Download Study Guide

j9rb-0201.qxd 11/12/03 2:08 PM Page 10
LESSON
Name
Date
2.1 Study Guide
For use with pages 63–68
GOAL
Use properties of addition and multiplication.
VOCABULARY
Lesson 2.1
Commutative Property of Addition: In a sum, you can add the
numbers in any order.
Associative Property of Addition: Changing the grouping of the
numbers in a sum does not change the sum.
Commutative Property of Multiplication: In a product, you can
multiply the numbers in any order.
Associative Property of Multiplication: Changing the grouping of
the numbers in a product does not change the product.
Identity Property of Addition: The sum of a number and the
additive identity, 0, is the number.
Identity Property of Multiplication: The product of a number and
the multiplicative identity, 1, is the number.
EXAMPLE
1 Using Properties of Addition
You listened to your radio for 27 minutes on Monday, 9 minutes on Tuesday, and
13 minutes on Wednesday. Find the total time you spent listening to your radio.
Solution
The total time is the sum of the three times. Use properties of addition to group
together times that are easy to add mentally.
27 ⫹ 9 ⫹ 13 ⫽ (27 ⫹ 9) ⫹ 13
⫽ (9 ⫹ 27) ⫹ 13
⫽ 9 ⫹ (27 ⫹ 13)
⫽ 9 ⫹ 40
⫽ 49
Use order of operations.
Commutative property of addition
Associative property of addition
Add 27 and 13.
Add 9 and 40.
Answer: The total time is 49 minutes.
EXAMPLE
2 Using Properties of Multiplication
Evaluate 2xy when x ⫽ 8 and y ⫽ ⫺35.
2xy ⫽ 2(8)(⫺35)
⫽ [2(8)](⫺35)
⫽ [8(2)](⫺35)
⫽ 8[2(⫺35)]
⫽ 8(⫺70)
⫽ ⫺560
10
Pre-Algebra
Chapter 2 Resource Book
Substitute 8 for x and ⫺35 for y.
Use order of operations.
Commutative property of multiplication
Associative property of multiplication
Multiply 2 and ⫺35.
Multiply 8 and ⫺70.
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
j9rb-0201.qxd 11/12/03 2:08 PM Page 11
LESSON
Name
Date
2.1 Study Guide
Continued
For use with pages 63–68
Exercises for Examples 1 and 2
Evaluate the expression. Justify each of your steps.
1. 64 ⫹ 15 ⫹ 6
2. 34 ⫹ 75 ⫹ 26
3. 48 ⫹ 36 ⫹ 22
4. Evaluate 15xy when x ⫽ 9 and y ⫽ 2.
Lesson 2.1
EXAMPLE
3 Using Properties to Simplify Variable Expressions
Simplify the expression.
21 ⫹ 3(8y) ⫹ 30 ⫽ 21 ⫹ (3 p 8)y ⫹ 30
⫽ 21 ⫹ 24y ⫹ 30
⫽ (21 ⫹ 24y) ⫹ 30
⫽ (24y ⫹ 21) ⫹ 30
⫽ 24y ⫹ (21 ⫹ 30)
⫽ 24y ⫹ 51
Associative property of multiplication
Multiply 3 and 8.
Use order of operations.
Commutative property of addition
Associative property of addition
Add 21 and 30.
Exercises for Example 3
Simplify the expression.
5. ⫺8 ⫹ x ⫹ 3
EXAMPLE
6. 3(21x)
4 Multiplying by a Conversion Factor
The African Elephant is the largest living land animal. Its average weight is
6 tons. What is the African Elephant’s average weight in pounds?
Solution
(1) Find a conversion factor that converts tons to pounds. The statement
1 ton ⫽ 2000 pounds gives you two conversion factors.
Unit analysis shows that a conversion factor that converts tons to pounds has
pounds in the numerator and tons in the denominator:
pounds
tons p ᎏᎏ ⫽ pounds
冫
冫
tons
(2) Multiply the African Elephant’s weight by the conversion factor from Step 1.
