossary/Glosario
circular en la dirección que se
indica.
a
b
c
,
d
2
4
3
6
2
4
For the proportion 3 6,
the cross products are
2 6 12 and 3 4 12.
ENGLISH
SPANISH
cube (geometric figure) A
rectangular prism with six
congruent square faces. (p. 477)
cubo (figura geométrica) Prisma
cube (in numeration) A number
cubo (en numeración) Número
raised to the third power. (p. 168)
elevado a la tercera potencia.
cubic function A polynomial
function of degree 3. (p. 338)
función cúbica Función polinomial
customary system of
measurement The measurement
sistema usual de medidas El
sistema de medidas que se usa
comúnmente en Estados Unidos.
system often used in the United
States. (p. SB15)
EXAMPLES
rectangular con seis caras cuadradas
congruentes.
23 2 2 2 8
8 is the cube of 2.
y = x3
de grado 3.
cylinder A three-dimensional
figure with two parallel congruent
circular bases. The third surface of
the cylinder consists of all parallel
circles of the same radius whose
centers lie on the segment joining
the centers of the bases. (p. 481)
cilindro Figura tridimensional con
decagon A polygon with ten sides.
decágono Polígono de diez lados.
inches, feet, miles, ounces,
pounds, tons, cups, quarts, gallons
dos bases circulares paralelas y
congruentes. La tercera superficie
del cilindro consiste en todos los
círculos paralelos del mismo radio
cuyo centro está en el segmento que
une los centros de las bases.
(p. SB16)
deductive reasoning The
process of using logic to draw
conclusions. (p. SB24)
razonamiento deuctivo Proceso
degree The unit of measure for
angles or temperature. (p. 379)
grado Unidad de medida para
ángulos y temperaturas.
degree of a polynomial The
grado de un polinomio La
highest power of the variable in a
polynomial. (p. 591)
potencia más alta de la variable en
un polinomio.
denominator The bottom
denominador Número que está
number of a fraction that tells how
many equal parts are in the whole.
(p. 66)
abajo en una fracción y que indica
en cuántas partes iguales se divide el
entero.
Density Property The property
Propiedad de densidad Propiedad
según la cual entre dos números
reales cualesquiera siempre hay otro
número real.
that states that between any two
real numbers, there is always
another real number. (p. 199)
en el que se utiliza la lógica para
sacar conclusions.
The polynomial 4x5 6x2 7
has degree 5.
2
In the fraction 5, 5 is the
denominator.
Glossary/Glosario
G9
ENGLISH
SPANISH
dependent events Events for
sucesos dependientes Dos
which the outcome of one event
affects the probability of the
other. (p. 569)
sucesos son dependientes si el
resultado de uno afecta la
probabilidad del otro.
diagonal A line segment that
diagonal Segmento de recta que
connects two non-adjacent
vertices of a polygon. (p. 403)
une dos vértices no adyacentes de
un polígono.
EXAMPLES
A bag contains 3 red marbles and
2 blue marbles. Drawing a red
marble and then drawing a blue
marble without replacing the first
marble is an example of
dependent events.
B
A
C
E
Diagonal
D
diameter A line segment that
passes through the center of a
circle and has endpoints on the
circle, or the length of that
segment. (p. 446)
diámetro Segmento de recta que
pasa por el centro de un círculo y
tiene sus extremos en la
circunferencia, o bien la longitud de
ese segmento.
difference The result when one
number is subtracted from
another. (p. 10)
diferencia El resultado de restar un
número de otro.
dimensions (geometry) The
dimensiones (geometría)
length, width, or height of a
figure. (p. 480)
Longitud, ancho o altura de una
figura.
direct variation A relationship
variación directa Relación entre
between two variables in which
the data increase or decrease
together at a constant rate. (p. 357)
dos variables en la que los datos
aumentan o disminuyen juntos a
una tasa constante.
In 16 5 11, 11 is the
difference.
4
y
2
x
⫺4 ⫺2
2
4
⫺4
y 2x
discount The amount by which
descuento Cantidad que se resta
the original price is reduced.
(p. 295)
del precio original de un artículo.
disjoint events Two events are
disjoint if they cannot occur in
the same trial of an experiment.
(p. 566)
sucesos desunidos Dos sucesos
Distributive Property The
Propiedad distributiva Propiedad
property that states if you multiply
a sum by a number, you will get the
same result if you multiply each
addend by that number and then
add the products. (p. 117)
que establece que, si multiplicas una
suma por un número, obtienes el
mismo resultado que si multiplicas
cada sumando por ese número y
luego sumas los productos.
dividend The number to be
dividendo Número que se divide en
un problema de división.
In 8 4 2, 8 is the dividend.
divisible Can be divided by a
divisible Que se puede dividir entre
18 is divisible by 3.
number without leaving a
remainder. (p. SB4)
un número sin dejar residuo.
divided in a division problem.
(p. SB7)
G10
Glossary/Glosario
son desunidos si no pueden ocurrir
en la misma prueba de un
experimento.
When rolling a number cube,
rolling a 3 and rolling an even
number are disjoint events.
5 21 5(20 1) (5 20) (5 1)
ENGLISH
Division Property of Equality
The property that states that if
you divide both sides of an
equation by the same nonzero
number, the new equation will
have the same solution. (p. 37)
SPANISH
Propiedad de igualdad de la
división Propiedad que establece
que puedes dividir ambos lados de
una ecuación entre el mismo número
distinto de cero, y la nueva ecuación
tendrá la misma solución.
EXAMPLES
4x 12
4x
12
4
4
x3
divisor The number you are
dividing by in a division problem.
(p. SB7)
divisor El número entre el que se
divide en un problema de división.
In 8 4 2, 4 is the divisor.
domain The set of all possible
input values of a function.
(p. 326)
dominio Conjunto de todos los
The domain of the function
y x2 1 is all real numbers.
double-bar graph A bar graph
gráfica de doble barra Gráfica de
barras que compara dos conjuntos
de datos relacionados.
Students at
Hill Middle School
100
Number of
students
that compares two related sets of
data. (p. SB17)
posibles valores de entrada de una
función.
80
60
40
20
0
Grade 6 Grade 7 Grade 8
Boys
edge The line segment along
arista Segmento de recta donde se
which two faces of a polyhedron
intersect. (p. 480)
intersecan dos caras de un poliedro.
endpoint A point at the end of a
line segment or ray. (p. 378)
extremo Un punto ubicado al final
de un segmento de recta o rayo.
Girls
Edge
equally likely Outcomes that
have the same probability.
(p. 564)
igualmente probables Resultados
que tienen la misma probabilidad de
ocurrir.
When tossing a coin, the
outcomes “heads” and “tails”
are equally likely.
equation A mathematical
sentence that shows that two
expressions are equivalent. (p. 32)
ecuación Enunciado matemático
que indica que dos expresiones son
equivalentes.
x47
6 1 10 3
equilateral triangle A triangle
triángulo equilátero Triángulo con
with three congruent sides.
(p. 393)
tres lados congruentes.
equivalent expressions
expresión equivalente Las
Equivalent expressions have the
same value for all values of the
variables. (p. 120)
expresiones equivalentes tienen el
mismo valor para todos los valores de
las variables.
4x 5x and 9x are equivalent
expressions.
Glossary/Glosario
G11
ENGLISH
SPANISH
EXAMPLES
razones equivalentes Razones que
representan la misma comparación.
1
2
and are equivalent ratios.
2
4
estimate (n) An answer that is
estimación (s) Una solución
close to the exact answer and is
found by rounding or other
methods.
(v) To find such an answer.
(p. 278)
aproximada a la respuesta exacta
que se halla mediante el redondeo u
otros métodos.
estimar (v) Hallar una solución
aproximada a la respuesta exacta.
500 is an estimate for the sum
98 287 104.
evaluate To find the value of a
evaluar Hallar el valor de una
numerical or algebraic
expression. (p. 6)
expresión numérica o algebraica.
even number A whole number
that is divisible by two. (p. SB4)
número par Número cabal divisible
event An outcome or set of
outcomes of an experiment or
situation. (p. 556)
suceso Un resultado o una serie de
resultados de un experimento o una
situación.
When rolling a number cube, the
event “an odd number” consists
of the outcomes 1, 3, and 5.
experiment (probability) In
probability, any activity based on
chance (such as tossing a coin).
(p. 556)
experimento (probabilidad) En
Tossing a coin 10 times and
noting the number of “heads”.
experimental probability The
probabilidad experimental Razón
ratio of the number of times an
event occurs to the total number
of trials, or times that the activity
is performed. (p. 560)
del número de veces que ocurre un
suceso al número total de pruebas o
al número de veces que se realiza el
experimento.
exponent The number that
exponente Número que indica
indicates how many times the
base is used as a factor. (p. 166)
cuántas veces se usa la base como
factor.
exponential form A number is
forma exponencial Se dice que un
in exponential form when it is
written with a base and an
exponent. (p. 166)
número está en forma exponencial
cuando se escribe con una base y un
exponente.
expression A mathematical
phrase that contains operations,
numbers, and/or variables. (p. 6)
expresión Enunciado matemático
face A flat surface of a
polyhedron. (p. 480)
cara Superficie plana de un
poliedro.
equivalent ratios Ratios that
name the same comparison.
(p. 224)
G12
Glossary/Glosario
Evaluate 2x 7 for x 3.
2x 7
2(3) 7
67
13
2, 4, 6
entre 2.
probabilidad, cualquier actividad
basada en la posibilidad, como
lanzar una moneda.
Kendra attempted 27 free throws
and made 16 of them. Her
experimental probability of
making a free throw is
16
number made
0.59.
number attempted
27
23 2 2 2 8;
3 is the exponent.
42 is the exponential form for 4 4.
6x 1
que contiene operaciones, números
y/o variables.
Face
ENGLISH
SPANISH
factor A number that is
factor Número que se multiplica
multiplied by another number to
get a product. (p. SB4)
por otro para hallar un producto.
Fahrenheit A temperature scale
in which 32°F is the freezing point
of water and 212°F is the boiling
point of water. (p. SB15)
Fahrenheit Escala de temperatura
en la que 32° F es el punto de
congelación del agua y 212° F es el
punto de ebullición.
fair When all outcomes of an
justo Se dice de un experimento
donde todos los resultados posibles
son igualmente probables.
experiment are equally likely, the
experiment is said to be fair.
(p. 564)
first quartile The median of the
lower half of a set of data; also
called lower quartile. (p. 542)
When tossing a coin, heads and
tails are equally likely, so it is a
fair experiment.
Lower quartile
Upper quartile
Minimum
Median
Maximum
mitad inferior de un conjunto de
datos. También se llama cuartil
FOIL Sigla en inglés de los términos
que se usan al multiplicar dos
binomios: los primeros, los externos,
los internos y los últimos (First,
Outer, Inner, Last).
formula A rule showing
fórmula Regla que muestra
relationships among quantities.
(p. 434)
relaciones entre cantidades.
fraction A number in the form ab,
where b 0. (p. 66)
fracción Número escrito en la
forma ab, donde b 0.
frequency table A table that lists
tabla de frecuencia Una tabla en
la que se organizan los datos de
acuerdo con el número de veces que
aparece cada valor (o la frecuencia).
items together according to the
number of times, or frequency,
that the items occur. (p. SB19)
7 is a factor of 21 since 7 3 21.
primer cuartil La mediana de la
inferior.
FOIL An acronym for the terms
used when multiplying two
binomials: the First, Inner, Outer,
and Last terms. (p. 618)
EXAMPLES
function An input-output
función Relación de entrada-salida
relationship that has exactly one
output for each input. (p. 326)
en la que a cada valor de entrada
corresponde exactamente un valor
de salida.
0
2
4
F
6
8
10
12
14
L
(x 2)(x 3) x 2 3x 2x 6
x2 x 6
I
O
A w is the formula for the
area of a rectangle.
2
3
Data set: 1, 1, 2, 2, 3, 4, 5, 5, 5, 6, 6
Frequency table:
Data
Frequency
1
2
2
2
3
1
4
1
5
3
6
2
6
5
2
1
Glossary/Glosario
⫺4
⫺1
0
G13
ENGLISH
SPANISH
graph of an equation A graph
gráfica de una ecuación Gráfica
of the set of ordered pairs that are
solutions of the equation. (p. 123)
del conjunto de pares ordenados que
son soluciones de la ecuación.
EXAMPLES
yx 1
4
y
2
x
⫺4 ⫺2 O
2
4
⫺4
great circle A circle on a sphere
círculo máximo Círculo de una
such that the plane containing the
circle passes through the center of
the sphere. (p. 508)
esfera tal que el plano que contiene
el círculo pasa por el centro de la
esfera.
greatest common divisor (GCD)
máximo común divisor (MCD) El
The largest whole number that
divides evenly into two or more
given numbers. (p. SB6)
mayor de los factores comunes
compartidos por dos o más números
dados.
height In a triangle or
quadrilateral, the perpendicular
distance from the base to the
opposite vertex or side. (p. 435)
altura En un triángulo o
cuadrilátero, la distancia
perpendicular desde la base de la
figura al vértice o lado opuesto.
In a trapezoid, the perpendicular
distance between the bases. (p. 440)
En un trapecio, la distancia
perpendicular entre las bases.
In a prism or cylinder, the
perpendicular distance between
the bases. (p. 413)
En un prisma o cilindro, la distancia
perpendicular entre las bases.
In a pyramid or cone, the
perpendicular distance from the
base to the opposite vertex. (p. 420)
En una pirámide o cono, la distancia
perpendicular desde la base al
vértice opuesto.
hemisphere A half of a sphere.
hemisferio La mitad de una esfera.
(p. 508)
heptagon A seven-sided
heptágono Polígono de siete lados.
polygon. (p. SB16)
hexagon A six-sided polygon.
(p. SB16)
G14
Glossary/Glosario
hexágono Polígono de seis lados.
Great circle
The GCD of 27 and 45 is 9.
…
b2
h
b1
h
Height
histogram A bar graph that
shows the frequency of data
within equal intervals. (p. SB19)
SPANISH
EXAMPLES
histograma Gráfica de barras que
Starting Salaries
muestra la frecuencia de los datos en
intervalos iguales.
Frequency
ENGLISH
40
30
20
10
0
9
9
–3
–2
20
30
9
–4
40
9
–5
50
Salary range (thousand $)
hypotenuse In a right triangle,
hipotenusa En un triángulo
the side opposite the right angle.
(p. 203)
rectángulo, el lado opuesto al
ángulo recto.
Identity Property of
Multiplication The property that
Propiedad de identidad del uno
states that the product of 1 and any
number is that number. (p. 37)
Propiedad que establece que el
producto de 1 y cualquier número es
ese número.
Identity Property of Addition
Propiedad de identidad del cero
The property that states the sum
of zero and any number is that
number. (p. 32)
Propiedad que establece que la
suma de cero y cualquier número es
ese número.
image A figure resulting from a
imagen Figura que resulta de una
transformation. (p. 410)
transformación.
hypotenuse
414
3 1 3
404
3 0 3
B⬘
B
C
A
C⬘
A⬘
impossible (probability) Can
imposible (en probabilidad) Que
never happen; an event that is
impossible has a probability of 0.
(p. 556)
no puede ocurrir. Suceso cuya
probabilidad de ocurrir es 0.
improper fraction A fraction in
which the numerator is greater
than or equal to the denominator.
