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Name _______________________________________ Date __________________ Class __________________
LESSON
5-8
Problem Solving
Dividing Fractions and Mixed Numbers
Write the correct answer in simplest form.
1. Horses are measured in units called
hands. One inch equals 1 hand. The
4
average Clydesdale horse is 17 1
5
hands high. What is the horse’s
height in inches? in feet?
2. Cloth manufacturers use a unit of
measurement called a finger. One
finger is equal to 4 1 inches. If 25
2
inches are cut off a bolt of cloth, how
many fingers of cloth were cut?
_______________________________________
________________________________________
3. People in England measure weights in
units called stones. One pound equals
1 of a stone. If a cat weighs 3 stone,
14
4
how many pounds does it weigh?
4. The hiking trail is 9 mile long. There
10
are 6 markers evenly posted along
the trail to direct hikers. How far apart
are the markers placed?
_______________________________________
________________________________________
Choose the letter for the best answer.
5. A cake recipe calls for 1 1 cups of
2
butter. One tablespoon equals 1
16
cup. How many tablespoons of butter
do you need to make the cake?
6. Printed letters are measured in units
called points. One point equals 1 inch.
72
If you want the title of a paper you are
typing on a computer to be 1 inch tall,
2
what type point size should you use?
A 24 tablespoons
F 144 point
B 8 tablespoons
C
3 tablespoon
32
G 36 point
H
1 point
36
I
1 point
144
D 9 tablespoons
8. Dry goods are sold in units called
pecks and bushels. One peck equals
1 bushel. If Peter picks 5 1 bushels
4
2
of peppers, how many pecks of
peppers did Peter pick?
7. Phyllis bought 14 yards of material to
make chair cushions. She cut the
material into pieces 1 3 yards long to
4
make each cushion. How many
cushions did Phyllis make?
A 4 cushions
C 8 cushions
F 1 3 pecks
8
H 20 pecks
B 6 cushions
D 24 1 cushions
2
G 11 pecks
I 22 pecks
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Name _______________________________________ Date __________________ Class __________________
LESSON
1-5
Problem Solving
Patterns and Sequences
1. A giant bamboo plant was 5 inches tall on Monday, 23 inches tall
on Tuesday, 41 inches tall on Wednesday, and 59 inches tall on
Thursday. Describe the pattern. If the pattern continues, how tall
will the giant bamboo plant be on Friday, Saturday, and Sunday?
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
2. A scientist was studying a cell. After the second hour there were
two cells. After the third hour there were four cells. After the
fourth hour there were eight cells. Describe the pattern. If the
pattern continues, how many cells will there be after the fifth,
sixth, and seventh hour?
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
Choose the letter for the best answer.
3. The first place prize for a sweepstakes is $8,000. The third
place prize is $2,000. The fourth place prize is $1,000. The
fifth place prize is $500. What is the second place prize?
A $7,000
C $4,000
B $6,000
D $3,000
4. The temperature was 59°F at 3:00 A.M., 62°F at 5:00 A.M.,
and 65°F at 7:00 A.M. If the pattern continues, what will the
temperature be at 9:00 A.M., 11:00 A.M., and 1:00 P.M.?
F 66°F at 9:00 A.M., 67°F at 11:00 A.M., 68°F at 1:00 P.M.
G 68°F at 9:00 A.M., 70°F at 11:00 A.M., 72°F at 1:00 P.M.
H 68°F at 9:00 A.M., 71°F at 11:00 A.M., 74°F at 1:00 P.M.
I 70°F at 9:00 A.M., 75°F at 11:00 A.M., 80°F at 1:00 P.M.
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Name _______________________________________ Date __________________ Class __________________
LESSON
7-3
Problem Solving
Proportions
Write the correct answer.
1. For most people, the ratio of the
length of their head to their total
height is 1:7. Use proportions to test
your measurements and see if they
match this ratio.
2. The ratio of an object’s weight on
Earth to its weight on the Moon is
6:1. The first person to walk on the
Moon was Neil Armstrong. He
weighed 165 pounds on Earth. How
much did he weigh on the Moon?
_______________________________________
_______________________________________
________________________________________
3. It has been found that the distance
from a person’s eye to the end of the
fingers of his outstretched hand is
proportional to the distance between
his eyes at a 10:1 ratio. If the
distance between your eyes is 2.3
inches, what should the distance
from your eye to your outstretched
fingers be?
4. Chemists write the formula of ordinary
sugar as C 12 H 22 O 11 , which means
that the ratios of 1 molecule of sugar
are always 12 carbon atoms to
22 hydrogen atoms to 11 oxygen
atoms. If there are 4 sugar
molecules, how many atoms of each
element will there be?
