6-1 Name Date

Homework

Write an equation and use it to solve the problem.

Draw a model if you need to.
Equations may vary.
1 Two professional baseball teams played a four-game series. Show your work.
Attendance for the first three games was 126,503 people,
What was the Game 4 attendance if 171,318 people
altogether attended the series?
44,815 people; 126,503 + n = 171,318; n = 171,318 − 126,503

2 In the past, shares of stock were bought and sold in fractions

of a dollar. Suppose one share of stock, purchased for 72__ 1
4
3
dollars per share, decreased in value to 66__ dollars per share.
8
What was the decrease in value per share?
3 =
5__
7
dollars; 72__
1 −
66__ n
8 4 8

3 Two shipping containers are being loaded into the cargo hold
of a ship. One container weighs 2.3 tons. What is the weight
of the other container if the total weight of both containers
is 4.15 tons?
1.85 tons; 2.3 + n = 4.15; n = 4.15 − 2.3

4 The heights of horses are often measured in units called hands.

Abigail’s pony is 13__
1
hands tall. How much taller is Jermaine’s
4
__
1
horse if it is 16 hands tall?
2
3 hands; 13__
__
1
n 16__
1 + = 1
; n = 16 __
1 −
13__
1
4 4 2 2 4
© Houghton Mifflin Harcourt Publishing Company

5 Jake plays baseball with two wooden bats—one made from

hickory and one made from white ash. What is the weight
of his white ash bat if his hickory bat weighs 32.4 ounces,
and both bats together weigh 64.33 ounces?
31.93 ounces; n + 32.4 = 64.33; n = 64.33 − 32.4

6 Seventeen fewer people attended the second basketball

game of the season than attended the first game. One
hundred ninety-two people attended the second game.
How many people attended the first game?
209 people; n − 17 = 192; n = 192 + 17

UNIT 6 LESSON 1 Situation and Solution Equations for Addition and Subtraction 129
 6-1 Name Date
Remembering

Add or subtract.

1 4__ 15 =
1 + __ 2 3 + __
4__ 61 = 3 6__
2 - __
51 =
8 8 5 5 3 3
6 3
5 or 5__
__ 10__
4
1__
1
8 4 5 3

3 - __
4 7 - 1__1 = 5 8__ 23 = 6 __
2 + __
4 =
2 4 4 7 7
5 __
1 6
__
2 6
7

7 15 8 5__
4 9 11__
1
5 5
- 3__
1 +1 __
1 3
- 9__
_7 _8 _4
6 37
11__ 6___ 9
1___
7 40 20
3
10 1__
5 11 2__
2 12 6__
6 3 7
1
+ __ 5
+ 7__ + 1___
1
_3 _9 __ 14

2__
1
10__
2 7___
7
or 7__
1
6 9 14 2

Copy each exercise. Then subtract.

13 12,389 - 2.75 = 14 165.98 - 127.2 = 15 326.55 - 23.81 =

12,386.25 38.78 302.74
© Houghton Mifflin Harcourt Publishing Company

16 Stretch Your Thinking Garrett wants to buy a new soccer

ball, a pair of shorts, and a pair of soccer shoes. The ball
costs $12.55, the shorts cost $22.98, and the shoes cost
$54.35. Garrett has $85.00. How much more money does
Garrett need? Write an equation to solve the problem.
Possible equation: $85.00 + n = $12.55 + $22.98 +
$54.35; Garrett needs $4.88.

130 UNIT 6 LESSON 1 Situation and Solution Equations for Addition and Subtraction
 6-2 Name Date
Homework

Solve each problem. Draw a model if you need to.

Equations and models may vary.
1 Spectators for a high school football game sit in bleachers Show your work.
along one side of the field. Altogether, the bleachers seat
1,152 spectators in 16 rows of equal length. How many
spectators can be seated in one row of the bleachers?
72 spectators; n = 1,152 ÷ 16

2 How many periods of time, each __

1
of an hour long, does
3
a 8-hour period of time represent?
24 periods; n = 8 ÷ __ 1
3

3 The area of a rectangular ceiling is 130.5 square feet, and

one measure of the ceiling is 14.5 feet. What is the other
measure of the ceiling?
9 feet; n = 130.5 ÷ 14.5

4 Sorbet is a frozen dessert that is often made from fruit.

How many portions, each weighing ___ 1
of a kilogram, can
10
a French dessert chef create from 3 kilograms of sorbet?
30 servings; n = 3 ÷ ___ 1
10

5 The family room floor in Zack’s home has a rectangular

area rug that measures 6.5 feet by 9 feet. The floor is
rectangular and measures 10 feet by 12 feet. What area
of the floor is not covered by the rug?
© Houghton Mifflin Harcourt Publishing Company

61.5 square feet; n = (10 ⋅ 12) − (9 ⋅ 6.5)