(p. SB9)
fracción impropia Fracción cuyo
numerador es mayor que o igual al
denominador.
17 3
, 5 3
independent events Events for
sucesos independientes Dos
which the outcome of one event
does not affect the probability of
the other. (p. 569)
sucesos son independientes si el
resultado de uno no afecta la
probabilidad del otro.
A bag contains 3 red marbles and
2 blue marbles. Drawing a red
marble, replacing it, and then
drawing a blue marble is an
example of independent events.
indirect measurement The
technique of using similar figures
and proportions to find a measure.
(p. 248)
medición indirecta La técnica de
When rolling a standard number
cube, rolling a 7 is an impossible
event.
usar figuras semejantes y
proporciones para hallar una
medida.
Glossary/Glosario
G15
ENGLISH
SPANISH
EXAMPLES
inductive reasoning The
process of conjecturing that a
general rule or statement is true
because specific cases are true.
(p. SB24)
razonamiento inductivo Proceso
de razonamiento por el que se
determina que una regal o
enunciado son verdaderos porque
ciertos casos específicos son
verdaderos.
inequality A mathematical
statement that compares two
expressions by using one of the
following symbols: , , , , or
. (p. 136)
desigualdad Enunciado
matemático que compara dos
expresiones por medio de uno de los
siguientes símbolos: , , , ,
ó .
58
5x 2 12
input The value substituted into
valor de entrada Valor que se usa
an expression or function. (p. 326)
para sustituir una variable en una
expresión o función.
For the function y 6x, the input
4 produces an output of 24.
integers The set of whole
enteros Conjunto de todos los
numbers and their opposites.
(p. 14)
números cabales y sus opuestos.
interest The amount of money
charged for borrowing or using
money. (p. 303)
interés Cantidad de dinero que se
interior angles Angles on the
ángulos internos Ángulos en los
inner sides of two lines cut by a
transversal. (p. 389)
lados internos de dos líneas
intersecadas por una transversal.
. . . 3, 2, 1, 0, 1, 2, 3, . . .
cobra por el préstamo o uso del
dinero.
r
t
s
v
r, s, t, and v are interior
angles.
intersecting lines Lines that
líneas secantes Líneas que se
cross at exactly one point. (p. 388)
cruzan en un solo punto.
m
n
interval The space between
marked values on a number line
or the scale of a graph. (p. SB18)
inverse operations Operations
intervalo El espacio entre los valores
marcados en una recta numérica o en
la escala de una gráfica.
operaciones inversas Operaciones
que se cancelan mutuamente: suma
y resta, o multiplicación y división.
Adding 3 and subtracting 3 are
inverse operations:
5 3 8; 8 3 5
Multiplying by 3 and dividing by
3 are inverse operations:
2 3 6; 6 3 2
irrational number A real
number that cannot be expressed
as a ratio of two integers. (p. 198)
número irracional Número real
que no se puede expresar como una
razón de dos enteros.
2, π
isolate the variable To get a
despejar la variable Dejar sola la
variable en un lado de una ecuación
o desigualdad para resolverla.
x 7 22
7 7
x
15
that undo each other: addition
and subtraction, or multiplication
and division. (p. 32)
variable alone on one side of an
equation or inequality in order to
solve the equation or inequality.
(p. 32)
G16
Glossary/Glosario
12
3x
3
3
4x
ENGLISH
isosceles triangle A triangle
with at least two congruent sides.
(p. 393)
lateral area The sum of the
areas of the lateral faces of a
prism or pyramid, or the area of
the lateral surface of a cylinder or
cone. (p. 498)
SPANISH
EXAMPLES
triángulo isósceles Triángulo que
tiene al menos dos lados
congruentes.
área lateral Suma de las áreas de
las caras laterales de un prisma o
pirámide, o área de la superficie
lateral de un cilindro o cono.
£ÓÊV“
ÈÊV“
nÊV“
Lateral area 2(8)(12) 2(6)(12)
336 cm2
lateral face In a prism or a
pyramid, a face that is not a base.
(p. 498)
cara lateral En un prisma o
pirámide, una cara que no es
la base.
Bases
Lateral face
Right prism
lateral surface In a cylinder, the
superficie lateral En un cilindro,
curved surface connecting the
circular bases; in a cone, the curved
surface that is not a base. (p. 499)
superficie curva que une las bases
circulares; en un cono, la superficie
curva que no es la base.
Lateral surface
Right cylinder
least common denominator
(LCD) The least common
mínimo común denominador
(mcd) El mínimo común múltiplo
multiple of two or more
denominators. (p. 70)
de dos o más denominadores.
least common multiple (LCM)
mínimo común múltiplo (mcm) El
menor de los números cabales,
distinto de cero, que es múltiplo de
dos o más números dados.
The least number, other than
zero, that is a multiple of two or
more given numbers. (p. SB6)
legs In a right triangle, the sides
that include the right angle; in an
isosceles triangle, the pair of
congruent sides. (p. 203)
catetos En un triángulo rectángulo,
los lados adyacentes al ángulo recto.
En un triángulo isósceles, el par de
lados congruentes.
3
5
The LCD of 4 and 6 is 12.
The LCM of 6 and 10 is 30.
leg
leg
like terms Two or more terms
that have the same variable raised
to the same power. (p. 120)
line A straight path that extends
without end in opposite
directions. (p. 378)
términos semejantes Dos o más
términos que contienen la misma
variable elevada a la misma potencia.
In the expression 3a 5b 12a,
3a and 12a are like terms.
línea Trayectoria recta que se
extiende de manera indefinida en
direcciones opuestas.
Glossary/Glosario
G17
SPANISH
line graph A graph that uses line
gráfica lineal Gráfica que muestra
segments to show how data
changes. (p. SB18)
cómo cambian los datos mediante
segmentos de recta.
EXAMPLES
Marlon’s Video Game Scores
Score
ENGLISH
1200
800
400
0
1
2
3
4
5
6
Game number
line of best fit A straight line
línea de mejor ajuste La línea recta
that comes closest to the points
on a scatter plot. (p. 549)
que más se aproxima a los puntos de
un diagrama de dispersión.
160
120
80
40
0
line of reflection A line that a
ínea de reflexión Línea sobre la
figure is flipped across to create a
mirror image of the original
figure. (p. 410)
cual se invierte una figura para crear
una imagen reflejada de la figura
original.
R
Q
line plot A number line with
marks or dots that show
frequency. (p. 532)
diagrama de acumulación Recta
numérica con marcas o puntos que
indican la frecuencia.
40 80 120160
S
S′
T
T′
X X
X X
X X
X
X
0
2
1
R′
Q′
X
3
4
Number of pets
line segment A part of a line
between two endpoints.
(p. 378)
segmento de recta Parte de una
línea con dos extremos.
linear equation An equation
ecuación lineal Ecuación cuyas
whose solutions form a straight
line on a coordinate plane.
(p. 330)
soluciones forman una línea recta en
un plano cartesiano.
linear function A function
whose graph is a straight line.
(p. 330)
función lineal Función cuya gráfica
GH
H
G
y 2x 1
es una línea recta.
yx 1
4
y
2
x
⫺4 ⫺2 O
2
4
⫺4
lower quartile The median of
cuartil inferior La mediana de la
the lower half of a set of data; also
called first quartile. (p. 542)
mitad inferior de un conjunto de
datos; también se llama primer
cuartil.
G18
Glossary/Glosario
Lower quartile
Upper quartile
Minimum
Median
Maximum
0
2
4
6
8
10
12
14
ENGLISH
SPANISH
EXAMPLES
markup The amount by which a
margen de beneficio Cantidad
wholesale cost is increased.
(p. 295)
que se agrega a un costo mayorista.
maximum The greatest value in a
máximo El valor mayor de un
conjunto de datos.
Data set: 4, 6, 7, 8, 10
Maximum: 10
mean The sum of a set of data
divided by the number of items in
the data set; also called average.
(p. 537)
media La suma de todos los
Data set: 4, 6, 7, 8, 10
Mean:
measure of central tendency
medida de tendencia dominante
A measure used to describe the
middle of a data set. (p. 538)
Medida que describe la parte media
de un conjunto de datos.
median The middle number, or
the mean (average) of the two
middle numbers, in an ordered
set of data. (p. 537)
mediana El número intermedio
metric system of measurement
sistema métrico de medición
A decimal system of weights and
measures that is used universally
in science and commonly
throughout the world. (p. SB15)
Sistema decimal de pesos y medidas
empleado universalmente en las
ciencias y de uso común en todo el
mundo.
midpoint The point that divides
a line segment into two congruent
line segments. (p. 393)
punto medio El punto que divide
minimum The least value in a
data set. (p. 543)
mínimo El valor meno de un
conjunto datos.
Data set: 4, 6, 7, 8, 10
Minimum: 4
mixed number A number made
número mixto Número compuesto
up of a whole number that is not
zero and a fraction. (p. SB9)
por un número cabal distinto de
cero y una fracción.
48
mode The number or numbers
that occur most frequently in a set
of data; when all numbers occur
with the same frequency, we say
there is no mode. (p. 537)
moda Número o números más
frecuentes en un conjunto de datos;
si todos los números aparecen con la
misma frecuencia, no hay moda.
Data set: 3, 5, 8, 8, 10
Mode: 8
monomial A number or a
monomio Un número o un
3x 2y 4
product of numbers and variables
with exponents that are whole
numbers. (p. 178)
producto de números y variables
con exponentes que son números
cabales.
data set. (p. 543)
elementos de un conjunto de datos
dividida entre el número de
elementos del conjunto. También se
llama promedio.
o la media (el promedio) de los dos
números intermedios en un
conjunto ordenado de datos.
4 6 7 8 10
35
7
5
5
mean or median
Data set: 4, 6, 7, 8, 10
Median: 7
centimeters, meters, kilometers,
gram, kilograms, milliliters, liters
un segmento de recta en dos
segmentos de recta congruentes.
C.
B is the midpoint of A
1
Glossary/Glosario
G19
ENGLISH
SPANISH
EXAMPLES
multiple The product of any
múltiplo El producto de cualquier
number and a non-zero whole
number is a multiple of that
number. (p. SB4)
número y un número cabal distinto
de cero es un múltiplo de ese
número.
Multiplication Property of
Equality The property that states
Propiedad de igualdad de la
multiplicación Propiedad que
that if you multiply both sides of
an equation by the same number,
the new equation will have the
same solution. (p. 38)
establece que puedes multiplicar
ambos lados de una ecuación por el
mismo número y la nueva ecuación
tendrá la misma solución.
multiplicative inverse One of
inverso multiplicativo Uno de dos
two numbers whose product is 1;
also called reciprocal. (p. 82)
números cuyo producto es 1;
también llamado recíproco.
3
4
mutually exclusive Two events
mutuamente excluyentes Dos
are mutually exclusive if they
cannot occur in the same trial of
an experiment. (p. 566)
sucesos son mutuamente
excluyentes cuando no pueden
ocurrir en la misma prueba de un
experimento.
When rolling a number cube,
rolling a 3 and rolling an even
number are mutually exclusive
events.
negative correlation Two data
correlación negativa Dos conjuntos
sets have a negative correlation if
one set of data values increases
while the other decreases. (p. 549)
de datos tienen correlación negativa
si los valores de un conjunto
aumentan a medida que los valores
del otro conjunto disminuyen.
negative integer An integer less
entero negativo Entero menor que
than zero. (p. 14)
cero.
net An arrangement of twodimensional figures that can be
folded to form a polyhedron.
(p. 496)
30, 40, and 90 are all multiplies
of 10.
1
x 7
3
1
(3) 3x (3)(7)
x 21
The multiplicative inverse of
is 43.
y
x
2 is a negative integer.
4 3 2 1
plantilla Arreglo de figuras
bidimensionales que se doblan para
formar un poliedro.
0
1
2
3
10 m
10 m
6m
6m
no correlation Two data sets
sin correlación Caso en que los
have no correlation when there is
no relationship between their
data values. (p. 549)
valores de dos conjuntos no
muestran ninguna relación.
y
x
numerator The top number of a
fraction that tells how many parts
of a whole are being considered.
(p. 66)
numerador El número de arriba de
numerical expression An
expresión numérica Expresión que
incluye sólo números y operaciones.
expression that contains only
numbers and operations. (p. 6)
G20
Glossary/Glosario
una fracción; indica cuántas partes
de un entero se consideran.
4
5
numerator
(2 3) 1
4
ENGLISH
SPANISH
obtuse angle An angle whose
measure is greater than 90° but
less than 180°. (p. 379)
ánlgulo obtuso Ángulo que mide
más de 90° y menos de 180°.
obtuse triangle A triangle
triángulo obtusángulo Triángulo
que tiene un ángulo obtuso.
containing one obtuse angle.
(p. 392)
octagon An eight-sided polygon.
EXAMPLES
octágono Polígono de ocho lados.
(p. SB16)
odd number A whole number
that is not divisible by two. (p. SB4)
opposites Two numbers that are
an equal distance from zero on a
number line; also called additive
inverse. (p. 14)
número impar Número cabal que
no es divisible entre 2.
1, 3, 5
opuestos Dos números que están a
la misma distancia de cero en una
recta numérica. También se llaman
5 and 5 are opposites.
inversos aditivos.
order of operations A rule for
orden de las operaciones Regla
evaluating expressions: First
perform the operations in
parentheses, then compute powers
and roots, then perform all
multiplication and division from
left to right, and then perform all
addition and subtraction from left
to right. (p. SB14)
para evaluar expresiones: primero se
hacen las operaciones entre
paréntesis, luego se hallan las
potencias y raíces, después todas las
multiplicaciones y divisiones de
izquierda a derecha, y por último,
todas las sumas y restas de izquierda
a derecha.
ordered pair A pair of numbers
par ordenado Par de números que
sirven para ubicar un punto en un
plano cartesiano.
that can be used to locate a point
on a coordinate plane. (p. 322)
5 units
5 units
⫺6 ⫺5 ⫺4 ⫺3 ⫺2 ⫺1
42 8 2
16 8 2
16 4
20
0
1
2
3
4
5
6
Simplify the power.
Divide.
Add.
B
4
y
2
x
–4
–2
O
2
4
The coordinates of B are (2, 3).
origin The point where the x-axis
and y-axis intersect on the
origen Punto de intersección entre
el eje x y el eje y en un plano
coordinate plane; (0, 0). (p. 322)
cartesiano: (0, 0).
origin
O
outcome (probability) A
possible result of a probability
experiment. (p. 556)
resultado (en probabilidad)
Posible resultado de un experimento
de probabilidad.
When rolling a number cube, the
possible outcomes are 1, 2, 3, 4, 5,
and 6.
Glossary/Glosario
G21
ENGLISH
outlier A value much greater or
SPANISH
much less than the others in a
data set. (p. 538)
valor extremo Un valor mucho
mayor o menor que los demás
valores de un conjunto de datos.
output The value that results
valor de salida Valor que resulta
from the substitution of a given
input into an expression or
function. (p. 326)
después de sustituir una variable por
un valor de entrada determinado en
una expresión o función.
parabola The graph of a
quadratic function. (p. 334)
parábola Gráfica de una función
cuadrática.
parallel lines Lines in a plane
líneas paralelas Líneas que se
encuentran en el mismo plano pero
que nunca se intersecan.
that do not intersect. (p. 384)
parallel planes Planes that do
planos paralelos Planos que no se
not intersect. (p. 385)
cruzan.