________________________________________
_______________________________________
________________________________________
Circle the letter of the correct answer.
5. A healthy diet follows the ratio for
meat to vegetables of 2.5 servings to
4 servings. If you eat 7 servings of
meat a week, how many servings of
vegetables should you eat?
A 28 servings
C 14 servings
B 17.5 servings
D 11.2 servings
6. A 150-pound person will burn
100 calories while sitting still for 1
hour. Following this ratio, how many
calories will a 100-pound person
burn while sitting still for 1 hour?
F 666 2 calories
3
H 6 2 calories
3
G 66 2 calories
3
I 6 calories
8. Recently, 1 U.S. dollar was worth
0.51 English pound. If you
exchanged 500 English pounds, how
many dollars would you get?
7. Recently, 1 U.S. dollar was worth
0.68 euros. If you exchanged $25 at
that rate, how many euros would you
get?
A 15.82 euros
F 255.00 U.S. dollars
B 17.00 euros
G 500.69 U.S dollars
C 23.42 euros
H 980.39 U.S. dollars
D 36.76 euros
I 998.31 U.S. dollars
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Name _______________________________________ Date __________________ Class __________________
LESSON
Problem Solving
10-4
Solving Inequalities
Write an inequality for each sentence. Then graph your
inequality on the number line.
1. A sign on a roller coaster states you must be
48 inches or taller to ride. Let h represent the
height of a person who can ride this ride.
___________________________
2. Tony is able to trade the tickets he won for a
prize that is valued at 300 tickets or less. Let t
represent the number of tickets the prize costs.
___________________________
3. Rosella bought some flowers that will only
bloom when the air temperature is greater than
62°. Let a represent the air temperature when
the flowers bloom.
___________________________
Solve each problem. Choose the letter of the best answer.
4. A basketball team scored at least
43 points in each game last season.
Let s represent the number of points
the team scored each game. Which
inequality represents this situation?
5. A widget must weigh less than
24 ounces to pass quality control.
Let w be the weight of a widget
manufactured at a plant. Which
inequality represents this situation?
A s > 43
C s ≥ 43
F w > 24
H w ≥ 24
B s < 43
D s ≤ 43
G w < 24
I w ≤ 24
6. The room temperature in an office
was 70 or less each day the office
was open. Let t represent the
temperature of the office each day.
Which inequality represents this
situation?
A t > 70
C t ≥ 70
B t < 70
D t ≤ 70
7. It is recommended that students
spend more than 30 minutes on
homework each night. Let x represent
the number of minutes a student
spends on homework each night.
Which inequality represents this
situation?
F x > 30
H x ≥ 30
G x < 30
I x ≤ 30
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Name _______________________________________ Date __________________ Class __________________
LESSON
2-2
Problem Solving
Variables and Expressions
Write the correct answer.
1. To cook 4 cups of rice, you use 8
cups of water. To cook 10 cups of rice,
you use 20 cups of water. Write an
expression to show how many cups of
water you should use if you want to
cook c cups of rice. How many cups
of water should you use to cook 5
cups of rice?
2. Sue earns the same amount of
money for each hour that she tutors
students in math. In 3 hours, she
earns $27. In 8 hours, she earns $72.
Write an expression to show how
much money Sue earns working h
hours. At this rate, how much money
will Sue earn if she works 12 hours?
_______________________________________
________________________________________
3. Bees are one of the fastest insects on
Earth. They can fly 22 miles in 2
hours, and 55 miles in 5 hours. Write
an expression to show how many
miles a bee can fly in h hours. If a bee
flies 4 hours at this speed, how many
miles will it travel?
4. A friend asks you to think of a
number, triple it, and then subtract 2.
Write an algebraic expression using
the variable x to describe your friend’s
directions. Then find the value of the
expression if the number you think of
is 5.
_______________________________________
________________________________________
Circle the letter of the correct answer.
6. The peso is the currency in Mexico.
In 2005, 1 United States dollar was
worth 10 pesos. How many pesos
were equivalent to 5 United States
dollars?
5. The ruble is the currency in Russia.
In 2005, 1 United States dollar was
worth 28 rubles. How many rubles
were equivalent to 10 United States
dollars?
A 28
F 1
B 38
G 10
C 280
H 15
D 2,800
I 50
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Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
5-5
Reading Strategies
Relate Words and Symbols
Repeated addition is a way to represent multiplication of fractions.
1 + 1 + 1 = 3
8
8
8
8
three times one-eight = three-eighths
3• 1 = 3
8
8
Repeated addition
Words
Symbols
Answer the following questions.