2000 pounds
6 tons ⫽ 6 冫
tons p ᎏᎏ ⫽ 12,000 pounds
ton
1冫
Answer: The average weight of the African Elephant is 12,000 pounds.
Exercise for Example 4
7. Use a conversion factor to convert 3 years to months.
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
Chapter 2
Pre-Algebra
Resource Book
11
j9rb-0202.qxd 11/12/03 2:08 PM Page 20
LESSON
Name
Date
2.2 Study Guide
For use with pages 71–75
GOAL
Use the distributive property.
VOCABULARY
Two numerical expressions that have the same value are called
equivalent numerical expressions.
Two variable expressions that have the same value for all values of the
variable(s) are called equivalent variable expressions.
EXAMPLE
1 Evaluating Numerical Expressions
You are raising money for a field trip. The school matches your earnings. You
earn $125 selling sandwiches and $95 at a car wash. Find the amount you have
toward your field trip with the school’s contribution.
Lesson 2.2
Solution
Method 1: Find the amount you earned. Then multiply the result by 2, because
your earnings are matched by the school.
Total amount toward trip ⫽ 2(125 ⫹ 95)
⫽ 2(220)
⫽ 440
Method 2: Find the amount earned and matched for selling sandwiches and
the amount earned and matched for washing cars. Then add the amounts.
Total amount toward trip ⫽ 2(125) ⫹ 2(95)
⫽ 250 ⫹ 190
⫽ 440
Answer: You have $440 for your field trip.
Exercise for Example 1
1. You and a friend each spend $5 on a movie ticket and $4 on snacks. Write
and evaluate two expressions that can be used to find the amount you
both spent.
EXAMPLE
2 Using the Distributive Property
You buy 5 shorts for $15.02 each. Use the distributive property and mental math
to find the total cost of the shorts.
Total cost ⫽ 5(15.02)
⫽ 5(15 ⫹ 0.02)
⫽ 5(15) ⫹ 5(0.02)
⫽ 75 ⫹ 0.10 ⫽ 75.10
Write expression for total cost.
Rewrite 15.02 as 15 ⫹ 0.02.
Distributive property
Multiply, then add, using mental math.
Answer: The total cost of the shorts is $75.10.
20
Pre-Algebra
Chapter 2 Resource Book
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
j9rb-0202.qxd 11/12/03 2:08 PM Page 21
LESSON
Name
Date
2.2 Study Guide
Continued
EXAMPLE
For use with pages 71–75
3 Writing Equivalent Variable Expressions
Use the distributive property to write an equivalent variable expression.
a. 15(3y ⫺ 4) ⫽ 15(3y) ⫺ 15(4)
⫽ 45y ⫺ 60
Distributive property
Multiply.
b. ⫺6(3x ⫺ 1) ⫽ ⫺6(3x) ⫺ (⫺6)(1)
⫽ ⫺18x ⫺ (⫺6)
⫽ ⫺18x ⫹ 6
Distributive property
Multiply.
Definition of subtraction
c. (2z ⫹ 5)(⫺11) ⫽ 2z(⫺11) ⫹ 5(⫺11)
⫽ ⫺22z ⫹ (⫺55)
⫽ ⫺22z ⫺ 55
Distributive property
Multiply.
Definition of subtraction
Exercises for Examples 2 and 3
Evaluate the expression using the distributive property and mental math.
2. 5(197)
3. 35(11)
4. 4(13.04)
5. 7(8.98)
6. 12(7x ⫹ 8)
EXAMPLE
7. 3(9y ⫺ 1)
8. ⫺5(9z ⫹ 6)
9. ⫺8(11m ⫺ 9)
4 Finding Areas of Geometric Figures
Find the area of the rectangle or triangle.
a.
b.
2y ⫹ 1
2
3x ⫺ 8
16
Solution
a. Use the formula for the area
of a rectangle.
b. Use the formula for the area
of a triangle.