6 A cargo van is carrying 20 identical steel cylinders. Each

cylinder contains compressed oxygen. Altogether, the
cylinders weigh __
1
of a ton.
2
a. In tons, what is the weight of each cylinder?
___
1
ton; n = __
1 ÷
20
40 2

b. One ton = 2,000 pounds. In pounds, what is the weight

of each cylinder?
50 pounds; n = 2,000 ⋅ ___ 1
40

UNIT 6 LESSON 2 Situation and Solution Equations for Multiplication and Division 131
 6-2 Name Date
Remembering

Multiply.
6
__ __
1 __
4
1
7
⋅ 42 = 36 2
3
⋅ 36 = 12 3
5
⋅ 15 = 12

__
1 5
__ 3
__
4
4
⋅ 28 = 7 5
9
⋅ 81 = 45 6
8
⋅ 72 = 27

Write an equation. Then solve. Equations may vary. Show your work.
7 There is __
1
of a peach pie left after a family picnic.
4
Four cousins share the leftover pie equally. What
fraction of a whole pie will each cousin receive?
x = __
1 ÷
4; ___
1
of a pie
4 16

8 Tully has 24 stamps in his collection. This is __

1
times
3
the number Jordan has. How many stamps does
Jordan have?
__
1
⋅ j = 24; 72 stamps
3

Write an equation to solve the problem. Draw a model

if you need to. Equations may vary.

9 Candace jumped 11.45 feet in a long jump competition.

What is the length of Maria’s jump if she jumped
1.05 fewer feet than Candace?
11.45 - 1.05 = n; 10.40 or 10.4 feet © Houghton Mifflin Harcourt Publishing Company

10 Stretch Your Thinking Ms. Jackson has $97.00 to spend

on games for her classroom. She buys six board games
that cost $11.95 each and a video game that costs $24.10.
How much money does Ms. Jackson have left to buy
more games? Write an equation to solve the problem.
$97.00 - (6 × $11.95 + $24.10) = $1.20;
Ms. Jackson has $1.20 left.

132 UNIT 6 LESSON 2 Situation and Solution Equations for Multiplication and Division
 6-3 Name Date
Homework

Write a word problem for the equation. Show your work.

Draw a model to show the situation.
Sample contexts and models shown.

1 __
2
⋅3=c
3

A recipe calls for __

2
cup of bran.
3
To make 3 times as many servings,
how many __
6
cups of bran are
3
needed? __
6
cups of bran
3

3
2 __
4
⋅ s = __38

Three-fourths of the students

in a class play on a sports team.
Three-eighths of the students in
the class play on the soccer team.
What fraction of the students
© Houghton Mifflin Harcourt Publishing Company

who play sports, play soccer?

3 2 ÷ __
1 =
q
4
If two whole grapefruit are each
4 fourths 4 fourths
cut into quarters, how many
grapefruit quarters will there be? 1 whole 1 whole

UNIT 6 LESSON 3 Write Word Problems 133

 6-3 Name Date
Remembering

Complete each fraction box.

3
__ 5 3 8
1 and __ 2 __ and ___
4 6 5 15
__
5 > __ 10 > ___
9
>
3
or ___ > 3 > ___
__ 8 9 > ___
or ___ 8
6 4 12 12 5 15 15 15
3 + ___
__ 8 = ___
9 + ___
8 = ___
17 = ___
+ __
5 + __3 = ___
10 + ___
9 = 19 = ___
___ 17 + 12
6 4 12 12 12 12 5 15 15 15 15 15
- __
5 - __3 = ___
10 - ___
9 = ___
1 - 3 - ___
__ 8 = ___
9 - ___
8 = ___
1
6 4 12 12 12 5 15 15 15 15
3 15 5
__ ⋅ __ = ___ = __
5 3 ___
⋅ 6 4 24 8 ⋅ __ ⋅ 8 = ___ 8
24 = ___
5 15 75 25

Solve. Show your work.

3 A $1,508 award is shared equally by 8 people. What is
each person’s share of the award?
$188.50

4 Felipe has 54 coins in his collection. His brother Pedro

has 1,269 coins. The number of coins Pedro has is how
many times the number his brother has?
23.5 or 23__1
times
2

Write an equation to solve the problem. Draw a model if

you need to. Equations and models may vary.