EXAMPLES
Most
of data Mean
Outlier
For the function y 6x, the
input 4 produces an output of 24.
r
s
Plane AEF and plane CGH are
parallel planes.
parallelogram A quadrilateral
paralelogramo Cuadrilátero con
with two pairs of parallel sides.
(p. 399)
dos pares de lados paralelos.
pentagon A five-sided polygon.
pentágono Polígono de cinco lados.
(p. SB16)
percent A ratio comparing a
porcentaje Razón que compara un
number to 100. (p. 274)
número con el número 100.
percent of change The amount
stated as a percent that a number
increases or decreases. (p. 294)
porcentaje de cambio Cantidad
en que un número aumenta o
disminuye, expresada como un
porcentaje.
percent of decrease A percent
change describing a decrease in a
quantity. (p. 294)
porcentaje de disminución
G22
Glossary/Glosario
Porcentaje de cambio en que una
cantidad disminuye.
45
45% 100
An item that costs $8 is marked
down to $6. The amount of the
decrease is $2, and the percent
2
of decrease is 8 0.25 25%.
ENGLISH
SPANISH
EXAMPLES
percent of increase A percent
change describing an increase in
a quantity. (p. 294)
porcentaje de incremento
Porcentaje de cambio en que una
cantidad aumenta.
The price of an item increases
from $8 to $12. The amount of
the increase is $4 and the percent
4
of increase is 8 0.5 50%
perfect square A square of a
cuadrado perfecto El cuadrado de
52 25, so 25 is a perfect square.
whole number. (p. 190)
un número cabal.
perimeter The sum of the
lengths of the sides of a polygon.
(p. 434)
perímetro La suma de las
18 ft
longitudes de los lados de un
polígono.
6ft
perimeter 18 6 18 6 48 ft
perpendicular bisector A line
mediatriz Línea que cruza un
that intersects a segment at its
midpoint and is perpendicular to
the segment. (p. 382)
segmento en su punto medio y es
perpendicular al segmento.
perpendicular lines Lines that
intersect to form right angles.
(p. 384)
líneas perpendiculares Líneas que
perpendicular planes Planes
that intersect at 90° angles. (p. 385)
planos perpendiculares Planos
pi (π) The ratio of the
pi (π ) Razón de la circunferencia de
un círculo a la longitud de su
diámetro; π 3.14 ó 272.
circumference of a circle to
the length of its diameter;
π 3.14 or 272. (p. 450)
Ű
n
al intersecarse forman ángulos
rectos.
m
que se cruzan en ángulos de 90°.
plane A flat surface that extends
plano Superficie plana que se
forever. (p. 378)
extiende de manera indefinida en
todas direcciones.
point An exact location in space.
punto Ubicación exacta en el
(p. 378)
espacio.
polygon A closed plane figure
polígono Figura plana cerrada,
formed by three or more line
segments that intersect only at
their endpoints (vertices). (p. 399)
formada por tres o más segmentos
de recta que se intersecan sólo en
sus extremos (vértices).
polyhedron A three-dimensional
figure in which all the surfaces or
faces are polygons. (p. 480)
poliedro Figura tridimensional
polynomial One monomial or
polinomio Un monomio o la suma
the sum or difference of
monomials. (p. 590)
o la diferencia de monomios.
population The entire group of
objects or individuals considered
for a survey. (p. SB22)
población Grupo completo de
objetos o individuos que se desea
estudiar.
A
C
B
R
P
cuyas superficies o caras tiene forma
de polígonos.
2x2 3xy 7y2
In a survey about study habits
of middle school students, the
population is all middle school
students.
Glossary/Glosario
G23
ENGLISH
SPANISH
positive correlation Two data
correlación positiva Dos conjuntos
sets have a positive correlation
when their data values increase or
decrease together. (p. 549)
de datos tienen una correlación
positiva cuando los valores de
ambos conjuntos aumentan o
disminuyen al mismo tiempo.
EXAMPLES
y
x
positive integer An integer
greater than zero. (p. 14)
entero positivo Entero mayor que
power A number produced by
potencia Número que resulta al
raising a base to an exponent.
(p. 166)
elevar una base a un exponente.
prime factorization A number
factorización prima Un número
written as the product of its prime
factors. (p. SB5)
escrito como el producto de sus
factores primos.
prime number A whole number
greater than 1 that has exactly two
factors, itself and 1. (p. SB5)
número primo Número cabal
mayor que 1 que sólo es divisible
entre 1 y él mismo.
principal The initial amount of
money borrowed or saved. (p. 302)
capital Cantidad inicial de dinero
depositada o recibida en préstamo.
principal square root The
raíz cuadrada principal Raíz
25
5; the principal square
nonnegative square root of a
number. (p. 190)
cuadrada no negativa de un número.
root of 25 is 5.
prism A three-dimensional figure
with two congruent parallel
polygonal bases. The remaining
edges join corresponding vertices
of the bases so that the remaining
faces are rectangles. (p. 480)
prisma Figura tridimensional con
dos bases poligonales congruentes y
paralelas. El resto de las aristas se
unen a los vértices correspondientes
de las bases de manera que el resto
de las caras sean rectángulos.
probability A number from 0 to 1
(or 0% to 100%) that describes
how likely an event is to occur.
(p. 556)
probabilidad Un número entre 0 y
product The result when two or
more numbers are multiplied.
(p. 26)
producto Resultado de multiplicar
dos o más números.
The product of 4 and 8 is 32.
profit The difference between
ganancia Diferencia entre el total
total income and total expenses.
(p. 299)
de ingresos y de gastos.
If total income is $2,400, and total
expenses are $2,100, the profit is
$2,400 $2,100 $300.
proportion An equation that
proporción Ecuación que establece
states that two ratios are
equivalent. (p. 232)
que dos razones son equivalentes.
2
4
3
6
protractor A tool for measuring
angles. (p. 478)
G24
Glossary/Glosario
cero.
1 (ó 0% y 100%) que describe qué tan
probable es un suceso.
transportador Instrumento para
medir ángulos.
{ Î Ó £
ä
£
Ó
Î
{
2 is a positive integer.
23 8, so 2 to the 3rd power is 8.
10 2 5,
24 23 3
5 is prime because its only
factors are 5 and 1.
A bag contains 3 red marbles and
4 blue marbles. The probability of
randomly choosing a red marble
3
is 7.
ENGLISH
SPANISH
pyramid A three-dimensional
figure with a polygonal base lying
in one plane plus one additional
vertex not lying on that plane. The
remaining edges of the pyramid
join the additional vertex to the
vertices of the base. (p. 480)
pirámide Figura tridimensional con
una base poligonal en un plano más
un vértice adicional que no está en
ese plano. El resto de las aristas de la
pirámide unen el vértice adicional
con los vértices de la base.
Pythagorean Theorem In a right
triangle, the square of the length
of the hypotenuse is equal to the
sum of the squares of the lengths
of the legs. (p. 203)
Teorema de Pitágoras En un
quadrant The x- and y-axes
cuadrante El eje x y el eje y dividen
divide the coordinate plane into
four regions. Each region is called
a quadrant. (p. 322)
el plano cartesiano en cuatro
regiones. Cada región recibe el
nombre de cuadrante.
EXAMPLES
13 cm
triángulo rectángulo, la suma de los
cuadrados de los catetos es igual al
cuadrado de la hipotenusa.
5 cm
12 cm
2
2
5 12 132
25 144 169
Quadrant II
Quadrant I
O
Quadrant III Quadrant IV
quadratic function A function of
the form y ax 2 bx c, where
a 0. (p. 334)
función cuadrática Función del
tipo y ax 2 bx c, donde a 0.
quadrilateral A four-sided
polygon. (p. 399)
cuadrilátero Polígono de cuatro
quarterly Four times a year.
trimestral Cuatro veces al año.
y x 2 6x 8
lados.
(p. 305)
quartile Three values, one of
which is the median, that divide a
data set into fourths. (p. 542)
cuartil Cada uno de tres valores,
uno de los cuales es la mediana,
que dividen en cuartos un conjunto
de datos.
Lower quartile
Upper quartile
Minimum
Median
Maximum
0
2
4
6
8
10
12
14
quotient The result when one
number is divided by another.
(p. SB7)
cociente Resultado de dividir un
número entre otro.
In 8 4 2, 2 is the quotient.
radical symbol The symbol símbolo de radical El símbolo 36
6
used to represent the nonnegative
square root of a number. (p. 192)
con que se representa la raíz
cuadrada no negativa de un número.
Glossary/Glosario
G25
ENGLISH
SPANISH
EXAMPLES
radius A line segment with one
endpoint at the center of the
circle and the other endpoint on
the circle, or the length of that
segment. (p. 446)
radio Segmento de recta con un
random sample A sample in
muestra aleatoria Muestra en la
which each individual or object in
the entire population has an equal
chance of being selected. (p. SB21)
que cada individuo u objeto de la
población tiene la misma posibilidad
de ser elegido.
range (in statistics) The
rango (en estadística) Diferencia
entre los valores máximo y mínimo
de un conjunto de datos.
Data set: 3, 5, 7, 7, 12
Range: 12 3 9
range (of a function) The set of
all possible output values of a
function. (p. 326)
rango (en una función) El
The range of y ⏐x⏐ is y 0.
rate A ratio that compares two
quantities measured in different
units. (p. 228)
tasa Una razón que compara dos
cantidades medidas en diferentes
unidades.
The speed limit is 55 miles per
hour or 55 mi/h.
rate of change A ratio that
tasa de cambio Razón que
compara la cantidad de cambio de la
variable dependiente con la cantidad
de cambio de la variable
independiente.
The cost of mailing a letter
increased from 22 cents in 1985
to 25 cents in 1988. During this
period, the rate of change was
change in cost
25 21
3
change in years
1988 1985
3
difference between the greatest
and least values in a data set.
(p. 537)
compares the amount of change
in a dependent variable to the
amount of change in an
independent variable. (p. 344)
Radius
extremo en el centro de un círculo y
el otro en la circunferencia, o bien la
longitud de ese segmento.
Mr. Henson chose a random
sample of the class by writing
each student’s name on a slip of
paper, mixing up the slips, and
drawing five slips without
looking.
conjunto de todos los valores de
salida posibles de una función.
1 cent per year.
rate of interest The percent
charged or earned on an amount
of money; see simple interest.
(p. 302)
tasa de interés Porcentaje que se
cobra por una cantidad de dinero
prestada o que se gana por una
cantidad de dinero ahorrada; ver
interés simple.
ratio A comparison of two
razón Comparación de dos
numbers or quantities. (p. 224)
números o cantidades.
rational number A number that
can be written in the form ab,
número racional Número que se
puede expresar como ab, donde a y b
son números enteros y b 0.
ray A part of a line that starts at
one endpoint and extends forever.
(p. 378)
rayo Parte de una línea que
where a and b are integers and
b 0. (p. 66)
real number A rational or
irrational number. (p. 198)
12
12 to 25, 12:25, 25
6
6 can be expressed as 1.
1
0.5 can be expressed as 2.
D
comienza en un extremo y se
extiende de manera indefinida.
número real Número racional o
irracional.
Real Numbers
Rational Numbers ()
27
___
4
−
0.3
Integers ()
-3
Natural Numbers ()
2
G26
Glossary/Glosario
- √
11
√2
0
3
1
4.5
√
17
-2
Whole Numbers ()
-1
Irrational Numbers
10
-___
11
e
__5
9
π
ENGLISH
SPANISH
reciprocal One of two numbers
recíproco Uno de dos números cuyo
whose product is 1; also called
multiplicative inverse. (p. 82)
producto es igual a 1. También se
llama inverso multiplicativo.
rectangle A parallelogram with
four right angles. (p. 399)
rectángulo Paralelogramo con
cuatro ángulos rectos.
rectangular prism A three-
prisma rectangular Figura
tridimensional que tiene tres pares
de caras opuestas, paralelas y
congruentes que son rectángulos.
dimensional figure that has three
pairs of opposite parallel
congruent faces that are
rectangles. (p. 480)
reflection A transformation of a
figure that flips the figure across a
line. (p. 410)
EXAMPLES
2
reflexión Transformación que
ocurre cuando se invierte una figura
sobre una línea.
B
A
regular polygon A polygon in
which all angles are congruent and
all sides are congruent. (p. SB16)
polígono regular Polígono en el
que todos los ángulos y todos los
lados son congruentes.
regular pyramid A pyramid
whose base is a regular polygon
and whose lateral faces are all
congruent. (p. 504)
pirámide regular Pirámide que
regular tessellation A repeating
pattern of congruent regular
polygons that completely covers
a plane with no gaps or overlaps.
(p. 416)
teselado regular Patrón que se
repite formado por polígonos
regulares congruentes que cubren
completamente un plano sin dejar
espacios y sin superponerse.
repeating decimal A rational
decimal periódico Número racional
number in decimal form in which
a group of one or more digits
(where all digits are not zero)
repeat infinitely. (pp. 66, 191)
en forma decimal en el que un grupo
de uno o más dígitos (donde todos los
dígitos son distintos de cero) se
repiten infinitamente.
rhombus A parallelogram with
all sides congruent. (p. 399)
rombo Paralelogramo en el que
todos los lados son congruentes.
right angle An angle that
ángulo recto Ángulo que mide
exactamente 90°.
measures 90°. (p. 379)
3
The reciprocal of 3 is 2.
B⬘
C
C⬘
A⬘
tiene un polígono regular como base
y caras laterales congruentes.
0.757575. . . 0.7
5
Glossary/Glosario
G27
ENGLISH
right cone A cone in which a
perpendicular line drawn from
the base to the tip (vertex) passes
through the center of the base.
(p. 504)
SPANISH
EXAMPLES
cono recto Cono en el que una
línea perpendicular trazada de la
base a la punta (vértice) pasa por el
centro de la base.
Axis
Right cone
right triangle A triangle
containing a right angle. (p. 392)
triángulo rectángulo Triángulo que
rise The vertical change when
the slope of a line is expressed as
rise
the ratio run , or “rise over run.”
(p. 345)
distancia vertical El cambio
rotation A transformation in
rotación Transformación que
ocurre cuando una figura gira
alrededor de un punto.
which a figure is turned around a
point. (p. 410)
tiene un ángulo recto.
vertical cuando la pendiente de una
línea se expresa como la razón
distancia vertical
distancia horizontal , o "distancia vertical
sobre distancia horizontal".
For the points (3, 1)
and (6, 5), the rise is
5 (1) 6.
F′
E′
G′
D′
G
D
F
E
run The horizontal change when
distancia horizontal El cambio
the slope of a line is expressed as
ris
e
the ratio run , or “rise over run.”
(p. 345)
horizontal cuando la pendiente de
una línea se expresa como la razón
distancia vertical
, o "distancia vertical
distancia horizontal
sobre distancia horizontal".
sales tax A percent of the cost
of an item, which is charged by
governments to raise money.
(p. 298)
impuesto sobre la venta
sample A part of the population.
muestra Una parte de la población.
In a survey about the study
habits of middle school students,
a sample is a group of 100
randomly chosen middle school
students.
sample space All possible
espacio muestral Conjunto de
outcomes of an experiment.
(p. 556)
todos los resultados posibles de un
experimento.
When rolling a number cube, the
sample space is 1, 2, 3, 4, 5, 6.
scale The ratio between two sets
escala La razón entre dos conjuntos
of measurements. (p. 252)
de medidas.