1. What is 2 • 2?
8
_____________________________________________________
2. What is three-eighths times two?
_____________________________________________________
3. What is 1 • 4?
8
_____________________________________________________
4. Write 1 + 1 + 1 + 1 as a multiplication problem.
8
8
8
8
___________________________________
Use the rectangle to answer each question.
5. What is two-tenths times two? ________________________________________________________
6. What is 1 • 4? ______________________________________________________________________
10
7. What is four-tenths times two? _______________________________________________________
8. Write 1 + 1 + 1 + 1 as a multiplication problem in words.
10 10 10 10
________________________________________________________________________________________
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Name _______________________________________ Date __________________ Class __________________
LESSON
1-3
Puzzles, Twisters & Teasers
Are You in Order?
What did one telephone say to the other when it proposed?
To answer the riddle, solve the following problems. Then write
the letter that is represented by each answer in the blanks
below.
1. 20 + 16 × 2 = __________ (I)
2. 55 ÷ (11 − 6) × 8 = __________ (W)
3. 4 + 9 − (2 + 6) + 3 = __________ (L)
4. (24 + 12) ÷ 12 = __________ (G)
5. (4 + 6 ÷ 2) × (1 + 9) = __________ (V)
6. 10 × (54 − 49) + 17 = __________ (E)
7. (36 ÷ 18)3 + 17 × 3 = __________ (Y)
8. 24 + (81 − 50) + 52 = __________ (O)
9. 21 ÷ (2 + 1) × 5 – 22 = __________ (U)
10. 6 ÷ (1 + 2) × 52 – 25 = __________ (A)
11. 32 × (3 + 2) + 8 ÷ 2 = __________ (R)
I
12. (63 ÷ 3) + 8 ÷ 2 = __________ (N)
______
______
______
______
88
52
8
8
______
______
______
______
______
______
______
3
52
70
67
59
99
31
______
______
______
______
______.
25
164
52
76
3
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Name _______________________________________ Date __________________ Class __________________
LESSON
5-7
Puzzles, Twisters & Teasers
All Mixed Up!
John was carrying a set of cards, but he tripped. The cards fell
on the floor and are all mixed up. Help John put them in order
by solving each problem.
Once you have solved the problems, place the cards in order
from least to greatest. When in order, the letters will spell out a
message!
B
O
J
O
6 • 22
3
31 •32
4
5
23 •32
4
3
11 • 4 5
2
6
D
O
G
5 1 • 12
2 5
4 •35
5
6
5•1
7 8
The message is... ___________________________.
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Name _______________________________________ Date ___________________ Class __________________
LESSON
11-4
Puzzles, Twisters & Teasers
Fill It All Together
Across
2. A way to indicate addition.
4. The sum of −4, −3, +5, −2, +4.
5. Many children start school at this age.
6. Intersection of the x-axis and the y-axis.
7. My name has the same number of
letters as my value.
10. Either x-_ _ _ _ or y-_ _ _ _.
11. The sign of the answer: (4 − 17)
Down
1. 8 + (−8)
2. The opposite of clue 11 across.
3. Can be positive or negative.
8. The first counting number.
9. Do this first to solve a word problem.
10. Same clue as the other #10.
Unscramble the letters that are circled to solve the riddle.
What kind of story is The Three Little Pigs?
_____ _____ _____ _____ _____ _____ _____
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Name _______________________________________ Date __________________ Class __________________
LESSON
7-3
Puzzles, Twisters & Teasers
Too Much!
Solve the problems and circle your answers.
Using the letters next to your answers, create three words that
mean different things, but are all pronounced the same! You will
use two of the letters more than once.
1. Chung is giving medicine to his cat Princess. The bottle
recommends 3 pills for a 15 pound cat, but Princess weighs only
10 pounds. How many pills should Chung give?
R 1 pill
W 2 pills
A 3 pills
2. Find the missing value: 5 = 15
21
n
O 7
D 3
M 5
3. Suri knows that she needs to study about twenty minutes a night
for each hour class in math, and about thirty minutes for each
hour class in history. Normally she has one hour of each class
every day. But today she had math class for an hour and a half
and only a half-hour history class. Will her homework take more,
less, or the same amount of time tonight?
F more
P same
T less
Now use the letters next to your answers to figure out the
three words.
A number:
_____
_____
_____
Also:
_____
_____
_____
A preposition:
_____
_____
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Name _______________________________________ Date __________________ Class __________________
LESSON
9-3
Puzzles, Twisters & Teasers
You’re All Wet
Find the area of each circle below.
Use 3.14 for pi. Round to the nearest
hundredth. To solve the riddle, match
the letter of the area to the problem number.
1.
2.