1
2
A ⫽ lw
1
2
A ⫽ ᎏᎏ bh ⫽ ᎏᎏ (16)(2y ⫹ 1)
⫽ (3x ⫺ 8)(2)
⫽ 8(2y ⫹ 1)
⫽ 3x(2) ⫺ 8(2)
⫽ (6x ⫺ 16) square units
⫽ 8(2y) ⫹ 8(1)
⫽ (16y ⫹ 8) square units
Exercises for Example 4
Find the area of the rectangle or triangle.
10.
11.
4x ⫺ 3
7
3x ⫹ 5
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
6
Chapter 2
Pre-Algebra
Resource Book
21
Lesson 2.2
Use the distributive property to write an equivalent variable expression.
j9rb-0203.qxd 11/12/03 2:09 PM Page 29
LESSON
Name
Date
2.3 Study Guide
For use with pages 78–83
GOAL
Simplify variable expressions.
VOCABULARY
The parts of an expression that are added together are called terms.
The coefficient of a term with a variable is the number part of the
term. A constant term, such as 7, has a number but no variable.
Like terms are terms that have identical variable parts.
EXAMPLE
1 Identifying Parts of an Expression
Identify the terms, like terms, coefficients, and constant terms of the expression
2y 3 ⫺ 7 ⫹ 2y ⫺ y 3 ⫹ 3.
Solution
(1) Write the expression as a sum: 2y 3 ⫹ (–7) ⫹ 2y ⫹ (⫺y 3) ⫹ 3.
(2) Identify the parts of the expression. Note that because ⫺y 3 ⫽ ⫺1y 3, the
coefficient of ⫺y 3 is ⫺1.
Terms: 2y 3, ⫺7, 2y, ⫺y 3, 3
Like terms: 2y 3 and ⫺y 3; ⫺7 and 3
Coefficients: 2, 2, ⫺1
Constant terms: ⫺7, 3
Exercises for Example 1
For the given expression, identify the terms, like terms, coefficients, and
constant terms.
1. 9t 2 ⫺ 12t ⫹ t 2 ⫺ 1
3. 5y ⫺ 3 ⫹ 2y
2 Simplifying an Expression
17x 2 ⫹ 2 ⫹ x 2 ⫺ 5 ⫽ 17x 2 ⫹ 2 ⫹ x 2 ⫹ (–5)
⫽ 17x 2 ⫹ x 2 ⫹ 2 ⫹ (–5)
⫽ 17x 2 ⫹ 1x 2 ⫹ 2 ⫹ (–5)
⫽ (17 ⫹ 1)x 2 ⫹ 2 ⫹ (–5)
⫽ 18x 2 ⫺ 3
Lesson 2.3
EXAMPLE
2. 11m 4 ⫹ 4m ⫺ 5 ⫺ 15m
Write as a sum.
Commutative property
Coefficient of x 2 is 1.
Distributive property
Simplify.
Exercises for Example 2
Simplify the expression.
4. 3x ⫺ 21 ⫺ 7x ⫹ 20
5. 2y 5 ⫹ 5y ⫺ y 5 ⫹ 5
6. 11z3 ⫺ 3z ⫺ 3 ⫹ z3 ⫹ 2z
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
Chapter 2
Pre-Algebra
Resource Book
29
j9rb-0203.qxd 11/12/03 2:09 PM Page 30
LESSON
Name
Date
2.3 Study Guide
Continued
EXAMPLE
For use with pages 78 –83
3 Simplifying Expressions with Parentheses
a. 5(x ⫺ 2) ⫺ 9x ⫹ 11 ⫽ 5x ⫺ 10 ⫺ 9x ⫹ 11
⫽ 5x ⫺ 9x ⫺ 10 ⫹ 11
⫽ ⫺4x ⫹ 1
Distributive property
Group like terms.
Combine like terms.
b. 6x ⫺ (8 ⫺ 14x) ⫹ 1 ⫽ 6x ⫺ 1(8 ⫺ 14x) ⫹ 1
⫽ 6x ⫺ 8 ⫹ 14x ⫹ 1
⫽ 6x ⫹ 14x ⫺ 8 ⫹ 1
⫽ 20x ⫺ 7
Identity property
Distributive property
Group like terms.