Porcentaje del costo de un artículo
que los gobiernos cobran para
recaudar fondos.
(p. SB21)
G28
Glossary/Glosario
For the points (3, 1) and (6, 5),
the run is 6 3 3.
1 cm : 5 mi
ENGLISH
SPANISH
scale drawing A drawing that
uses a scale to make an object
smaller than (a reduction) or
larger than (an enlargement) the
real object. (p. 252)
dibujo a escala Dibujo en el que se
usa una escala para que un objeto se
vea menor (reducción) o mayor
(agrandamiento) que el objeto real al
que representa.
EXAMPLES
A
E
F
D
B C
H
G
A blueprint is an example of a
scale drawing.
scale factor The ratio used to
enlarge or reduce similar figures.
(p. 253)
factor de escala Razón empleada
para agrandar o reducir figuras
semejantes.
scale model A proportional
model of a three-dimensional
object. (p. 252)
modelo a escala Modelo
proporcional de un objeto
tridimensional.
scalene triangle A triangle with
triángulo escaleno Triángulo que
no congruent sides. (p. 393)
no tiene lados congruentes.
scatter plot A graph with points
plotted to show a possible
relationship between two sets of
data. (p. 548)
diagrama de dispersión Gráfica de
puntos que muestra una posible
relación entre dos conjuntos de
datos.
y
8
6
4
2
x
0
scientific notation A method of
writing very large or very small
numbers by using powers of 10.
(p. 182)
notación científica Método que se
second quartile The median of
segundo cuartil Mediana de un
a set of data. (p. 476)
conjunto de datos.
sector A region enclosed by two
sector Región encerrada por dos
radii and the arc joining their
endpoints. (p. 447)
radios y el arco que une sus
extremos.
usa para escribir números muy
grandes o muy pequeños mediante
potencias de 10.
2
4
6
8
12,560,000,000,000 1.256 1013
Data set: 4, 6, 7, 8, 10
Second quartile: 7
segment A part of a line between
segmento Parte de una línea entre
two endpoints. (p. 378)
dos extremos.
side One of the segments that
lado Uno de los segmentos que
form a polygon. (p. 399)
forman un polígono.
GH
H
G
-ˆ`i
similar Figures with the same
shape but not necessarily the
same size are similar. (p. 244)
semejantes Figuras que tienen la
misma forma, pero no
necesariamente el mismo tamaño.
Glossary/Glosario
G29
ENGLISH
SPANISH
EXAMPLES
simple interest A fixed percent
interés simple Un porcentaje fijo
of the principal. It is found using
the formula I Prt, where P
represents the principal, r the rate
of interest, and t the time. (p. 302)
del capital. Se calcula con la fórmula
I Cit, donde C representa el
capital, i, la tasa de interés y t, el
tiempo.
simplest form A fraction is
mínima expresión Una fracción
8
Fraction: 12
in simplest form when the
numerator and denominator
have no common factors other
than 1. (p. SB8)
está en su mínima expresión cuando
el numerador y el denominador no
tienen más factor común que 1.
Simplest form: 3
simplify To write a fraction or
expression in simplest form.
(p. SB8)
simplificar Escribir una fracción o
expresión numérica en su mínima
expresión.
skew lines Lines that lie in
different planes that are neither
parallel nor intersecting. (p. 384)
líneas oblicuas Líneas que se
encuentran en planos distintos, pore
so no se intersecan ni son paralelas.
$100 is put into an account with
a simple interest rate of 5%.
After 2 years, the account
will have earned
I 100 0.05 2 $10.
2
A
B
E
F
C
D
G
H
and CD
are skew lines.
AE
slant height The distance from
altura inclinada Distancia de la
the base of a cone to its vertex,
measured along the lateral
surface. (p. 504)
base de un cono a su vértice, medida
a lo largo de la superficie lateral.
slope A measure of the steepness
pendiente Medida de la inclinación
de una línea en una gráfica. Razón
de la distancia vertical a la distancia
horizontal.
of a line on a graph; the rise
divided by the run. (p. 345)
Slant
height
rise
3
Slope run
4
y
4
2
(2, 2)
(⫺2, ⫺1)
⫺4
O
2
x
4
⫺2
⫺4
solution of an equation A value
solución de una ecuación Valor o
or values that make an equation
true. (p. 32)
valores que hacen verdadera una
ecuación.
solution of an inequality A
solución de una desigualdad
value or values that make an
inequality true. (p. 140)
Valor o valores que hacen verdadera
una desigualdad.
solution set The set of values that
make a statement true. (p. 136)
conjunto solución Conjunto de
valores que hacen verdadero un
enunciado.
Equation: x 2 6
Solution: x 4
Inequality: x 3 10
Solution: x 7
Inequality: x 3 5
Solution set: x 2
⫺4 ⫺3 ⫺2 ⫺1
solve To find an answer or a
resolver Hallar una respuesta o
solution. (p. 32)
solución.
G30
Glossary/Glosario
0
1
2
3
4
5
6
ENGLISH
sphere A three-dimensional
figure with all points the same
distance from the center.
(p. 508)
SPANISH
EXAMPLES
esfera Figura tridimensional en la
que todos los puntos están a la
misma distancia del centro.
square A rectangle with four
cuadrado Rectángulo con cuatro
congruent sides. (p. 399)
lados congruentes.
square (numeration) A number
cuadrado (en numeración)
raised to the second power. (p. 192)
Número elevado a la segunda
potencia.
square root One of the two
equal factors of a number. (p. 190)
raíz cuadrada Uno de los dos
factores iguales de un número.
stem-and-leaf plot A graph
used to organize and display data
so that the frequencies can be
compared. (p. 533)
diagrama de tallo y hojas Gráfica
que muestra y ordena los datos, y
que sirve para comparar las
frecuencias.
In 52, the number 5 is squared.
16 4 4, or 16 4 4, so 4
and 4 are square roots of 16.
Stem
3
4
5
Leaves
234479
0157778
1223
Key: 3 2 means 3.2
straight angle An angle that
measures 180°. (p. 379)
ángulo llano Ángulo que mide
exactamente 180°.
substitute To replace a variable
sustituir Reemplazar una variable
with a number or another
expression in an algebraic
expression. (p. 6)
por un número u otra expresión en
una expresión algebraica.
Subtraction Property of
Equality The property that states
Propiedad de igualdad de la resta
that if you subtract the same
number from both sides of an
equation, the new equation will
have the same solution. (p. 33)
Propiedad que establece que puedes
restar el mismo número de ambos
lados de una ecuación y la nueva
ecuación tendrá la misma solución.
sum The result when two or
suma Resultado de sumar dos o
more numbers are added. (p. 18)
más números.
supplementary angles Two
angles whose measures have a
sum of 180°. (p. 379)
ángulos suplementarios Dos
surface area The sum of the
areas of the faces, or surfaces, of a
three-dimensional figure. (p. 498)
área total Suma de las áreas de las
ángulos cuyas medidas suman 180°.
Substituting 3 for m in the
expression 5m 2 gives
5(3) 2 15 2 13.
x6
8
6
6
x
2
The sum of 6 7 1 is 14.
30°
150°
caras, o superficies, de una figura
tridimensional.
12 cm
6 cm
8 cm
Surface area 2(8)(12) 2(8)(6) 2(12)(6) 432 cm2
Glossary/Glosario
G31
ENGLISH
SPANISH
EXAMPLES
sistema de ecuaciones Conjunto
de dos o más ecuaciones que
contienen dos o más variables.
x y 3
term (in an expression) The
término (en una expresión) Las
3x2 parts of an expression that are
added or subtracted. (p. 120)
partes de una expresión que se
suman o se restan.
terminating decimal A decimal
number that ends or terminates.
(p. 66)
decimal finito Decimal con un
número determinado de posiciones
decimales.
tessellation A repeating pattern
of plane figures that completely
cover a plane with no gaps or
overlaps. (p. 416)
teselado Patrón repetido de figuras
planas que cubren totalmente un
plano sin superponerse ni dejar
huecos.
theoretical probability The
probabilidad teórica Razón del
ratio of the number of equally
likely outcomes in an event to the
total number of possible
outcomes. (p. 564)
número de resultados igualmente
probables en un suceso al número
total de resultados posibles.
third quartile The median of the
tercer cuartil La mediana de la
upper half of a set of data; also
called upper quartile. (p. 542)
mitad superior de un conjunto de
datos. También se llama cuartil
system of equations A set of
two or more equations that
contain two or more variables.
(p. 131)
superior.
transformation A change in the
size or position of a figure. (p. 410)
x y 1
Term
Term
Lower quartile
Upper quartile
Minimum
Median
Maximum
0
2
4
6
figura a lo largo de una línea recta.
trapecio Cuadrilátero con un par de
exactly one pair of parallel sides.
(p. 399)
lados paralelos.
Glossary/Glosario
12
14
C
J
A′
A′B′C′
C′
J′
M′
K′
L′
M
L
transversal Línea que cruza dos o
más líneas.
trapezoid A quadrilateral with
G32
10
B′
K
transversal A line that intersects
two or more lines. (p. 389)
8
B
ABC
of a figure along a straight line.
(p. 410)
Term
When rolling a number cube,
the theoretical probability of
1
rolling a 4 is 6.
A
traslación Desplazamiento de una
8
6.75
transformación Cambio en el
tamaño o la posición de una figura.
translation A movement (slide)
6x 1 2
5 6
3 4
7 8
B
A
Transversal
C
D
ENGLISH
SPANISH
tree diagram A branching
diagram that shows all possible
combinations or outcomes of an
event. (p. SB23)
diagrama de árbol Diagrama
ramificado que muestra todas las
posibles combinaciones o resultados
de un suceso.
trial In probability, a single
repetition or observation of an
experiment. (p. 556)
prueba En probabilidad, una sola
triangle A three-sided polygon
triángulo Polígono de tres lados.
EXAMPLES
H
T
1 2 3 4 5 6
1 2 3 4 5 6
When rolling a number cube,
each roll is one trial.
repetición u observación de un
experimento.
(p. 392)
Triangle Sum Theorem The
theorem that states that the
measures of the angles in a
triangle add up to 180°. (p. 392)
Teorema de la suma del triángulo
triangular prism A threedimensional figure with two
congruent parallel triangular
bases and whose other faces are
rectangles. (p. 485)
prisma triangular Figura
trinomial A polynomial with
three terms. (p. 590)
trinomio Polinomio con tres
unit analysis The process of
changing one unit of measure to
another. (p. 237)
conversión de unidades Proceso
que consiste en cambiar una unidad
de medida por otra.
unit conversion factor A
factor de conversión de unidades
fraction used in unit conversion
in which the numerator and
denominator represent the same
amount but are in different units.
(p. 237)
Fracción que se usa para la
conversión de unidades, donde el
numerador y el denominador
representan la misma cantidad pero
están en unidades distintas.
unit price A unit rate used to
precio unitario Tasa unitaria que
compare prices. (p. 229)
sirve para comparar precios.
unit rate A rate in which the
second quantity in the
comparison is one unit. (p. 228)
tasa unitaria Una tasa en la que la
segunda cantidad de la comparación
es la unidad.
upper quartile The median of
the upper half of a set of data; also
called third quartile. (p. 542)
cuartil superior La mediana de la
Teorema que establece que las
medidas de los ángulos de un
triángulo suman 180°.
tridimensional con dos bases
triangulares congruentes y paralelas
cuyas otras caras son rectángulos.
4x2 3xy 5y2
términos.
1h
60 min
or 60 min
1h
Cereal costs $0.23 per ounce.
10 cm per minute
Lower quartile
Upper quartile
Minimum
Median
Maximum
mitad superior de un conjunto de
datos; también se llama tercer cuartil.
0
2
4
6
8
Glossary/Glosario
10
12
G33
14
ENGLISH
SPANISH
variable A symbol used to
variable Símbolo que representa
represent a quantity that can
change. (p. 6)
una cantidad que puede cambiar.
vertex (of an angle) The
vértice de un ángulo Extremo
común de los lados del ángulo.
common endpoint of the sides of
the angle. (p. 379)
EXAMPLES
In the expression 2x 3, x is the
variable.
A is the vertex of CAB.
vertex (of a polygon) The
intersection of two sides of the
polygon. (p. 399)
vértice (de un polígono) La
intersección de dos lados del
polígono.
6iÀÌiÝ
A, B, C, D, and E are vertices
of the polygon.
vertex (of a polyhedron) A
point at which three or more
edges of a polyhedron intersect.
(p. 480)
vértice (de un poliedro) Un punto
en el que se intersecan tres o más
aristas de un poliedro.
vertical angles A pair of
ángulos opuestos por el vértice
opposite congruent angles
formed by intersecting lines.
(p. 388)
Par de ángulos opuestos
congruentes formados por líneas
secantes.
6iÀÌiÝ
2
1
3 4
1 and 3 are vertical angles.
vertical line test A test used to
prueba de linea vertical Prueba
determine whether a relation is a
function. If any vertical line
crosses the graph of a relation
more than once, the relation is
not a function. (p. 327)
utilizada para determinar si una
relación es una función. Si una línea
vertical corta la gráfica de una
relación más de una vez, la relación
no es una función.
volume The number of cubic
volumen Número de unidades
cúbicas que se necesitan para llenar
un espacio.
units needed to fill a given space.
(p. 485)
5
y
-5
5
-5
4 ft
3 ft
12 ft
Volume 3 4 12 144 ft3
x-axis The horizontal axis on a
eje x El eje horizontal del plano
coordinate plane. (p. 322)
cartesiano.
x-axis
O
G34
Glossary/Glosario
x
ENGLISH
SPANISH
EXAMPLES
x-coordinate The first number in
an ordered pair; it tells the
distance to move right or left from
the origin (0, 0). (p. 322)
coordenada x El primer número de
5 is the x-coordinate in (5, 3).
y-axis The vertical axis on a
eje y El eje vertical del plano
coordinate plane. (p. 322)
cartesiano.
un par ordenado; indica la distancia
que debes moverte hacia la
izquierda o la derecha desde el
origen, (0, 0).
y-axis
O
y-coordinate The second
coordenada y El segundo número
number in an ordered pair; it tells
the distance to move up or down
from the origin (0, 0). (p. 322)
de un par ordenado; indica la
distancia que debes avanzar hacia
arriba o hacia abajo desde el origen,
(0, 0).
zero pair A number and its
par nulo Un número y su opuesto,
cuya suma es 0.
opposite, which add to 0. (p. 42)
3 is the y-coordinate in (5, 3).