_______________________
3.
________________________
4.
_______________________
5.
Area
Letter
(square units)
63.59
O
65.39
I
94.99
M
99.49
N
30.18
T
31.08
S
132.67
T
123.67
R
19.63
O
131.04
E
113.04
B
________________________
6.
_______________________
________________________
Where is the ocean the deepest?
ON THE
____
____
____
____
____
____
1.
2.
3.
4.
5.
6.
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Name _______________________________________ Date __________________ Class __________________
LESSON
7-7
Puzzles, Twisters & Teasers
Teacher’s Favorite!
Decide whether each statement is true or false. If the statement
is true, follow the directions to navigate the maze. If the
statement is false, ignore the directions and go to the next
problem. Unscramble the letters that you land on to solve
the riddle.
1. A tip is an amount added to a bill. Begin at start and move four
spaces up.
2. A discount is an amount added to a bill. Move five spaces
diagonally down and to the left.
3. Sihla is buying several CDs, totaling $45. If the sales tax is
5%, she will pay $47.25 total. Move three spaces left. Then move
three spaces diagonally down and to the left.
4. You can find 10% of a number by moving the decimal point one
place to the right. Move 6 spaces up.
5. A sign in a store reads “15% off all items”. This is the same as a
15 percent discount on all items. Move three spaces diagonally
down and to the right. Then move to the right as far as you can.
What is your teacher’s favorite candy?
_____ _____ _____ _____ _____
–OLATE
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Name _______________________________________ Date __________________ Class __________________
LESSON
9-4
Reading Strategies
Compare Methods
Compare these two methods for finding the area of the shaded
figure.
Method 1
Divide the figure into a trapezoid and
a rectangle.
Method 2
Find the area of the outer rectangle
and subtract the area of the triangle.
area of trapezoid:
1
1
A = h(b1 + b2 ) = (8)(3 + 7) = 40 m2
2
2
area of rectangle:
A = bh = 13 • 7 = 91 m2
area of rectangle:
A = bh = 7 • 5 = 35 m2
area of triangle:
1
1
A = bh = (8)(4) = 16 m2
2
2
Now add the areas.
total area: A = 40 + 35 = 75 m2
Now subtract the areas.
total area: A = 91 − 16 = 75 m2
Answer the question.
1. Which of the above methods do you think is easier? Why?
________________________________________________________________________________________
________________________________________________________________________________________
2. Describe two different ways you can find the
shaded area at right.
________________________________________________________
________________________________________________________
________________________________________________________
3. Find the shaded area. ________________________
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Name _______________________________________ Date __________________ Class __________________
LESSON
10-3
Reading Strategies
Follow a Procedure
The individual pieces of an expression are called terms. The
expression 5x + 2 has two terms: 5x and 2. 5x is called the variable
term because it is the term that has the variable.
To solve two-step equations, follow these steps.
To Solve Two-Step Equations
5x + 8 = 23
Step 1: Get the variable
term by itself. Undo the
operation.
Step 2: Isolate the variable.
Use the inverse
operation.
5x + 8 − 8 = 23 − 8
5x = 15
5x
15
=
5
5
Subtract 8 from both
sides.
Divide both sides by 5.
x=3
Answer the following questions.
1. What is step 1 in solving a two-step equation?
________________________________________________________________________________________
________________________________________________________________________________________
2. Which term on the left side of the equation above does not
contain a variable?
________________________________________________________________________________________
3. What operation was performed to remove that term?
________________________________________________________________________________________
________________________________________________________________________________________
4. What is step 2 in solving a two-step equation?
________________________________________________________________________________________
5. Which term in the equation contains a variable?
________________________________________________________________________________________
6. What operation was performed to get the x by itself?
________________________________________________________________________________________
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Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
5-2
Reading Strategies
Use Fraction Bars
You can use fraction bars to show 1 and 1
2
3
These fractions have denominators that are different. They are
called unlike fractions.
To add or subtract unlike fractions, the denominators must be the
same. They must have a common denominator.
The common denominator for 1 and 1 is 6.
2
3
To get a common denominator for two fractions, multiply the
denominators.
halves • thirds = sixths, or 2 • 3 = 6
1. What are unlike fractions?
________________________________________________________________________________________
2. If you want to add or subtract unlike fractions, what do you need
to do?
________________________________________________________________________________________
3. How do you get a common denominator for 1 and 1 ?
2
3
________________________________________________________________________________________
4. How many sixths are in one-half?
________________________________________________________________________________________
5. How many sixths are in one-third?
________________________________________________________________________________________
6. What is the sum of one-half and one-third?
________________________________________________________________________________________
7. What is the difference between one-half and one-third?
_________________________________________________________________
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Name _______________________________________ Date __________________ Class __________________
LESSON
5-2
Review for Mastery
Adding and Subtracting with Unlike Denominators
Unlike fractions have different denominators. To add and subtract
fractions, you must have a common denominator. The least common
denominator (LCD) is the least common multiple of the denominators.