Combine like terms.
Exercises for Example 3
Simplify the expression.
7. 5y ⫹ 7(2y ⫹ 1) ⫺ 5
EXAMPLE
8. 8k ⫺ 5 ⫹ 5(2k ⫺ 3) ⫺ 7
9. 11n ⫺ (n ⫺ 5) ⫹ 3n
4 Writing and Simplifying an Expression
You spend a total of 50 minutes talking long-distance to your friend and
grandparents. It costs 4 cents per minute to call your friend and 6 cents
per minute to call your grandparents.
a. Let t be the time you talk with your friend (in minutes). Write an
expression in terms of t for the cost of both phone calls.
b. Find the cost of the phone calls if you talk with your friend for 25 minutes.
Solution
a. Write a verbal model for the cost of the phone calls.
Lesson 2.3
Length of
Long-distance
Length of
Long-distance
call with
rate for calling p call with ⫹ rate for calling p
grandparents
friend
friend
grandparents
0.04t ⫹ 0.06(50 ⫺ t) ⫽ 0.04t ⫹ 3 ⫺ 0.06t
⫽ 3 ⫺ 0.02t
Distributive property
Combine like terms.
b. Evaluate the expression in part (a) when t ⫽ 25.
3 ⫺ 0.02t ⫽ 3 ⫺ 0.02(25) ⫽ $2.50
Exercise for Example 4
10. You spend a total of 25 minutes typing an e-mail to your friend and writing
a letter to your aunt. You can type 60 words per minute and handwrite
20 words per minute. Let m be the number of minutes you type the e-mail
to your friend. Write an expression in terms of m for the total number of
words you wrote. Evaluate the expression if you spend 10 minutes typing
the e-mail to your friend.
30
Pre-Algebra
Chapter 2 Resource Book
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
j9rb-0204.qxd 11/12/03 2:09 PM Page 39
LESSON
Name
Date
2.4 Study Guide
For use with pages 85–89
GOAL
Solve equations with variables.
VOCABULARY
An equation is a mathematical sentence formed by placing an equal
sign, ⫽, between two expressions. A solution of an equation with a
variable is a number that produces a true statement when it is
substituted for the variable.
Finding all solutions of an equation is called solving the equation.
EXAMPLE
1 Writing Verbal Sentences as Equations
Verbal Sentence
a. The sum of 3y and 1 is 10.
Equation
3y ⫹ 1 ⫽ 10
b. The difference of t and 2 is 11.
t ⫺ 2 ⫽ 11
c. The product of ⫺1 and m is ⫺5.
⫺m ⫽ ⫺5
d. The quotient of 2x and 5 is 10.
2x
ᎏᎏ ⫽ 10
5
Exercises for Example 1
Write the verbal sentence as an equation.
1. 7x divided by 3 equals 2.
EXAMPLE
2. The difference of 3 and 2x is 5.
2 Checking Possible Solutions
Tell whether 3 or ⫺3 is a solution of 6y ⫺ 5 ⫽ 13.
a. Substitute 3 for y.
b. Substitute ⫺3 for y.
6y ⫺ 5 ⫽ 13
6(3) ⫺ 5 ⱨ 13
6y ⫺ 5 ⫽ 13
6(⫺3) ⫺ 5 ⱨ 13
18 ⫺ 5 ⱨ 13
⫺18 ⫺ 5 ⱨ 13
13 ⫽ 13 ✓
Answer: 3 is a solution.
⫺23 ⫽ 13
Answer: ⫺3 is not a solution.
Exercises for Example 2
Tell whether the given value of the variable is a solution of the equation.
y
2
5. ᎏᎏ ⫹ 1 ⫽ 7; y ⫽ 6
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
Lesson 2.4
3. 8 ⫺ 3m ⫽ 17; m ⫽ ⫺3
4. 5x ⫺ 7 ⫽ 13; x ⫽ ⫺4
k
3
6. ᎏᎏ ⫺ 3 ⫽ ⫺36; k ⫽ ⫺99
Chapter 2
Pre-Algebra
Resource Book
39
j9rb-0204.qxd 11/12/03 2:09 PM Page 40
LESSON
Name
Date
2.4 Study Guide
Continued
EXAMPLE
For use with pages 85–89
3 Solving Equations Using Mental Math
Equation
Question
Solution
a. ⫺3t ⫽ 39
⫺3 times what number
equals 39?