18 and 18
Glossary/Glosario
G35
Index
Absolute value, 15
Abstract art, 599
Academic Vocabulary, 4, 62, 114, 166,
222, 272, 320, 376, 432, 476, 528, 588
Acute angles, 379
Acute triangles, 392, SB17
Addition
Associative Property of, 116–117
of decimals, 74, SB12
of fractions, 75, SB10
with unlike denominators, 87–89,
SB10
of integers, 18–19
of mixed numbers, 87–89
of polynomials, 603–604
modeling, 602
of rational numbers, 74–75
properties, 23, 33, 116
solving equations by, 32–34
solving inequalities by, 140–141
Addition Property of Equality, 33
Additive inverse, 18
Adjacent angles, 388
Alaska, 282
Algebra
The development of algebra skills and
concepts is a central focus of this
course and is found throughout this
book.
absolute value, 15
combining like terms, 120–121, 124,
596–597
equations, 32
addition, 32–33
checking solutions of, 32, 33, 37–38
decimal, solving, 94, 98
division, 37–38
linear, 330, 331
multi-step, see Multi-step equations
multiplication, 37–38
solutions of, 32
subtraction, 32–33
systems of, 131
two-step, see Two-step equations
expressions, 6–7, 10–11, 120–121
algebraic, 6–7
numerical, 6–7
variables and, 6–7
functions, 326
cubic, 338–339
graphing, 326–327, 334–335,
338–339
linear, see Linear functions
quadratic, 334–335
tables and, 326
inequalities, see Inequalities
I2
Index
linear functions, 330–331
multi-step equations, 124–125
properties
Addition, of Equality, 33
Associative, 116
of circles, 446–447
Commutative, 116
Distributive, 117
Division, of Equality, 37
Identity, 32, 37
Multiplication, of Equality, 38
Subtraction, of Equality, 33
proportions,
and indirect measurement, 248–249
in scale drawings, models, and
maps, 252–253, 257–258
solving, 232–234
solving equations
by adding or subtracting, 32–34
modeling, 41–42
by multiplying or dividing, 37, 38
two-step, 43–45, 98–99
with variables on both sides,
129–131
solving inequalities
by adding or subtracting, 140–141
by multiplying or dividing, 144–145
two-step, 148–149
tiles, 41–42, 128, 594–595, 602, 607,
616–617
translating between words and math,
63
translating words into math, 10–11
variables, 6–7
on both sides, solving equations
with, 128–131
dependent, 344
independent, 344
isolating, 32
solving for, 32
Algebra tiles, 41–42, 128, 594–595, 602,
607, 616–617
Algebraic expressions, 6, 10–11
evaluating, 6–7
simplifying, 120–121
writing, 10–11
Algebraic inequalities, 136
Alternate exterior angles, 389
Alternate interior angles, 389
American Samoa, 396
Analysis
dimensional, 237–239
unit, 237
Anamorphic images, 498
Angles, 379
acute, 379
adjacent, 388
alternate exterior, 389
alternate interior, 389
bisector, 382
central, of a circle, 447
classifying, 379
complementary, 379
congruent, 406
corresponding, 389
in polygons, 403
obtuse, 379
of quadrilaterals, 403
of triangles, 392–393
points and lines and planes and,
378–380
relationships of, 388–389
right, 379
straight, 379
supplementary, 379
vertical, 388
Animals, 81
Answer choices, eliminating, 56–57
Answering context–based test items,
582–583
Ant lions, 505
Applications
Animals, 81
Architecture, 23, 195, 254, 255, 352, 493
Art, 194, 247, 500, 514, 604
Astronomy, 35, 139, 178, 187, 335
Banking, 28
Business, 28, 39, 123, 131, 132, 139,
143, 178, 226, 281, 337, 513, 597,
606, 609, 611
Chemistry, 17
Computer, 193
Construction, 352, 620
Consumer Economics, 80, 300
Consumer Math, 45, 46, 100, 118, 142,
559
Cooking, 226
Economics, 21, 151
Energy, 77
Entertainment, 9, 150, 226, 231, 453
Environment, 225, 333
Finance, 9, 126, 281
Food, 240, 453
Games, 195, 573
Geography, 248, 254, 277, 285
Geometry, 122, 127, 169, 182, 183, 606
Health, 19, 81, 540, 615
History, 187, 208, 209
Hobbies, 46, 122, 183, 195, 227, 336
Home Economics, 329
Language Arts, 143, 287
Life Science, 73, 101, 171, 174, 175, 187,
240, 241, 253, 284, 289, 290, 295,
361, 489, 505, 511, 568, 598
Literature, 297
Manufacturing, 280, 352
Measurement, 69, 90
Meteorology, 73
Money, 307
Multi-Step, 39, 80, 90, 91, 97, 199, 209,
231, 277, 287, 297, 442, 502
Music, 40, 449, 487
Nutrition, 39, 96, 141
Patterns, 174, 286
Recreation, 40, 79, 88, 126, 196, 284, 515
Safety, 352, 561
School, 72, 80, 149, 573
Science, 7, 17, 28, 29, 36, 91, 96, 127,
133, 187, 199, 226, 228, 281, 288,
297, 336, 507, 545
Social Studies, 25, 35, 71, 86, 146, 188,
282, 286, 396, 438, 489, 491, 507, 545
Sports, 14, 27, 38, 68, 72, 74, 76, 123,
127, 151, 194, 240, 281, 328, 336,
453, 502, 541
Transportation, 240, 241, 593
Travel, 125, 126
Weather, 119, 325
Approximating square roots, 197
Arc, of a circle, 446
Architecture, 23, 195, 254, 255, 352, 493
Are You Ready?, 3, 61, 113, 165, 221, 271,
375, 431, 475, 527, 587
Area, 435
of circles, 451
of irregular figures, 458–459
lateral, 498
of parallelograms, 435–436
of rectangles, 435–436
of squares, 192
surface, 498
of cones, 504–505
of cylinders, 496–499
of prisms, 496–499
of pyramids, 504–505
of spheres, 509
of trapezoids, 440–441
of triangles, 440–441
Arguments, writing convincing, 223
Art, 194, 247, 500, 514, 604
Ashurbanipal, King, 446
Aspect ratio, 231
Assessment
Chapter Test, 55, 109, 159, 217, 265,
315, 369, 427, 469, 523, 581, 629
Cumulative Assessment, 58–59,
110–111, 162–163, 218–219, 268–269,
316–317, 372–373, 428–429,
472–473, 524–525, 584–585,
630–631
Mastering the Standards, 58–59,
110–111, 162–163, 218–219, 268–269,
316–317, 372–373, 428–429,
472–473, 524–525, 584–585,
630–631
Ready to Go On?, 30, 48, 92, 102, 134,
152, 190, 210, 242, 258, 292, 308,
342, 404, 420, 444, 462, 494, 516,
554, 574, 600, 622
Strategies for Success
Any Type: Using a Graphic, 470–471
Extended Response: Write Extended
Responses, 370–371
Gridded Response: Write Gridded
Responses, 160–161
Multiple Choice
Answering Context-Based Test
Items, 582–583
Eliminate Answer Choices, 56–57
Short Response: Write Short
Responses, 266–267
Study Guide: Review, 52–54, 106–108,
156–158, 214–216, 262–264, 312–314,
366–368, 424–426, 466–468, 520–522,
578–580, 626–628
Associative Property
of Addition, 116–117
of Multiplication, 116–117
Astronomy, 35, 139, 178, 187, 335
Axes, 322
Back-to-back stem-and-leaf plot,
533–534
Bacteria, 171, 211
Balance of trade, 21
Balance scale, 32
Banking, 28
Bar graphs, 531, SB18
histograms, SB20
Base, 480–481
of polyhedrons, 480
Bases, 168
Benchmarks, 278
Berkeley, 119
Best fit, lines of, 549
Biased samples, SB22
Binary fission, 171
Binomials, 590
multiplication of, 616–617, 618–619
special products of, 619
Bisecting figures, 382
Bisectors
constructing, 382–383
perpendicular, 382
Blood pressure, 236
Board foot, 597
Boeing 747, 443
Book, using your, for success, 5
Box-and-whisker plots, 542–544,
creating, 543, 547
British thermal units (Btu), 77
Buffon, Comte de, 576
Business, 28, 39, 123, 131, 132, 139, 143,
178, 226, 281, 337, 513, 597, 606,
609, 611
Calculator
approximating square roots on a, 197
graphing, see Graphing calculator
California locations
Berkeley, 119
Carlsbad, 515
Joe Matos Cheese Factory, 240
Legoland, 515
Mammoth Lakes, 374
Menlo Park, 164
Monterey Bay Aquarium, 240
Rincon Park, 220
San Diego, 270
San Francisco, 220
Santa Monica International Chess Park,
195
Santa Rosa, 240
Stanford Linear Accelerator Center, 164
Yosemite National Park, 252
California Link, 9, 77, 143, 195, 240, 515
Capacity, 512
customary units of, SB15
metric units of, SB15
Carlsbad, CA, 515
Caution! 10, 26, 169, 200, 436
Celsius temperature
scale, 103, 331
Center
of a circle, 446
of rotation, 410
Central angles, 447
Central tendency, measures of, 538
Certain event, 556
Challenge
Challenge exercises are found in
every lesson. Some examples: 9, 13,
17, 21, 25
Change
percents of, 294
rates of, 344–345, see also Rates of
change
Chapter Project Online, 2, 60, 112, 164,
220, 270, 318, 374, 474, 526, 586
Chapter Test, 55, 109, 159, 217, 265, 315,
369, 427, 469, 523, 581, 629, see also
Assessment
Chemistry, 17
Chess, 195
Choose a Strategy, 9, 29, 86, 133, 171, 241,
287, 297, 337, 396, 502, 515, 606, 611
Chord, of a circle, 446
Circle(s), 446–447, 450–451
arcs of, 446
area of, 451
central angles, 447
chords of, 446
circumference, 450
diameter, 446, 450
graphs, 447, SB21
great, 508
properties of, 446–447
radius, 446, 450
Circle graphs, 447, SB21
interpreting, 447
making, SB21
reading, 447
Circumference, 450–451
Classifying
angles, 379
polygons, 399, SB16–SB17
polynomials, 590–591
quadrilaterals, 399
real numbers, 200–201
three-dimensional figures, 481
triangles, 392–393, SB17
Closed circle, 137
Coefficients, 120
Index
I3
Combining like terms, 120–121
Combining transformations, 415
Commission, 298
Commission rate, 298
Common denominator, 70, 87
Common multiple, SB6
least (LCM), SB6
Communicating Math
apply, 487
choose, 229
compare, 19, 27, 137, 149, 169, 289,
335, 436, 505, 509, 544, 561, 604,
609, 613
compare and contrast, 481
decide, 193
demonstrate, 285
describe, 19, 23, 34, 71, 99, 117, 121,
141, 149, 186, 193, 225, 234, 253,
280, 331, 335, 359, 412, 417, 441,
487, 491, 513, 539, 550, 566, 591
determine, 79, 186, 197, 280
discuss, 197
draw, 447
explain, 7, 15, 19, 23, 34 , 67, 71, 75, 84,
89, 95, 99, 117, 131, 137, 141, 145,
169, 177, 181, 186, 193, 201, 207, 225,
234, 239, 249, 253, 275, 289, 323,
331, 351, 389, 394, 400, 407, 417, 447,
481, 500, 505, 509, 513, 539, 544,
591, 604, 609
express, 11, 173, 436
give, 11, 67, 131, 145, 225, 229, 239,
561
give an example, 7, 75, 79, 89, 225,
275, 351, 539, 566, 571, 597, 619
identify, 327
list, 27, 125, 177
model, 487, 491
name, 285, 323
show, 169, 275, 285
suppose, 27, 323
tell, 7, 84, 89, 121, 125, 173, 181, 201, 234,
389, 407, 571, 597
Think and Discuss
Think and Discuss is found in every
lesson. Some examples: 7, 11, 15,
19, 23
use, 201
Write About It
Write About It exercises are found in
every lesson. Some examples: 9, 13,
17, 21, 25
Commutative Property
of Addition, 116–117
of Multiplication, 116–117
Comparing
customary units and metric units, SB15
data sets, 544
numbers in scientific notation, 186
rational numbers, 70–71
ratios, 225, 232
volumes and surface areas, 509
Comparing and ordering whole
numbers, SB3
I4
Index
Compass, 382–383
Compatible numbers, 117, 278
Complementary angles, 379
Composite figures
area of, 436
perimeter of, 436
volume of, 487
Composite numbers, SB5
Compound events, 569–571
Compound inequalities, 137
Compound interest, 302, 304
computing, 304–305
exploring, 302
Computer graphics, 398
Computer spreadsheets, 530–531
Computer, 193
Computing compound interest, 302,
304–305
Concept Connection, 49, 103, 153, 211,
259, 309, 363, 421, 463, 517, 575, 623
Concept maps, 433
Conclusions, see Reasoning
Concorde, 443
Cones, 481, 490
nets of, 503
right, 504
surface area of, 504–505
volume of, 490–491
Congruence, 406–407
Congruent angles, constructing,
382–383
Congruent figures, 382
Congruent triangles, 406
Constant of variation, 357
Constant rate of change, 344–345
Constants, 120
Constructing
bisectors and congruent angles,
382–383
graphs, using spreadsheets for,
530–531
nets, 496–497, 503
scale drawings and scale models,
256–257
Construction, 352, 620
Consumer application, 559
Consumer Economics, 80, 300
Consumer Math, 45, 46, 100, 118, 142,
559
Context-based test items, answering,
582–583
Converse of the Pythagorean Theorem,
206–207
Conversion factors, 237, SB15
units of measure, 237–239
Conversions, metric, SB15
Converting, 224
customary units to metric units, SB15
metric units to customary units, SB15
Convincing arguments, writing, 223
Cooking, 226
Coordinate geometry, 398–400
Coordinate plane, 322–323
graphing on a, 330, 334, 338
Coordinates, 322–323
Cornell system of note taking, 167
Correlation, 549–550
Correlation types, 549
Correspondence, 406
Corresponding angles, 389
Corresponding sides, 406–407
Countdown to Mastery, CA4–CA27
Creating
box-and-whisker plots, 547
graphs, using spreadsheets for,
530–531
histograms, SB20
scatter plots, 553
tessellations, 416–417
Cross products, 232
Cubic functions, 338–339
Cubic units, 485
Cullinan diamond, 96
Cumulative Assessment, 58–59, 110–111,
162–163, 218–219, 268–269, 316–317,
372–373, 428–429, 472–473, 524–525,
584–585, 630–631, see also
Assessment
Cupid’s Span, 220
Customary system of measurement,
237–239, SB15
converting between metric and, SB15
Cylinders, 481, 485
nets of 497
surface area of, 498–500
exploring, 496–497
volume of, 485–487
da Vinci, Leonardo, 506
Data, see also Displaying and organizing
data