To add or subtract unlike fractions, first find the LCD of the fractions.
2 + 1
4
3
Multiples of 4: 4, 8, 12, …
Multiples of 3: 3, 6, 9, 12, …
The LCD is 12.
Next, use fraction strips to find equivalent fractions.
Then use fraction strips to find the sum or difference.
8 + 3 = 11
12 12 12
So, 2 + 1 = 11 .
4 12
3
Use fraction strips to find each sum or difference. Write your
answer in simplest form.
1. 1 + 1
4
8
_______________
5. 3 + 1
4
6
_______________
3. 3 − 1
4
3
2. 5 − 2
3
6
_______________
_______________
6. 1 + 3
2
8
7. 2 − 1
3
6
_______________
_______________
4. 3 + 3
5 10
________________
8. 1 − 1
4
3
________________
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Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
7-7
Review for Mastery
Applying Percents
There are many uses for percents.
Common Uses of Percents
Discounts
Tips
Sales Tax
A discount is an amount that is subtracted from the regular price
of an item.
discount = regular price • discount rate
A tip is an amount added to a bill.
tip = total bill • tip rate
Sales tax is an amount added to the price of an item.
sales tax = purchase price • sales tax rate
Rachel is buying a sweater that costs $42. The sales tax rate is 5%.
About how much will the total cost of the sweater be?
You can use fractions to find the amount of sales tax.
First round $42 to $40.
Think: 5% is equal to 1 .
20
So, the amount of tax is about 1 • $40.
20
The tax is about $2.00.
Then find the sum of the price of the sweater and the tax.
$42 + $2.00 = $44.00
Rachel will pay about $44.00 for the sweater.
Solve each problem.
1. About how much would you pay for a meal that costs $29.75 if
you left a 15% tip?
________________________________________________________________________________________
2. About how much do you save if a book whose regular price is
$25.00 is on sale for 10% off?
________________________________________________________________________________________
3. About how much would you pay for a box of markers whose
price is $5.99 with a sales tax rate of 9.5%?
________________________________________________________________________________________
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Name _______________________________________ Date __________________ Class __________________
LESSON
9-4
Review for Mastery
Area of Composite Figures
You can find the area of a composite figure by dividing it into
rectangles, triangles, or other simple shapes.
To find the shaded area at right, divide the figure into a
triangle and a semicircle as shown.
area of triangle:
A=
1
1
bh = (11)(7) = 38.5 m2
2
2
area of semicircle:
A=
1 2 1
π r = (3.14)(3.5)2 ≈ 19.2 m2
2
2
Add the area of the trianlge and the area of the semicircle.
total area A = 38.5 + 19.2 = 57.7 m2
Find the shaded area. Round to the nearest tenth, if necessary.
1.
2.
_______________________________________
________________________________________
3.
4.
_______________________________________
________________________________________
5.
6.
_______________________________________
________________________________________
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A85
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Name _______________________________________ Date __________________ Class __________________
LESSON
5-8
Review for Mastery
Dividing Fractions and Mixed Numbers
Two numbers are reciprocals if their product is 1. 2 and 3 are
2
3
reciprocals because 2 • 3 = 6 = 1.
3 2
6
Dividing by a number is the same as multiplying by its reciprocal.
1 ÷2= 1
1 • 1 = 1
4
4 2
8
8
So, you can use reciprocals to divide by fractions.
To find 2 ÷ 4, first rewrite the expression as a multiplication
3
expression using the reciprocal of the divisor, 4.
2 • 1
3 4
Then use canceling to find the product in simplest form.
2 ÷4= 2 • 1 = 1 • 1 = 1
3 4
3 2
3
6
To find 3 1 ÷ 1 1 , first rewrite the expression using improper fractions.
4
2
13 ÷ 3
2
4
Next, write the expression as a multiplication expression.
13 • 2
4
3
3 1 ÷ 1 1 = 13 ÷ 3 = 13 • 2 = 13 • 1 = 13 = 2 1
4
2
4
2
4
2
3
3
6
6
Divide. Write each answer in simplest form.