⫺13
b. 11 ⫺ m ⫽ 4
11 minus what number
equals 4?
7
c. 25 ⫹ k ⫽ 13
25 plus what number
equals 13?
70
m
d. ᎏᎏ ⫽ 35
⫺12
70 divided by what
number equals 35?
2
Check
⫺3(⫺13) ⫽ 39 ✓
11 ⫺ 7 ⫽ 4 ✓
25 ⫹ (⫺12) ⫽ 13 ✓
70
ᎏᎏ ⫽ 35 ✓
2
Exercises for Example 3
Solve the equation using mental math.
84
x
7. ᎏᎏ ⫽ ⫺7
EXAMPLE
8. 5x ⫽ 100
9. 20 ⫺ n ⫽ 3
10. m ⫹ 3 ⫽ ⫺1
4 Writing and Solving an Equation
You divide an 8-quart bag of potting soil into 4 portions for flowers you are
planting. Find the size of each portion of potting soil.
Solution
First write a verbal model for this situation.
Number of portions p Size of each portion ⫽ Total amount in bag
Let p represent the size of each portion.
4p ⫽ 8
4(2) ⫽ 8
Substitute for quantities in verbal model.
Use mental math to solve for p.
Answer: Because p ⫽ 2, each portion is 2 quarts.
Exercises for Example 4
11. Your 19-year-old sister is 4 years older than you. Write and solve an equation
to find your age.
Lesson 2.4
12. You earn $6 per lawn you mow. Yesterday you earned $24. Write and solve
an equation to find the number of lawns you mowed yesterday.
40
Pre-Algebra
Chapter 2 Resource Book
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
j9rb-0205.qxd 11/12/03 2:10 PM Page 47
LESSON
Name
Date
Lesson 2.5
2.5 Study Guide
For use with pages 90–95
GOAL
Solve equations using addition or subtraction.
VOCABULARY
Inverse operations are two operations that undo each other, such as
addition and subtraction.
Equivalent equations are equations that have the same solution(s).
EXAMPLE
1 Solving an Equation Using Subtraction
Solve m 12 7.
m 12 7
m 12 12 7 12
m 5
Write original equation.
Subtract 12 from each side.
Simplify.
Answer: The solution is 5.
✓ Check m 12 7
5 12 ⱨ 7
77 ✓
EXAMPLE
Write original equation.
Substitute 5 for m.
Solution checks.
2 Solving an Equation Using Addition
Solve 2 x 9.
2 x 9
2 9 x 9 9
7x
Write original equation.
Add 9 to each side.
Simplify.
Answer: The solution is 7.
Exercises for Examples 1 and 2
Solve the equation. Check your solution.
1. 7 k 42
2. 21 y 14
3. m 9 13
4. 3 n 7
5. j 13 2
6. 1 x 5
7. f 11 2
8. y 12 8
9. z 5 7
11. k 2 15
12. j 17 13
10. x 1 0
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
Chapter 2
Pre-Algebra
Resource Book
47
j9rb-0205.qxd 11/12/03 2:10 PM Page 48
LESSON
Name
Date
Lesson 2.5
2.5 Study Guide
Continued
EXAMPLE
For use with pages 90–95
3 Writing and Solving an Equation
You are traveling to Louisville, Kentucky. You have already traveled 122 miles,
and you just passed a road sign that said Louisville is 76 miles away. How far is
Louisville from the start of your trip?
Solution
Let d represent the distance from the start of your trip to Louisville. Write a
verbal model. Then use the verbal model to write an equation.
Distance from the
start to Louisville
Distance
traveled
Remaining
distance
d 122 76
d 122 122 76 122
d 198
Substitute.