bar graphs, 531, SB18
box-and-whisker plots, 543–544
circle graphs, 477, SB21
collecting, 531
displaying, 447, 530–534, 543–544,
SB18–SB21
double-bar graphs, SB18
histograms, SB20
line graphs, SB19
line plots, 532
organizing, 532–534
stem-and-leaf plots, 533
back-to-back, 533–534
Decagon, SB16
Decimals
addition of, 74, 75, 94
comparing, 71
converting between percents and
fractions and, 274–275
division of, 83
equivalent fractions and, 67
fractions and, 66
multiplication of, 79, 94
by powers of ten, SB7
ordering, 71
repeating, 64–65, 66–67
rounding, SB2
solving equations with, 94
subtraction of, 74, 75, 94
terminating, 64–65, 66–67
writing as percents, 274–275
Decrease, percent of, 294–295
Deductive reasoning, SB24
Degrees of polynomials, 591
Denominator(s), 66
like, adding and subtracting with, 75
unlike, adding and subtracting with,
87–88
Density, 228
Density Property of real numbers,
201
Dependent events, 569–571
finding probability of, 570–571
Dependent variable, 344
Devils Postpile National Monument, 374
Diagonals, 169
Diagram
tree, SB23
Diameter, 446, 450
Diastolic blood pressure, 236
Dimensional analysis, 237–239
Dimensions
changing, exploring effects of, 486,
505, 512–513
Direct variation, 357–359
Discounts, 295
Disjoint events, 566
Displaying and organizing data, 447,
530–534, 543–544, SB18–SB21
bar graphs, 531, SB18
box-and-whisker plots, 543–544
circle graphs, 447, SB21
double-bar graphs, SB18
histograms, SB20
line graphs, SB19
line plot, 532
stem-and-leaf plots, 533
back-to-back, 533–534
Distracter, 56
Distributive Property, 117, 121, 597
Divisibility rules, SB4
Division
of decimals, 83, SB13
and mixed numbers, 82
by powers of ten, SB7
of fractions, 82–84
of integers, 26–27
long, SB7
of monomials, 180–181
of numbers in scientific notation, 189
of powers, 176–177
by powers of ten, SB7
of rational numbers, 82–84, SB11, SB13
solving equations by, 37–39
solving inequalities by, 144–145
of whole numbers, SB7
Division Property of Equality, 37
DNA model, 253
Double-bar graphs, SB18
Draw three-dimensional figures,
477
Drawings, scale, 252–253
Duckweed plants, 187
Earth, 186, 187, 508
Earthquakes, 563
Economics, 21, 151, 301
Edge, of a three-dimensional figure,
480
Edison, Thomas, 329
Effective notes, taking, 167
Eggs, 511
Eliminating answer choices, 56–57
Energy, 77
Enlargement, 253
Entertainment, 9, 150, 226, 231, 453
Environment, 225, 333
Equality
Addition Property of, 32
Division Property of, 37
Multiplication Property of, 38
Subtraction Property of, 33
Equally likely outcomes, 564
Equations, 32
graphs of, 330–331, 334–335, 338–339
linear, see Linear equations
multi-step, see Multi-step equations
with no solutions, 130
one-step, see One-step equations
solutions of, 32
solving, see Solving equations
systems of, see Systems of equations
and tables and graphs, 326, 330, 331,
334, 335, 338, 339
two-step, see Two-step equations
with variables on both sides,
modeling, 128
Equilateral triangles, 393, SB17
Equivalent expressions, 120
Equivalent fractions
decimals and, 274
Equivalent ratios, 224–225, 232
Escher, M. C., 419
Estimate, 278
Estimating
square roots, 196–197
with percents, 278–280
Estimation, 24, 86, 90, 171, 179, 194, 231,
281, 493, 541
Evaluating
algebraic expressions, 6–7
expressions using the order of
operations, 169
expressions with rational numbers, 75,
83, 89
negative exponents, 172–173
Events, 556
disjoint, 566
independent, see Independent events
mutually exclusive, 566
Exam, preparing for your final, 589
Experiment, 556
Experimental probability, 560–561
Exploring
compound interest, 302
effects of changing dimensions, 486,
505, 512–513
Pythagorean Theorem, 204
rational numbers, 64–65
three-dimensional figures, 478–479
volume of prisms, 484
Exponential form, 168
Exponents, 168–169
integer, 172–173
negative, 172–173
properties of, 176–177
Expressions
algebraic, 6–7, 10–11
simplifying, 120–121
writing, 10–11
equivalent, 120
evaluating, with rational numbers, 75,
83, 89
numerical, 6–7
variables and, 6–7
Extended Response, 91, 175, 231, 297,
370–371, 391, 515, 536, 546, 611
Write Extended Responses, 370–371
Extra Practice, EP2–EP25
Face
lateral, 498
of a three-dimensional figure, 480
Factor(s), SB4
common, SB6
conversion, 237
scale, 253
Factorization, prime, SB5
Fahrenheit scale, 331
Fahrenheit temperature
converting between Celsius and,
103, 331
scale, 103
Fair objects, 564
Ferris wheel, 430, 453
Figures
bisecting, 382
built of cubes, 498
composite, 436, 487
congruent, 382
geometric, 374–525
irregular, area of, 458–459
similar, see Similar figures
three-dimensional,
Index
I5
see Three-dimensional figures
two-dimensional,
see Two-dimensional figures
Final Exam, study for a, 589
Finance, 9, 126, 281
Finding
numbers when percents are known,
288–289
percents, 283–285
probability of dependent events,
570–571
probability of independent events,
569–570
surface area of prisms and cylinders,
498–500
surface area of pyramids, 504
surface area of similar solids, 513
unit prices to compare costs, 229
volume of prisms and cylinders,
485–487
volume of pyramids and cones,
490–491
volume of similar solids, 513
Fireworks, 591
Flip, see Reflection
Fluid ounce, SB15
Focus on Problem Solving
Look Back, 93, 601
Make a Plan, 135, 293, 495, 555
Solve, 31, 191, 243, 343
Understand the Problem, 405
FOIL mnemonic, 618
Food, 240, 453
Foot, SB15
Formulas, learning and using, 477,
see also inside back cover
Fraction(s)
addition of, 75
with unlike denominators, 87–89
decimals and percents and, 274–275
division of
and mixed numbers, 82–84
equivalent, see Equivalent fractions
improper, SB9
multiplication of, and mixed numbers,
78–79
relating, to decimals and percents,
274–275
simplest form, SB8
solving equations with, 94–95, 124–125
subtraction of, 75
with unlike denominators, 87–89
unit, 104
writing as mixed numbers, SB9
writing as terminating and repeating
decimals, 66
Fraction form, dividing rational numbers
in, 82
Frequency tables, SB20
Fulcrum, 232
Functions, 326–339
cubic, 338–339
linear, 330–331
I6
Index
quadratic, 334–335
tables and, 326, 330, 331, 334, 335,
338, 339
graphs and, 330, 331, 334, 335, 338, 339
Gallon, SB15
Game Time
24 Points, 154
Buffon’s Needle, 576
Circles and Squares, 464
Coloring Tessellations, 422
Copy-Cat, 260
Crazy Cubes, 50
Egg Fractions, 104
Egyptian Fractions, 104
Equation Bingo, 212
Magic Cubes, 518
Magic Squares, 212
Math Magic, 50
Percent Puzzlers, 310
Percent Tiles, 310
Planes in Space, 518
Polygon Rummy, 422
Rolling for Tiles, 624
Shape Up, 464
Short Cuts, 624
Squared Away, 364
Tic-Frac-Toe, 260
Trans-Plants, 154
What’s Your Function?, 364
Game Time Extra, 104, 154, 212, 260,
310, 364, 422, 464, 518, 576, 624
Games, 195, 573
Gas mileage, 593
GCD (greatest common divisor), SB6
Geography, 248, 254, 277, 285
Geometric patterns, SB16
Geometry
angles, 379–380, 388–389, 392–394,
406–407
area, 435–436, 440–441, 451
building blocks of, 378–380
circles, 446–447, 450–451
area of, 451
circumference of, 450
circumference, 450
cones, 481
volume of, 490–492
surface area of, 504–505
constructing bisectors and congruent
angles, 382–383
congruent figures, 406–407
coordinate, 398–400
cylinders, 481
volume of, 485–487
surface area of, 496–497, 498–499
lines, 378–380
parallel, 384–385, 388–389
perpendicular, 384–385, 388
of reflection, 410
skew, 384
transversal, 388–389
nets, 496–497, 503
parallel line relationships, 389
parallelograms, 399
area of, 435
perimeter of, 434
planes, 378
polygons, 399
finding angle measures in, 403
regular, SB16
polyhedrons, 480
prisms, 484, 485–487
volumes of, 484, 485–487
surface area of, 496–497,
498–499
pyramids, 480, 490–491
volume of, 490–491
surface area of, 504–505
quadrilaterals, 399, 403, SB16, SB17
rays, 378
rectangles, 434–436
area of, 435–436
perimeter of, 434–436
rhombuses, 399, SB17
rhombuses, 399, SB17
scale drawings and scale models,
252–253, 256–257, 259
similar figures, 244–245
surface area and volume, 512–513
sphere, 508–509
squares, 399, SB17
surface area, 498–500, 503, 504–505,
509
tessellations, 416–417
three-dimensional figures, 474–525
introduction to, 480–481
modeling, 256–257
trapezoids
area of, 440–441
perimeter of, 439
triangles, 392–394, SB16–SB17
area of, 440–441
perimeter of, 439
two-dimensional figures, 430–473
volume, 484–487, 490–491
Giant Ocean Tank, 489
Giant shark, 288, 289
Gigabyte, 179
Global temperature, 73
go.hrw.com, see Online Resources
Googol, 179
Gram, SB15
Graph(s)
bar, 531, SB18
circle, 447, SB21, see also Circle graphs
constructing, using spreadsheets for,
530–531
creating, using technology for, 530
double-bar, SB18
of equations, 330–331, 334–335,
338–339
interpreting, 353–354
line, 330–331, SB19
tables and, 326, 330, 334, 338
Graphing
on a coordinate plane, 322–323
inequalities, 137, 140–141, 144, 148–149
integers on a number line, 14
linear equations, 330
linear functions, 330–331
points, 14, 322–323
Technology Labs, see Technology Lab
transformations, 410–412, 415
Graphing calculator
creating box-and-whisker plots, 547
creating scatter plots, 553
multiplying and dividing numbers in
scientific notation, 189
Great circle, 508
Great Lakes, 31
Great Pyramid of Giza, 491
Greatest common divisor (GCD), SB6
Gridded Response, 9, 21, 25, 36, 40, 69,
77, 86, 101, 123, 127, 147, 160–161, 171,
209, 236, 241, 247, 287, 291, 301, 337,
352, 361, 381, 402, 409, 443, 449, 453,
471, 502, 507, 511, 559, 568, 573, 593,
606, 621
Write Gridded Responses, 160–161
Hands-On Lab
Angles in Polygons, 403
Combine Transformations, 415
Construct Bisectors and Congruent
Angles, 382–383
Construct Scale Drawings and Scale
Models, 256–257
Explore Compound Interest, 302
Explore Rational Numbers, 64–65
Explore the Pythagorean Theorem, 204
Explore Three-Dimensional Figures,
478–479
Explore Volume of Prisms, 484
Find Surface Areas of Prisms and
Cylinders, 496–497
Find Volumes of Prisms and Cylinders,
484
Identify and Construct Altitudes, 397
Make a Scale Model, 257–258
Model Equations with Variables on
Both Sides, 128
Model Polynomial Addition, 602
Model Polynomial Subtraction, 607
Model Polynomials, 594–595
Model Two-Step Equations, 41–42
Multiply Binomials, 616–617
Nets of Cones, 503
Nets of Prisms and Cylinders, 496
Hawaiian alphabet, 287
Health, 19, 81, 540, 615
Heart rate
maximum, 615
target, 615
Height
of parallelograms, 435–436
slant, 504
using indirect measurement to find,
248–249
using scales and scale drawings to
find, 512–513
Helpful Hint, 11, 18, 32, 34, 38, 44, 67,
117, 120, 129, 130, 137, 140, 180, 193,
205, 207, 232, 285, 406, 410, 435, 480,
508, 618
Hemispheres, 508
Heptagons, SB16
Hexagons, 403, SB16
Hill, A. V., 621
Histograms, SB20
History, 187, 208, 209, 483
Hobbies, 46, 122, 183, 195, 227, 336
Home Economics, 329
Homework Help Online
Homework Help Online is available
for every lesson. Refer to the
go.hrw.com box at the beginning of
each exercise set. Some examples: 8,
12, 16, 20, 24
Hot Tip!, 57, 59, 111, 161, 163, 219, 267,
269, 317, 371, 471, 525, 583, 585, 631
Hurricanes, 325, 545
Hypotenuse, 205
Ice Hotel, 17
Identifying
irrational numbers, 200–201
proportions, 232–233
right triangles, 206–207
Identity Property of Addition, 32
Identity Property of Multiplication, 37
Image(s), 410
anamorphic, 498
Impossible event, 556
Improper fractions, SB9
Inch, SB15
Increase, percent of, 294
Independent events, 569–571
finding probability of, 569–570
Independent variable, 344
Indirect measurement, 248–249
Inductive reasoning, SB24
Industrial supplies, 21
Inequalities, 136–137
algebraic, 136
compound, 137
graphing, 137, 140–141, 144
solving,
by adding or subtracting, 140–141
by multiplying or dividing, 144–145
translating word phrases into, 136
two-step, solving, 148–149
writing, 136, 141
compound, 137
Input, 326
Integer exponents, 172–173
Integers, 14
absolute value, 15
addition of, 18–19
comparing, 14
division of, 26–27
multiplication of, 26–27
and order of operations, 27
ordering, 14–15
subtraction of, 22–23
Interest, 303
compound, see Compound interest
rate of, 303
simple, 303–304
Interpreting
circle graphs, 447
graphics, 529
graphs, 353–354
Interstate highway system, 47
Inverse operations, 32
Inverse Property
of Multiplication, 82
Inverse
additive, 18
multiplicative, 82
Investment time, 303
Ions, 36
Irrational numbers, 200
Irregular figures, area of, 458–459
Isolating the variable, 32
Isosceles triangles, 393, SB17
It’s in the Bag!