1. 1 ÷ 3
4
3. 3 ÷ 2
8
2. 1 1 ÷ 1 1
2
4
4. 2 1 ÷ 1 3
4
3
3 ÷
2
4
3 ÷
1
8
3
_______ • _______
_______ • _______
_______ • _______
_______ • _______
________________
________________
________________
________________
1 ÷
4
1
5. 1 ÷ 2
5
_______________
6. 1 1 ÷ 2 2
6
3
7. 1 ÷ 4
8
_______________
_______________
÷
4
8. 3 1 ÷ 1
2
8
________________
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Name _______________________________________ Date __________________ Class __________________
LESSON
10-2
Review for Mastery
Graphing Functions
You can express solutions of equations as ordered pairs.
To express solutions of y = x − 3 as ordered pairs, substitute the
given values for x in the equation. Then write the solutions as
ordered pairs.
x
x−3
y
ordered pair (x, y)
9
9−3
6
(9, 6)
7
7−3
4
(7, 4)
5
5−3
2
(5, 2)
3
3−3
0
(3, 0)
Use the given x-values to write solutions of y = 2x as
ordered pairs.
1.
x
2x
y
ordered pair (x, y)
1
2
3
4
You can check whether an ordered pair is a solution of an equation
by substituting the x- and y-values into the equation.
Is (2, 3) a solution of y = x + 1?
y=x+1
3=2+1
3=3
Write the equation.
Substitute 3 for y and 2 for x.
So (2, 3) is a solution of y = x + 1.
Determine whether each ordered pair is a solution of the given
equation.
2. (1, 4); y = 4x
_______________________
3. (3, 1); y = 2x − 3
________________________
4. (2, 8); y = 2x + 4
________________________
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654
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Name _______________________________________ Date __________________ Class __________________
LESSON
10-2
Review for Mastery
Graphing Functions (continued)
Look at the graph.
What is the value of y when x = 2?
Start at the origin and move 2 units right.
Move down until you reach the graph.
Move left to find the y-value on the y-axis.
When x = 2, y = 3.
The ordered pair is (2, 3).
Use the graph above to find the value of y for each
given value of x.
5. x = 1
6. x = 0
________________
________________
You can graph solutions of an equation on
a coordinate plane. If the graph of the
solution is a straight line, then the equation
is a linear equation.
Use ordered pairs to graph functions.
The first number, the x-coordinate, tells
you how far to move right or left from
the origin. The second coordinate, the
y-coordinate, tells you how far to
move up or down.
7. Graph the function described by y = 2x.
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Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
5-5
Review for Mastery
Multiplying Fractions by Whole Numbers
You can use fraction strips to multiply fractions by whole numbers.
To find 3 • 2 , first think about the expression in words.
3
2
3•
means “3 groups of 2 .”
3
3
Then model the expression.
+
+
The total number of 1 fraction pieces is 6.
3
2
2
2
So, 3 •
=
+
+ 2 =
3
3
3
3
6 = 2 in simplest form.
3
Use fraction strips to find each product.
1. 4 • 1
8
_______________
2. 2 • 2
5
4. 8 • 1
4
3. 6 • 1
8
_______________
_______________
________________
You can also use counters to multiply fractions by whole numbers.
To find 1 • 12, first think about the expression in words.
2
1 • 12 = 12 , which means “12 divided into 2 equal groups.”
2
2
Then model the expression.
The number of counters in each group is the product.
1 • 12 = 6.
2
Use counters to find each product.
5. 1 • 15
3
_______________
7. 1 • 16
4
6. 1 • 24
8
_______________
_______________
8. 1 • 24
12
________________
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Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Review for Mastery
LESSON
5-7
Multiplying Mixed Numbers
To find 1 of 2 1 , first change 2 1 to an improper fraction.
2
2
3
21 = 5
2
2
Then multiply as you would with two proper fractions.
Check to see whether you can divide by the GCF to make the problem
simpler. Then multiply the numerators and multiply the denominators.
The problem is now 1 • 5 .
3 2
1•5
= 5
3•2
6
So, 1 • 2 1 is 5 .
2
3
6
Rewrite each mixed number as an improper fraction. Is it
possible to simplify before you multiply? If so, what is the GCF?
Find each product. Write the answer in simplest form.
1. 1 • 1 1
4
3
= 1 • ______
4
_______________
5. 1 1 • 1 2
3
3
3
•
3
_______________
9. 3 1 • 2
3 5
_______________
2. 1 • 2 1
2
6
3. 1 • 1 1
2
8
= 1 • ______
6
_______________
2
•
= 1 • ______
8
= 1 • ______
3
_______________
________________
7. 1 3 • 2 1
2
4
6. 1 1 • 1 1
2
3
4
3
_______________
•
2
_______________
11. 1 3 • 2 1
2
4
10. 2 1 • 1
2 5
_______________
4. 1 • 1 2
3
5
_______________
8. 1 1 • 2 2
6
3
6
•
3
________________
12. 3 1 • 1 1
5
3
________________
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Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
1-3
Review for Mastery
Order of Operations
A mathematical phrase that includes only numbers and operations
is called a numerical expression.