Add 122 to each side.
Simplify.
Answer: Louisville is 198 miles from the start of your trip.
Exercises for Example 3
13. You have $37 left after shopping. You started with $85. How much money
did you spend?
14. You are in a 50-kilometer bike race. You have to bike 21 kilometers until
you reach the finish line. How far have you already biked?
48
Pre-Algebra
Chapter 2 Resource Book
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
j9rb-0206.qxd 11/12/03 2:10 PM Page 55
LESSON
Name
Date
2.6 Study Guide
For use with pages 96–101
GOAL
EXAMPLE
Solve equations using multiplication or division.
1 Solving an Equation Using Division
Solve 9x ⫽ ⫺108.
Write original equation.
9x
⫺108
ᎏᎏ ⫽ ᎏᎏ
9
9
Divide each side by 9.
x ⫽ ⫺12
Lesson 2.6
9x ⫽ ⫺108
Simplify.
Answer: The solution is ⫺12.
✓ Check
EXAMPLE
9x ⫽ ⫺108
9(⫺12) ⱨ ⫺108
⫺108 ⫽ ⫺108 ✓
Write original equation.
Substitute ⫺12 for x.
Solution checks.
2 Solving an Equation Using Multiplication
k
25
Solve ᎏᎏ ⫽ 5.
k
ᎏᎏ ⫽ 5
25
k
25 p ᎏᎏ ⫽ 25 p 5
25
k ⫽ 125
Write original equation.
Multiply each side by 25.
Simplify.
Answer: The solution is 125.
Exercises for Examples 1 and 2
Solve the equation. Check your solution.
1. 3x ⫽ 3
2. 8a ⫽ 32
3. ⫺m ⫽ 5
4. 7n ⫽ ⫺49
5. ⫺8b ⫽ 96
6. ⫺3y ⫽ ⫺27
m
5
7. ᎏᎏ ⫽ 9
n
12
y
10. ᎏᎏ ⫽ 1
5
j
12. ᎏᎏ ⫽ ⫺3
⫺8
8. ᎏᎏ ⫽ 5
x
7
9. 8 ⫽ ᎏᎏ
c
2
11. ⫺60 ⫽ ᎏᎏ
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
Chapter 2
Pre-Algebra
Resource Book
55
j9rb-0206.qxd 11/12/03 2:10 PM Page 56
LESSON
Name
Date
2.6 Study Guide
Continued
EXAMPLE
For use with pages 96 –101
3 Writing and Solving an Equation
If you divide your camera film equally over your 7-day vacation, you will take
25 pictures a day. How many exposures do you have?
Lesson 2.6
Solution
Let e represent the number of exposures you have. Write a verbal model.
Then use the verbal model to write an equation.
Total number of exposures
⫽ Number of pictures taken per day
Number of days
e
ᎏᎏ ⫽ 25
7
e
7 p ᎏᎏ ⫽ 7 p 25
7
e ⫽ 175
Substitute values.
Multiply each side by 7.
Simplify.
Answer: You have 175 exposures.
Exercises for Example 3
13. Your parents divide money evenly among you and your three siblings. Each
of you receives $75. Find the total amount your parents gave.
14. You purchase 9 yards of fabric. The total cost is $45. Find the cost per yard
of the fabric.
56
Pre-Algebra
Chapter 2 Resource Book
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
j9rb-0207.qxd 11/12/03 2:10 PM Page 65
LESSON
Name
Date
2.7 Study Guide
For use with pages 102–107
GOAL
EXAMPLE
Solve equations involving decimals.
1 Adding and Subtracting Decimals
a. Find the sum ⫺3.7 ⫹ 1.82.
Use the rule for adding numbers with different signs.
Subtract 1.82 from ⫺3.7.
⫺3.7 ⫹ 1.82 ⫽ ⫺1.88
⫺3.7 > 1.82, so the sum has the
same sign as ⫺3.7.
b. Find the difference ⫺5.06 ⫺ 4.05.