A Worthwhile Wallet, 261
Canister Carry-All, 105
Graphing Tri-Fold, 365
It’s a Wrap, 213
Note-Taking Taking Shape, 51
Origami Percents, 311
Perfectly Packaged Perimeters, 465
Picture Envelopes, 155
Polynomial Petals, 625
Probability Post-Up, 577
Project CD Geometry, 423
The Tube Journal, 519
Journal, math, keeping a, 321
Jupiter, 186
Kasparov, Garry, 195
Kente cloth, 421
Kilobyte, 179
Kilogram, SB15
Kiloliter, SB15
Kilometer, SB15
Kilowatt-hour, 39
Kite(s), SB17
Krill, 175
Kwan, Michelle, 410
Index
I7
Lab Resources Online, 41, 64, 128, 189,
204, 382, 478, 484, 496, 503, 530, 547,
553, 594, 602, 607, 616
Landscaping, 455
Language Arts, 143, 287
Lateral area, 498
Lateral faces, 498
Lateral surface, 499
LCD (least common denominator), 70
LCM (least common multiple), 70
Leaf, 533
Least common denominator (LCD), 70,
87–88
Least common multiple (LCM), 70, SB6
Lee, Harper, 297
Leg, of a triangle, 205
LEGOLAND, 515
Length
customary units of, SB15
metric units of, SB15
Lessons, reading, for understanding, 115
Life Science, 73, 101, 171, 174, 175, 187,
240, 241, 253, 289, 290, 295, 361, 489,
505, 511, 568, 598, 621
Lift, 443
Light bulb filament, 329
Light sticks, 281
Like denominators, adding and
subtracting with, 74–75
Like terms, 120, 596
solving equations with, 124–125
Lincoln, Abraham, 88
Line graphs, SB19
Line plots, 532
Line segments, 378
Line(s), 378
of best fit, 549
graphing, 330–331
parallel, 384–385
perpendicular, 384–385
points and planes and angles and,
378–380
of reflection, 410
segments, 378
skew, 384–385
slope of a, 349–351
transversals to, 389
Linear equations, 330
graphing, 330–331
Linear functions, 330
graphing, 330–331
Link
Animals, 81
Architecture, 255, 493
Art, 247, 419, 599
Business, 606
Economics, 21, 301
Energy, 77
Entertainment, 9
I8
Index
Environment, 333
Games, 195
Health, 236
History, 209, 483
Home Economics, 329
Language Arts, 143
Life Science, 101, 171, 175, 187, 289,
361, 489, 505, 511, 568, 621
Literature, 297
Meteorology, 73
Money, 307
Recreation, 88, 515
Science, 17, 29, 91, 133, 175, 281
Social Studies, 25, 47, 291, 414, 591
Sports, 127, 541
Weather, 325
Liquid mirror, 335
Liter, SB15
Literature, 297
Long division, 83, SB7
Louvre Pyramid, 245, 493
Lower quartile, 542–543
Luxor Hotel, 352
Magic squares, 212
Making
circle graphs, SB21
conjectures, SB24
scale models, 257–258
Mammoth Lakes, CA, 374
Manufacturing, 280, 352
Map, concept, 433
Mars, 187
Mass, metric units of, SB16
Mastering the Standards, 58–59,
110–111, 162–163, 218–219, 268–269,
316–317, 372–373, 428–429, 472–473,
524–525, 584–585, 630–631, see also
Assessment
Math
translating between words and, 63
translating words into, 10–11
Math expressions
translating, into word phrases, 11
translating word phrases into, 10
Math journals, keeping, 321
Matrushka dolls, 86
Maximum, 543
Mean, 537–538
Measurement, 69, 90
conversion tables, SB15
customary system of, 237–239
indirect, 248–249
metric system of, 237–239, SB15
Measures of central tendency and
range, 537–538
Median, 537–538
Menkaure Pyramid, 209
Merced River, 112
Mercury (planet), 35, 186
Metamorphoses, 419
Meteorites, 535
Meteorology, 73
Meter, SB15
Methane, 333
Metric conversions, 237, SB15
Metric system of measurement, SB15
converting between customary and,
SB15
Midpoint, 393
Mile, SB15
Milligram, SB15
Milliliter, SB15
Millimeter, SB15
Minimum, 543
Mirror, liquid, 335
Mixed numbers,
addition of, 87–88
dividing fractions and, 82–84
equivalent fractions and, SB9
multiplying fractions and, 78–79
subtraction of, 87
Mode, 537
Modeling
equations with variables on both sides,
128
polynomial addition, 602
polynomial subtraction, 607
polynomials, 594–595
two-step equations, 41–42
Models
scale, 252–253, 259, see also Scale
models
Mona Lisa, 247
Money, 38, 307
Monomials, 180
division of, 180–181
multiplication of, 180
multiplication of polynomials by,
612–613
raising, to powers, 181
square roots of, 193
Monterey Bay Aquarium, 240
Mountain bikes, 541
Multiple,
least common (LCM), 70, SB6
Multiple Choice
Multiple Choice test items are found
in every lesson. Some examples: 9,
13, 17, 21, 25
Answering Context-Based Test Items,
582–583
Eliminate Answer Choices, 56–57
Multiplication
Associative Property of, 116–117
of binomials, 616–617, 618–619
of decimals, 79, 94
of fractions
and mixed numbers, 78–79
of integers, 26–27
of monomials, 180
of numbers in scientific notation,
189
of polynomials, by monomials,
612–613
of powers, 176
by powers of ten, 184, SB7
properties, 38
of rational numbers, 78–79
solving equations by, 37–39
solving inequalities by, 144–145
Multiplication Property of Equality,
38
Multiplicative inverse, 82
Multi-Step, 39, 80, 90, 91, 97, 199, 209,
231, 287, 296, 438, 440, 502
Multi-Step Application, 439, 619
Multi-step equations
solving, 124–125, 128–131
Muscle contractions, 621
Music, 40, 449, 487
Mutually exclusive events, 566
Negative correlation, 549
Negative exponents, 172–173
Negative slope, 349
Neptune, 187
Nets
of cones, 503
of prisms and cylinders, 496–497
Newborns, 274
Newtons (N), 34
n-gons, SB16
Niagara Falls, 91
Nickels, 275
Nielsen Television Ratings, 283
No correlation, 549
Nonagons, SB16
Notation
scientific, see Scientific notation
set-builder, 142
Note-Taking Strategies, see Reading and
Writing Math
Notes, taking effective, 167
Number line, 18
Numbers
compatible, 278
composite, SB5
division of, in scientific notation, 189
finding, when percents are known,
288–289
irrational, 200
mixed, SB9, see also Mixed numbers
multiplication of, in scientific notation,
189
percents of, 283–284
prime, SB5
rational, 60–111, 200–201, see also
Rational numbers
real, 200–201
Numerator, 66
Numerical expressions, 6–7
Nutrition, 39, 96, 141, 356
Obtuse angles, 379
Obtuse triangles, 392, SB17
Ocean trenches, 29
Octagons, SB16
Of Mice and Men (Steinbeck), 143
One-step equations
solving, with decimals, 94
solving, with fractions, 94–95
solving, with integers, 32–34, 37–38
solving, with rational numbers, 94–95
Online Resources
Chapter Project Online, 2, 60, 112, 164,
220, 270, 318, 374, 474, 526, 586
Game Time Extra, 104, 154, 212, 260,
310, 364, 422, 464, 518, 576, 624
Homework Help Online
Homework Help Online is available for
every lesson. Refer to the go.hrw.com
box at the beginning of each exercise
set. Some examples: 8, 12, 16, 20, 24
Lab Resources Online, 41, 64, 128, 189,
204, 382, 478, 484, 496, 530, 547,
553, 594, 602, 607, 616
Parent Resources Online
Parent Resources Online is available
for every lesson. Refer to the
go.hrw.com box at the beginning of
each exercise set. Some examples: 8,
12, 16, 20, 24
Standards Practice Online, 58, 110, 162,
218, 268, 316, 372, 428, 472, 524,
584, 630
Web Extra!, 25, 101, 195, 209, 236, 255,
291, 419, 443, 483, 563, 599, 606
Open circle, 137
Operations
inverse, 32
order of, 6, 23–24, 27
Opposites, 14
Order of operations, 6, SB14
using, 169, 173
Ordered pairs, 322
Ordering
measurements, customary and metric,
237
rational numbers, 71
Organizing data, 532–534, SB18–21
Origami, 311
Origin, 322
Ounce, fluid, SB15
Outcomes, 556
equally likely, 564
Outlier, 538–539
Output, 326
Pacific Wheel, 430, 453
Pairs, ordered, 322
Pandas, 6
Parabola, 334
Parallel lines, 388–389
properties of transversals to, 389
and skew lines, 384–385
Parallelograms, 399, SB17
area of, 435–436
perimeter of, 434–436
Parent Resources Online
Parent Resources Online are available
for every lesson. Refer to the
go.hrw.com box at the beginning of
each exercise set. Some examples: 8,
12, 16, 20, 24
Parentheses, 6
Parthenon, 483
Patterns, 174, 286
in integer exponents, looking for,
172–173
Pediment, 445
Pei, I. M., 493
Peirsol, Aaron, 74
PEMDAS mnemonic, 6
Pentagons, 403, SB16
Percent problems, solving, 283–285,
288–289
Percent(s)
applications of, 298–299
of change, 294
of decrease, 294–295
defined, 274
estimating with, 278–280
finding, 283–285
using an equation, 283, 284
using a proportion, 283, 285
fractions and decimals and,
274–275
of increase, 294–295
known, finding numbers for, 288–289
of numbers, 283–284
Perfect squares, 192
Perimeter, 196, 434
of parallelograms, 434–436
of rectangles, 434–436
of trapezoids, 439–441
of triangles, 439–441
Periscopes, 391
Perpendicular bisectors, 382
Perpendicular lines, 384–385, 388–389
Person-day, 39
Person-hour, 38
Physics, 591
Pi (), 203, 450
Pint, SB15
Pixels, 193
Place value, SB2
Planes, 378
points and lines and angles and,
378–380
Pluto, 187
Points, 378
on the coordinate plane, 322–323
graphing, 14, 322–323
Index
I9
lines and planes and angles and,
378–380
plotting, 323
Polygons, 399
angles in, 392–393, 403
classifying, 399, SB16–17
regular, SB16
Polyhedrons, 480–481
Polynomials
classifying, 590–591
addition of, 603–604
modeling, 602
defined, 590–591
degrees of, 591
modeling, 594–595
multiplication of, by monomials, 612–613
simplifying, 596–597
subtraction of, 608–609
modeling, 607
Population(s), SB22
samples and, SB22
Positive correlation, 549
Positive slope, 349
Pound, SB15
Powers, 168
division of, 176–177
multiplication of, 176
of products, 181
raising monomials to, 181
raising powers to, 177
and roots, 192
simplifying, 168–169
of ten, 184
zero, 173
Preparing for your final exam, 589
Price, unit, 229
Prime factorization, SB5
Prime numbers, SB5
Principal, 303
Principal square root, 192
Prisms, 480, 485
lateral faces, 498
naming, 480
nets of, 496
rectangular, 485, see also Rectangular
prism
surface area of, 498–500
triangular, 485
volume of, 485–487
exploring, 484
Probability
defined, 556–558
of dependent events, finding, 570–571
of disjoint events, 566
experimental, 560–561
of independent events, finding,
569–570
theoretical, 564–566
Problem Solving
Problem solving is a central focus of
this course and is found throughout
this book.
Problem Solving Application, 34, 84,
98–99, 145, 206, 238, 249, 613
I10
Index
Problems, reading, for understanding,
273
Production costs, 586
Profit, 298–299
Properties
Addition, of Equality, 33
Associative, 603
of Addition, 116–117
of Multiplication, 116–117
Commutative
of Addition, 116–117
of Multiplication, 116–117
Density, of real numbers, 201
Distributive, 117
Division, of Equality, 37
Identity
of Addition, 32
of Multiplication, 37
Inverse
of Multiplication, 82
Multiplication, of Equality, 38
of circles, 446–447, 450–451
of exponents, 176–177
Subtraction, of Equality, 33
Proportions, 232–234
identifying, 232
and indirect measurement, 248
and percent, 283
ratios and, 232
similar figures and, 244
solving, 233–234
using, to find scales, 252
writing, 233–234
Protractors, 382–383
Punnett squares, 568
Pyramid of Khafre, 209
Pyramids, 480, 490
naming, 480
regular, 504
stone, 483
surface area of, 504–505
volume of, 490–491
Pythagorean Theorem, 205–207
and area, 439
converse of the, 206–207
exploring the, 204
Quadrants, 322
Quadratic functions, 334–335
Quadrilaterals
angles of, 403, SB16
classifying, 399
Quart, SB15
Quartiles, 542–543
Radical symbol, 192
Radius, 446, 450
Raising
monomials to powers, 181
powers to powers, 177
Random samples, SB22
Range, 537
Rate of change, 344–345
slope and, 344–345
Rate of interest, 303
Rates, 228–229
commission, 298
of interest, 303
unit, 228–229, see also Unit rates
Rational numbers, 60–111, 200–201
addition of, 74–75
comparing, 70–71
decimal expansion of, 64–65
defined, 66
division of, 82–84
exploring, 64–65
multiplication of, 78–79
ordering, 71
solving equations with, 94–95, 98–99
subtraction of, 74–75
Ratios, 224–225
comparing, 225, 232
equivalent, 224–225, 232
and proportions, 232
writing, in simplest form, 224
Rays, 378
Reading
circle graphs, 77
graphics, 529
lessons for understanding, 115
numbers in scientific notation, 185
problems for understanding, 273
Reading and Writing Math, 5, 63, 115,
167, 223, 273, 321, 377, 433, 477, 529,
589
Reading Math, 82, 137, 168, 177, 252,
274, 349, 379, 411, 440, 446, 486, 513
Reading Strategies, see also Reading
and Writing Math
Interpret Graphics, 529
Read a Lesson for Understanding, 115
Read Problems for Understanding, 273
Use Your Book for Success, 5
Ready to Go On?, 30, 48, 92, 102, 134,
152, 190, 210, 242, 258, 292, 308, 342,
362, 404, 420, 444, 462, 494, 516, 554,
574, 600, 622, see also Assessment
Real numbers, 200–201
Density Property of, 201
Reasoning
Reasoning is a central focus of this
course and is found throughout this
book. Some examples: 13, 16, 17, 29,
39, 40, 45, 69, 71, 72, 76, 83, 90, 95,
98, 119, 122, 127, 142, 143, 150,
171, 174, 183, 195, 199, 208, 226,
SB24
deductive, SB24
inductive, SB24
proportional, 220–269
Reciprocals, 82
Recreation, 40, 79, 88, 126, 196, 284, 515
Rectangles, 399, SB17
area of, 435–436
perimeter of, 434–436
Rectangular prism, 485
volume of, 485–487
exploring, 484
Rectangular pyramid, 490
Recycling, 225
Reduction, 253
Reflection(s), 410
line of, 410
translations and rotations and, 410–412
Regular polygons, SB16
Regular pyramids, 504
Regular tessellations, 416
Relating decimals, fractions, and
percents, 274–275
Relationships, angle, 388–389
Remember!, 6, 14, 67, 70, 75, 94, 121,
125, 144, 148, 149, 181, 275, 345, 450,
480
Repeating decimals
defined, 66
exploring, 64–65
period of, 65
writing, as fractions, 67
Representations of data, see also
Displaying and organizing data
multiple, using, 377
Reptiles, 361
Reptiles, (M.C. Escher), 419
Reticulated python, 289
Rhombuses, SB17
Right angles, 379
Right cones, 504
Right triangles, 392, SB17
finding angles in, 392
finding lengths of sides in, 205–206
identifying, 206–207
Rincon Park, 220
Rise, 345–346
Roots
square, 192–193
square, estimating, 196–197
Rotation(s), 410
center of, 410, 412
translations and reflections and,
410–412
Rounding
decimals, SB2
whole numbers, SB2
Rules, divisibility, SB4
Run, 345–346
Safety, 352, 561
Sales tax, 298–299
Sample(s), SB22
biased, SB22
populations and, SB22
random, SB22
surveys and, SB22
Sample spaces, 556
San Diego, 270
San Francisco, CA, 220