9 + 8 × 3 ÷ 6 is a numerical expression.
When you evaluate a numerical expression, you find its value.
You can use the order of operations to evaluate a numerical expression.
Order of Operations
1. Do all operations within parentheses.
2. Find the values of numbers with exponents.
3. Multiply and divide in order from left to right.
4. Add and subtract in order from left to right.
Evaluate the expression.
60 ÷ (7 + 3) + 32
60 ÷ 10 + 32
Do all operations within parentheses.
60 ÷ 10 + 9
Find the values of numbers with exponents.
6+9
Multiply and divide in order from left to right.
15
Add and subtract in order from left to right.
Evaluate each expression.
1. 7 × (12 + 8) – 6
7 × _______ – 6
_______
–6
_______________________
4.
23 +
(10 – 4)
_______________________
7.
52 −
(2 × 8) + 9
_______________________
2. 10 × (12 + 34) + 3
10 × _______ + 3
_______
+3
10 + _______ – 7
_______
________________________
5. 7 + 3 × (8 + 5)
________________________
8. 3 × (12 ÷ 4) −
3. 10 + (6 × 5) – 7
22
________________________
–7
________________________
6. 36 ÷ 4 + 11 × 8
________________________
9. (33 + 10) – 2
________________________
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Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
1-5
Review for Mastery
Patterns and Sequences
Find the next three numbers in the sequence.
8, 12, 16, 20, 24, __, __, __, …
Step 1: Look at pairs of numbers to find the pattern.
8, 12, 16, 20, __, __, __, __, …
8 + 4 = 12
12 + 4 = 16
16 + 4 = 20
The pattern is to add 4.
Step 2: Use the pattern to name the next three numbers.
24 + 4 = 28
28 + 4 = 32
32 + 4 = 36
The next three numbers are 28, 32, and 36.
Find the next three numbers in each sequence.
1. 5, 8, 6, 9, 7 __, __, __, …
2. 90, 80, 70, 60, __, __, __, …
_______________________________________
________________________________________
3. 2, 8, 4, 16, 8, __, __, __, …
4. 10, 14, 18, 22, __, __, __, …
_______________________________________
________________________________________
5. 13, 21, 29, 37, __, __, __, …
6. 24, 12, 16, 8, __, __, __, …
_______________________________________
________________________________________
7. 14, 12,10, 8, __, __, __, …
8. 1, 7, 13, 19, __, __, __, …
_______________________________________
________________________________________
9. 1, 3, 6, 10, __, __, __, …
10. 40, 38, 36, __, __, __, …
_______________________________________
________________________________________
11. 54, 45, 36, __, __, __, …
12. 10, 25, 40, __, __, __, …
_______________________________________
________________________________________
13. 36, 29, 22, __, __, __, …
14. 18, 36, 72, __, __, __, …
_______________________________________
________________________________________
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Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
7-6
Review for Mastery
Percent Problems
You can use proportions to solve percent problems.
To find 25% of 72, first set up a proportion.
25 = x
72
100
25 • 72 = 100 • x
Next, find cross products.
1,800 = 100x
1,800
= 100x
100
100
Then solve the equation.
18 = x
So, 18 is 25% of 72.
Use a proportion to find each number.
1. Find 3% of 75.
_______________
2. Find 15% of 85.
_______________
3. Find 20% of 50.
_______________
4. Find 6% of 90.
________________
You can use multiplication to solve percent problems.
To find 9% of 70, first write the percent as a decimal.
9% = 0.09
Then multiply using the decimal.
0.09 • 70 = 6.3
So, 9% of 70 = 6.3.
Use multiplication to find each number.
5. Find 80% of 48.
_______________
9. Find 70% of 70.
150.
_______________
6. Find 6% of 30.
7. Find 40% of 120.
_______________
_______________
10. Find 35% of 120.
11. Find 9% of 50.
_______________
_______________
8. Find 20% of 98.
________________
12. Find 40% of
________________
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472
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Name _______________________________________ Date __________________ Class __________________
LESSON
7-3
Review for Mastery
Proportions
A proportion is an equation that shows two equivalent ratios.
3 = 9 is an example of a proportion.
4 12
3 • 12 = 36 and 4 • 9 = 36.
The cross products of proportions
are equal.
You can use cross products to find the missing value in a proportion.
3 = 12
x
48
12 • x = 3 • 48
To find x, first find the cross products.