First rewrite the difference as a sum: ⫺5.06 ⫹ (⫺4.05). Then use the rule
for adding numbers with the same sign.
Add ⫺5.06 and ⫺4.05.
⫺5.06 ⫹ (⫺4.05) ⫽ ⫺9.11
Lesson 2.7
Both decimals are negative, so the
sum is negative.
Exercises for Example 1
Find the sum or difference.
EXAMPLE
1. ⫺2.15 ⫹ (⫺7.5)
2. ⫺3.68 ⫹ 0.23
3. 5.27 ⫹ (⫺7.12)
4. ⫺8.25 ⫺ 1.28
5. ⫺2.65 ⫺ (⫺4.9)
6. ⫺11.43 ⫺ (5.28)
2 Multiplying and Dividing Decimals
a. ⫺0.25(9.95) ⫽ ⫺2.4875
Different signs: Product is negative.
b. ⫺2.85(⫺4.8) ⫽ 13.68
Same sign: Product is positive.
c. ⫺45.92 ⫼ (⫺8.2) ⫽ 5.6
Same sign: Quotient is positive.
d. ⫺180.12 ⫼ 15.8 ⫽ ⫺11.4
Different signs: Quotient is negative.
Exercises for Example 2
Find the product or quotient.
7. 3.8(⫺8.2)
9. ⫺2.7(⫺0.3)
11. ⫺30.6 ⫼ 8.5
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.
8. ⫺5.4(1.2)
10. 7.875 ⫼ ⫺6.3
12. ⫺21.46 ⫼ ⫺2.9
Chapter 2
Pre-Algebra
Resource Book
65
j9rb-0207.qxd 11/12/03 2:10 PM Page 66
LESSON
Name
Date
2.7 Study Guide
Continued
EXAMPLE
For use with pages 102–107
3 Solving Addition and Subtraction Equations
Solve the equation.
a. z ⫹ 1.85 ⫽ 0.78
Solution
a.
z ⫹ 1.85 ⫽ 0.78
z ⫹ 1.85 ⫺ 1.85 ⫽ 0.78 ⫺ 1.85
z ⫽ ⫺1.07
b.
EXAMPLE
x ⫺ 2.59 ⫽ ⫺1.45
x ⫺ 2.59 ⫹ 2.59 ⫽ ⫺1.45 ⫹ 2.59
x ⫽ 1.14
b. x ⫺ 2.59 ⫽ ⫺1.45
Write original equation.
Subtract 1.85 from each side.
Simplify.
Write original equation.
Add 2.59 to each side.
Simplify.
4 Solving Multiplication and Division Equations
Solve the equation.
y
⫺9.6
Lesson 2.7
a. ⫺0.4b ⫽ 1
b. ᎏᎏ ⫽ ⫺8.1
Solution
a. ⫺0.4b ⫽ 1
Write original equation.
1
⫺0.4b
ᎏᎏ ⫽ ᎏ ᎏ
⫺0.4
⫺0.4
b ⫽ ⫺2.5
y
ᎏᎏ ⫽ ⫺8.1
b.
⫺9.6
y
⫺9.6 ᎏᎏ ⫽ ⫺9.6(⫺8.1)
⫺9.6
冢
Divide each side by ⫺0.4.
Simplify.
Write original equation.
冣
Multiply each side by ⫺9.6.
y ⫽ 77.76
Simplify.
Exercises for Examples 3 and 4
Solve the equation. Check your solution.
13. a ⫹ 6.98 ⫽ ⫺3.54
14. t ⫹ 70.12 ⫽ 4.28
15. x ⫺ 4.79 ⫽ ⫺11.82
16. m ⫺ 13.56 ⫽ ⫺12.02
17. 12.4x ⫽ ⫺169.88
18. ⫺7.9y ⫽ ⫺40.29
c
⫺50.12
19. ᎏᎏ ⫽ ⫺0.04
66
Pre-Algebra
Chapter 2 Resource Book
x
⫺13.2
20. ᎏᎏ ⫽ 20.1
Copyright © McDougal Littell/Houghton Mifflin Company
All rights reserved.