Santa Rosa, CA, 240
Scale, 252
Scale drawings, 252
constructing, 256
Scale factors, 253
Scale models, 252–253, 259
constructing, 256–257
Scalene triangles, 393, SB17
Scaling three-dimensional figures,
512–513
Scatter plots, 548–550
creating, 553
School, 72, 80, 149, 234
Science, 7, 17, 28, 29, 36, 91, 96, 127, 133,
187, 199, 226, 228, 281, 289, 297, 336,
507
Scientific notation, 184–186
comparing numbers in, 186
division of numbers in, 189
multiplication of numbers in, 189
reading numbers in, 185
writing numbers in, 184–185
Sections, 463
Sector, 447
Segments, line, 378
Selected Answers, SA1–SA14
Semiregular tessellations, 418
Set-builder notation, 142
Short Response, 13, 29, 97, 151, 179, 188,
195, 227, 251, 255, 266–267, 333, 356,
396, 414, 419, 438, 470, 471, 563,
599, 615
Write Short Responses, 266–267
Sides, corresponding, 406–407
Silos, 488
Similar figures, 244
finding missing measures in, 245
and indirect measurement, 248–249
and scale drawings and models,
252–253
proportions and, 244
three-dimensional
surface area of, 513
volume of, 513
using, 248–249
Similar polygons, 244–245
Simple interest, 303–304
Simplest form, 67
writing ratios in, 224
Simplifying
algebraic expressions, 120–121
negative exponents, 172–173
polynomials, 596–597
powers, 168–169, 172–173
Skew lines, 384
Skills Bank, SB2–SB24
Slant height, 504
Slide, see Translations
Slope, 345–346, 398
of a line, 349–351
rates of change and, 344–345
Snakes, 101
Snowboard half-pipe, 502
Social Studies, 25, 35, 47, 71, 86, 146,
188, 282, 286, 291, 396, 438, 489, 491,
507
Solid figures, see Three-dimensional
figures
Solution set, 136
Solutions, 32
of equations, 32
Solving
equations, see Solving equations
inequalities, see Solving inequalities
multi-step equations, 124–125, 129–131
percent problems, 283–285, 288–289
proportions, 232–234
two-step equations, 43–45, 98–99
Solving equations
by addition, 32–34
with decimals, 94, 98–99
by division, 37–38
with fractions, 94–95, 99
linear, 330–331
by multiplication, 37–38
multi-step, 124–125, 129–131
with rational numbers, 94–95, 98–99
by subtraction, 32–34
two-step, 43–45, 98–99
using addition and subtraction
properties, 32–34
using multiplication and division
properties, 37–38
with variables on both sides, 129–131
Solving inequalities,
by adding or subtracting, 140–141
by multiplying or dividing, 144–145
two-step, 148–149
Special products, 619
Speed, 228–229, 234, 238, 239
Spheres, 508–509
surface area of, 509
volume of, 508
Spiral Standards Review
Spiral Standards Review questions
are found in every lesson. Some
examples: 9, 13, 17, 21, 25
Sports, 14, 27, 38, 68, 72, 74, 76, 123,
127, 151, 194, 240, 281, 328, 336, 453,
541
Spreadsheets
using, to construct graphs, 530–531
Square roots
approximating,
to the nearest hundredth, 197
using a calculator, 197
estimating, 196–197
of monomials, 193
principal, 192
squares and, 192–193
Square units, 485
Square(s), 192, 399, SB17
area of, 435
Index
I11
magic, 212
perfect, 192
square roots and, 192–193
Standard form, 185
Standards Practice Online, 58, 110, 162,
218, 268, 316, 372, 428, 472, 524, 584,
630
Stanford Linear Accelerator Center,
164
Statisticians, 270
Steinbeck, John, 143
Stem, 533
Stem-and-leaf plots, 533
back-to-back, 533–534
Step Pyramid of King Zoser, 507
Straight angles, 379
Strategies for Success, see also
Assessment
Any Type: Using a Graphic, 470–471
Extended Response: Write Extended
Responses, 370–371
Gridded Response: Write Gridded
Responses, 160–161
Multiple Choice
Answering Context-Based Test Items,
582–583
Eliminate Answer Choices, 56–57
Short Responses, 266–267
Study for a Final Exam, 589
Study Guide: Review, 52–54, 106–108,
156–158, 214–216, 262–264, 312–314,
366–368, 424–426, 466–468, 520–522,
578–580, 626–628, see also
Assessment
Study Strategies, see also Reading and
Writing Math
Concept Map, 433
Study for a Final Exam, 589
Take Effective Notes, 167
Subscripts, 440
Substitute, 6
Subtraction
of decimals, 74
of fractions, 75
with unlike denominators, 87–89
of integers, 22–23
of mixed numbers, 87–89
of polynomials, 608–609
modeling, 607
of rational numbers, 74–75
solving equations by, 32–34
solving inequalities by, 140–141
Subtraction Property of Equality, 33
Supplementary angles, 379
Surface area, 498
of cones, 504–505
exploring, 503
of cylinders, 498–500
exploring, 496–497
of figures built of cubes, 498
of prisms, 498–500
exploring, 496–497
of pyramids, 504–505
I12
Index
of similar three-dimensional figures,
512–513
of spheres, 509
Surface, lateral, 499
Surveys, samples and, SB22
Systems of equations, 131
solving, 131
writing, 131
Systolic blood pressure, 236
Tables
frequency, SB20
functions and, 326, 327, 330, 331, 334,
335, 338, 339
graphs and, 330, 331, 334, 335, 338,
339
Taiwan, 188
Taking effective notes, 167
Target heart rate, 615
Tax, sales, 298
Tax brackets, 301
Technology Lab
Make a Box-and-Whisker Plot, 547
Make a Scatter Plot, 553
Multiply and Divide Numbers in
Scientific Notation, 189
Use a Spreadsheet to Make Graphs,
530–531
Television Ratings, Nielsen, 283
Temperature
conversions, 103
global, 73
scales, 103, 331
Terabyte, 179
Terminating decimals
defined, 66
exploring, 64–65
writing, as fractions, 67
Terms, 120
like, 120
not like, 596
Tessellations, 416–417
regular, 416
semiregular, 418
Test, cumulative, studying for a, 589
Test items, context-based, answering,
582–583
The Grapes of Wrath (Steinbeck), 143
Theorem, Pythagorean, see Pythagorean
Theorem
Theoretical probability, 564–566
Think and Discuss
Think and Discuss is found in every
lesson. Some examples: 7, 11, 15, 19,
23
Three-dimensional figures
classifying, 481
drawing, 477
exploring, 478–479
introduction to, 480–481
scaling, 512–513
surface area of, 496, 509
volume of, 484–487, 508
Tides, 28
Tiles, algebra, 41–42, 128, 594–595, 602,
607, 616–617
Time, investment, 303
Timeline, 25
Tips, 279
To Kill a Mockingbird (Lee), 297
Ton, SB15
Torus, 518
Toys, 606
Transamerica Pyramid, 492
Transformations, 410
combining, 415
graphing, 410–412
Translating
math expressions into word phrases,
11
sentences into two-step equations, 43
word phrases into inequalities, 136
word phrases into math expressions,
10
between words and math, 63
Translations, 410
rotations and reflections and, 410–412
Transportation, 240, 241, 593
Transversals, 389
to parallel lines, properties of, 389
Trapezoids, 399, SB17
area of, 440–441
isosceles, SB17
perimeter of, 439
Travel, 125, 126
Tree diagrams, SB23
Trenches, ocean, 29
Trial, 556
Triangle Sum Theorem, 392
Triangles, 392–394, SB16–SB17
acute, 392, SB17
angles in, 392–394
area of, 440–441
classifying, 392–393
congruent, 406
equilateral, 393, SB17
isosceles, 393, SB17
obtuse, 392, SB17
perimeter of, 439
right, 392, SB17, see also Right triangles
scalene, 393, SB17
similar, 244–245
Triangular prism, 485
Triangular pyramid, 490
Trinomials, 590
Trump Tower, 257
Turns, see Rotation(s)
Twins, 406
Two-dimensional figures, 430–473
Two-step equations
modeling, 41–42
solving, 43–45
solving, with rational numbers, 98–99
Two-step inequalities, solving, 148–149
Umbra, 507
Undefined slope, 350
Understanding
reading lessons for, 115
reading problems for, 273
Unisphere, 483
Unit(s)
conversion factors, 237
customary, SB15
metric, SB15
Unit analysis, 237
Unit conversion factor, 237
Unit fractions, 104
Unit price, 229
Unit rates, 228–229
estimating, 229
rates and, 228–229
United States census, 291
Unlike denominators
addition of fractions with, 87–89
subtraction of fractions with, 87–89
Unpacking the Standards, 4, 62, 114,
166, 222, 272, 320, 376, 432, 476, 528,
588
Upper quartile, 542–543
Use your book for success, 5
Use your own words, 377
Using
formulas, 477
graphics, 470–471
nets to build prisms and cylinders,
496–497
similar figures, 248–249
slopes, 350
spreadsheets to construct graphs,
530–531
technology to make graphs, 530–531
your book for success, 5
your own words, 377
Value, absolute, 15
Variable(s)
on both sides
modeling equations with, 128
solving equations with, 129–131
expressions and, 6–7
Variable rate of change, 344
Variation, direct, 357–359
Venn diagrams, 200
Venus, 187
Vertex
of an angle, 379
of a cone, 481
of a polygon, 399–400
of a polyhedron, 480
of a three-dimensional figure, 480
Vertical angles, 388
Vertical line test, 327
Volume, 485
of cones, 490–491
of cylinders, 485–487
of prisms, 485–487
exploring, 484
of pyramids, 490–491
of similar three-dimensional figures,
512–513
of spheres, 508
Weather, 119, 325
Web Extra!, 25, 101, 195, 209, 236, 255,
291, 419, 443, 483, 493, 563, 599, 606,
Weight, customary units of, SB15
Whales, 175
What’s the Error?, 13, 21, 36, 69, 73, 81,
97, 119, 123, 127, 139, 147, 179, 183,
195, 203, 227, 231, 241, 277, 325, 352,
391, 453, 489, 493, 546, 559, 593
What’s the Question?, 307, 329, 333,
402, 541, 615
Wheel, 446
Whole numbers
comparing and ordering, SB3
dividing, SB7
long division, SB7
rounding, SB2
Word phrases
translating, into inequalities, 136
translating, into math expressions, 10
translating math expressions into, 11
Words
into math, translating, 136
and math, translating between, 63
use your own, 377
Write a Problem, 40, 77, 143, 151, 188,
208, 247, 251, 282, 361, 409, 507, 573,
606
Write About It
Write About It exercises are found in
every lesson. Some examples: 9, 13,
17, 21, 25
Writing
convincing arguments, 223
extended responses, 370–371
gridded responses, 160–161
inequalities, 136, 141
compound, 137
numbers in scientific notation, 184–185
numbers in standard form, 185
proportions, 232
short responses, 266–267
Writing Math, 66, 192, 388
Writing Strategies, see also Reading and
Writing Math
Draw Three-Dimensional Figures, 477
Keep a Math Journal, 321
Translate Between Words and Math, 63
Use Your Own Words, 377
Write a Convincing Argument, 223
x-axis, 322
x-coordinate, 322
Yard, SB15
y-axis, 322
y-coordinate, 322
Yosemite National Park, 88, 112, 252
Zero power, 173
Zero slope, 349
Index
I13
Credits
Staff Credits
Bruce Albrecht, Margaret Chalmers, Tica Chitrarachis, Lorraine Cooper, Marc Cooper,
Jennifer Craycraft, Martize Cross, Nina Degollado, Julie Dervin, Michelle Dike,
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PhotoDisc/Picture Quest; 329 Schenectady Museum/Hall of Electrical History
Foundation/CORBIS; 333 © Ron Kimball Stock; 334 © Chip Simons Photography;
337 Sam Dudgeon/HRW; 341 © Andrew Sacks/Time Life Pictures/Getty Images;
357 © Sindre Ellingsen/Alamy; 361 E.R. Degginger/Bruce Coleman, Inc.; 363 (tr),
Harry Engels/Photo Researchers, Inc.; 363 (b), Alan and Sandy Carey/Photo
Researchers, Inc.; 363 (tl), Stephanie Friedman/HRW; 364 (b), Randall Hyman/HRW;
365 Sam Dudgeon/HRW
Chapter Eight: 374-375 (all), © VEER/Christopher Talbot Frank/Getty Images;
384 © 2008 Sol LeWitt/Artists Rights Society (ARS), New York; 387 Mark
Schneider/Visuals Unlimited/Getty Images; 388 © Rodolfo Arpia/Alamy; 398 (all),
Courtesy of Lucasfilm, Ltd. Star Wars: Episode I - The Phantom Menace © 1999
Lucasfilm Ltd. & TM. All rights reserved. Used under authorization. Unauthorized
duplication is a violation of applicable law.; 406 (r), Seth Kushner/Getty Images/
Stone; 406 (l), Science Photo Library/Photo Researchers, Inc.; 410 © Matthew
Stockman/Getty Images; 416 Harry Lentz/Art Resource, NY; 421 Bob Burch/Index
Stock Imagery, Inc.; 422 Jenny Thomas/HRW; 423 Sam Dudgeon/HRW
Chapter Nine: 430-431 (all), © Richard Cummins/CORBIS; 439 © Louie Psihoyos/
CORBIS; 443 (t), © Royalty-Free/Corbis; 445 (b), Dave G. Houser/Houserstock;
446 (all), © Archivo Iconografico, S.A./CORBIS; 458 Larry Lefever/Grant Heilman
Photography; 461 (t), William Hamilton/SuperStock; 463 (t), PhotoDisc/Getty
Images; 463 (b), Grant Heilman /Grant Heilman Photography, Inc.; 464 Jenny
Thomas/HRW; 465 Sam Dudgeon/HRW
Chapter Ten: 474-475 © Robert Landau/CORBIS; 483 (tr), © Charles & Josette
Lenars/CORBIS; 483 (bl), © Kevin Fleming/CORBIS; 483 (tl), Steve Vidler/SuperStock;
483 (br), R.M. Arakaki/Imagestate; 485 Kenneth Hamm/Photo Japan; 489 (r), Dallas
and John Heaton/CORBIS; 489 (l), G. Leavens/Photo Researchers, Inc.; 490 © Tor
Eigeland/Alamy; 493 (l), Owen Franken/CORBIS; 493 (r), Steve Vidler/SuperStock;
495 (b), Sam Dudgeon/HRW; 498 © 2004 Kelly Houle; 505 (l), Robert & Linda
Mitchell Photography; 506 Baldwin H. Ward & Kathryn C. Ward/CORBIS; 508 ©
NASA/Corbis; 511 (t), Darryl Torckler/Getty Images/Stone; 511 (tc), Dwight Kuhn
Photography; 511 (bc), Sinclair Stammers/Science Photo Library/Photo Researchers,
Inc.; 511 (b), Ron Austing; Frank Lane Picture Agency/CORBIS; 515 Chris
Lisle/CORBIS; 515 © 2006 The LEGO Group; 517 Victoria Smith/HRW; 518 Sam
Dudgeon/HRW; 519 Sam Dudgeon/HRW
Chapter Eleven: 526-527 © Court Mast/Marling Mast/Getty Images; 532 Digital
Vision; 541 © Karl Weatherly/CORBIS; 542 Peter Van Steen/HRW/Kittens courtesy of
Austin Humane Society/SPCA; 548 © Royalty Free/CORBIS; 560 AP Photo; 563 (l),
Reuters/CORBIS; 563 (r), David Weintraub/Photo Researchers, Inc.; 564 Peter Van
Steen/HRW; 568 Sam Dudgeon/HRW; 575 Design Pics; 576 Sam Dudgeon/HRW;
577 Sam Dudgeon/HRW
Chapter Twelve: 586-587 (all), © Armando Arorizo/epa/Corbis; 590 © Dave G.
Houser/CORBIS; 599 (t), © Paul Eekhoff/Masterfile; 599 (b), Private Collection/
Bridgeman Art Library/© 2002 Fletcher Benton/Artists Rights Society (ARS),, New
York; 601 Steve Gottlieb/Stock Connection/PictureQuest; 603 Sam Dudgeon/HRW;
604 Sam Dudgeon/HRW; 606 Stephen Mallon/The Image Bank/Getty Images;
612 Sam Dudgeon/HRW; 613 Victoria Smith/HRW; 615 Victoria Smith/HRW;
618 © Mark Gibson Photography; 621 (b), Sam Dudgeon/HRW; 623 (t), iStock
Photo; 623 (bl), © Jeff Greenberg/Photo Edit, Inc.; 623 (br), Photodisc/Getty
Images; 624 (b), Sam Dudgeon/HRW; 625 (b), Sam Dudgeon/HRW; 586-587 (all), ©
Armando Arorizo/epa/Corbis
Student Handbook TOC: 632 John Langford/HRW; 633 Sam Dudgeon/HRW
Credits
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