12x = 144
Think: 144 ÷ 12 = x
x = 12
So, 3 = 12 .
12
48
Then use a related math sentence to
solve the equation.
Find the cross products to solve each proportion.
1. x = 3
4
8
x • 4 = ______
_______________
5. 3 = 12
x
8
_______________
9. 3 = 15
4
x
_______________
3. 2 = 4
x
5
2. 2 = x
3
6
2 • 6 = ______
_______________
6. 3 = 6
x
5
2 • x = ______
6 • 3 = ______
_______________
________________
7. x = 2
8
16
_______________
_______________
10. 1 = x
2
30
11. x = 24
30
5
_______________
4. 6 = 1
x
3
_______________
8. 2 = 4
x
9
________________
12. 25 = 5
x
35
________________
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Name _______________________________________ Date __________________ Class __________________
LESSON
10-4
Review for Mastery
Solving Inequalities
An inequality is a statement that two expressions are not equal. For inequalities with a
variable, any value of the variable that makes the inequality statement true is a
solution of the inequality.
Inequalities are written using the symbols: < (less than), > (greater than), ≤ (less than
or equal to), or ≥ (greater than or equal to). When graphing the solution of an
inequality, use an empty circle for < or > and a solid circle for ≤ or ≥.
You use inverse operations to solve inequalities. This should be familiar since you use
inverse operations to solve equations, too.
Solve the inequality 4x ≤ 12.
4x ≤ 12
4x 12
Divide both sides of the inequality by 4.
≤
4
4
x ≤ 3 x is less than or equal to 3.
To graph the solutions, place a solid circle at 3
and shade to the left.
Graph each inequality.
1. x > 4
2. x ≤ 1
Solve and graph each inequality.
3. x + 2 ≥ 6
4. 5x > 20
_______________________________________
________________________________________
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A94
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
9-8
Review for Mastery
Surface Area
You can use what you know about finding the area of polygon to find
the surface area of a three-dimensional figure.
To find the surface area of the prism above, first find the area of
each face.
2 congruent triangular bases
1
bh
2
= 1 (3 • 4)
2
= 6 unit2
A=
3 rectangular faces
A = w
A = w
A = w
=3•6
=4•6
=5•6
= 18 unit2
= 24 unit2
= 30 unit2
Then, find the sum of all of the faces of the prism.
SA = 6 + 6 + 18 + 24 + 30
= 84 square units
Find the surface area of each figure.
1.
2.
_______________________________________
________________________________________
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\
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A89
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
LESSON
9-6
Review for Mastery
Volume of Prisms
Volume is the number of cubic units needed to fill a space. To find
the volume of a rectangular prism, first find the area of the base.
length = 3 units
width = 2 units
A=
= 3 • 2 = 6 square units.
The area of the base tells you how many cubic units are in the first
layer of the prism.
Next, multiply the result by the number of layers in the prism.
The prism has 4 layers, so multiply 6 by 4.
6 • 4 = 24
So, the volume of the rectangular prism is 24 cubic units.
Find the volume of each rectangular prism.
1.
2.
_______________________________________
________________________________________
To find the area of a triangular prism, first find the area of the base.
A = 1 bh
2
= 1 (5 • 4)
2
= 10 square units
Then multiply the result by the height of the prism.
10 • 3 = 30
The volume of the triangular prism is 30 cubic units.
Find the volume of each triangular prism.
3.
4.
_______________________________________
________________________________________
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Name _______________________________________ Date __________________ Class __________________
LESSON
2-2
Review for Mastery
Variables and Expressions
A variable is a letter or a symbol that stands for a number that can
change. A constant is an amount that does not change.
A mathematical phrase that contains at least one variable is an
algebraic expression. In the algebraic expression x + 5, x is a variable and
5 is a constant.
When you evaluate an algebraic expression, substitute a number for
the variable and then find the value.
To evaluate the algebraic expression m − 8 for m = 12, first replace
the variable m in the expression with 12.
m−8
12 − 8
Then find the value of the expression.
12 − 8 = 4
The value of m − 8 is 4 when m = 12.
Evaluate each expression for the given value of the variable.
1. x + 5, for x = 6
2. 3p, for p = 5
_______________
3. z ÷ 4, for z = 24
4. w − 7, for w = 15
_______________
________________
_______________
To find the missing values in a table, use the given values of the variable.
x
4x
3
12
Think: x = 3, so 4x = 4 • 3 = 12
Think: x = 4, so 4x = 4 • 4 = 16
Think: x = 5, so 4x = 4 • 5 = 20
4
5
Evaluate each expression to find the missing values in the tables.
5.
x
3
5
7
x+7
10
6.
y
9
10
14
y−2
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