5 How many periods of time, each __

1
of an hour long, does
6
© Houghton Mifflin Harcourt Publishing Company
a 10-hour period of time represent?
n = 10 ÷ __1
; 60 periods
6

6 Stretch Your Thinking Write a word problem for the following

equation. __ ⋅ 1 + __35 = d Possible answer:
4 __
5 4
One-fourth of the __ 4
mile route Ken walks
5
each weekday is in a park. On Saturday,
he walked an additional __
3
mile in the park.
5
How far did Ken walk in the park on Saturday?
__
4
mile
5

134 UNIT 6 LESSON 3 Write Word Problems

 6-4 Name Date
Homework

Write an equation to solve the problem. Use mental math

or estimation to show that your answer is reasonable.
Equations and estimates may vary. Show your work.
1 In a speed test, a computer took 12.4 seconds to complete
one task, and 37.8 seconds to complete a more difficult task.
How much time was needed to complete both tasks?
50.2 seconds; 12.4 + 37.8 = n
Equation:
Round 12.4 to 10 and 37.8 to 40, then add.
Estimate:
My answer is reasonable because my estimate
is 10 + 40 or about 50 seconds.
2 To walk to school, Pablo first walks __
1
kilometer to Tanya’s house.
2
3
__
Then Pablo and Tanya walk kilometer to school. How far
5
does Pablo walk to school?
3
1___
1
km; n = __
1 + __
Equation: 10 2 5
3
__ is greater than __1
. My answer is reasonable
Estimate: 5 2
because the sum of __ 1
and a fraction greater
2
than __1
is greater than 1.
2
3 Each Saturday morning, Andy works 4 hours and earns $34.
At that rate, what does Andy earn for each hour he works?
÷4=n
Equation: $8.50; 34

Estimate: Andy earns between $8 and $9 per hour

© Houghton Mifflin Harcourt Publishing Company

because 4 × 8 = 32 and 4 × 9 = 36.

4 Yuri completed a race in 0.88 fewer seconds than Josie.

Josie’s time was 23.95 seconds. How long did it take
Yuri to complete the race?

Equation: 23.07 seconds; 23.95 − 0.88 = n

Estimate: Round 23.95 to 24 and round 0.88 to 1.

My answer is reasonable because my
estimate is 24 − 1 or about 23 seconds.

UNIT 6 LESSON 4 Determine Reasonable Answers 135

 6-4 Name Date
Remembering

Write an estimated answer for each problem. Then find

and write each exact answer. Estimates may vary.

Estimated Answer Exact Answer

1 41 × 77 ≈ 40 × 80 ≈ 3,200 41 × 77 = 3,157

7.22
2 3.8 × 1.9 ≈ 4 × 2 ≈ 8 3.8 × 1.9 =

36.573
3 7.3 × 5.01 ≈ 7 × 5 ≈ 35 7.3 × 5.01 =

Divide.

_ 149 R28 _ 129 R23 _ 111 R15

4 45⟌ 6,733 5 61⟌ 7,892 6 28⟌ 3,123

Write a word problem for the equation. Draw a model to

show the situation. Sample context and model are shown.
5
__ 20
7
6
⋅ c = ___
6
5
A recipe calls for __ of a cup of flour.
6
To make 4 times the number of
servings, how many cups of flour are
20
needed? ___ cups
© Houghton Mifflin Harcourt Publishing Company
6

3
8 Stretch Your Thinking Kaley has 2__ yards of fabric.
8
___
1
She cuts and uses 1 yards from the fabric. She
16
estimates that less than 1 yard of fabric is left
over. Is her estimate reasonable? Explain.
No. Possible explanation: Using benchmarks,
3
2__ rounds to 2__
1
and 1___
1
rounds to 1;
8 2 16
2__
1 - = __
1 11
2 2

136 UNIT 6 LESSON 4 Determine Reasonable Answers

 6-5 Name Date
Homework

Solve each problem. Show your work.

1 Michael has 21 T-shirts. One third of them are blue. How
many of Michael’s T-shirts are blue?
7 T-shirts

2 There are 476,092 fish in the city aquarium. That number

of fish is 476,070 more fish than Nadia has in her aquarium.
How many fish does Nadia have in her aquarium?
22 fish

3 Anne-Marie has saved 9 dollars for a new coat. That is __

1
as
6
much money as she needs. How much does the coat cost?
$54

4 Last year it rained on 63 days in Mudville. There were

7 times as many days of rain in Mudville as in Desert Hills.
How many days did it rain in Desert Hills last year?
9 days

5 Maria wants to buy a new car. She will choose a green car
or a silver car. The green car costs $16,898, and the silver
car costs $1,059.75 less than the green car. What is the
cost of the silver car?
$15,838.25
© Houghton Mifflin Harcourt Publishing Company

6 At a country-music concert, 48 people played guitars.

That number is 6 times as many as the number of people
who played banjos. How many people at the concert
played banjos?
8 people

7 There are 8 apples left on the table. There are __

1
as
4
many apples as bananas left on the table. How many
bananas are there?
32 bananas

UNIT 6 LESSON 5 Language of Comparison Problems 137

 6-5 Name Date
Remembering

Add or subtract.

6
1 6__ 2 1__
2 3 12__
4
7 3 5
3
+ 2___ 5
- __ 5
- 8___
__ 14 _9 __ 10
9___
1
1__
1 3
4___
14 9 10
3
4 11 5 7__
1 6 9__
5 4
5
- 5___ + 1__
2 5
+ 2__
__ 11 _3 _6
6 13
5___ 8___ 12___
7
11 15 12
7 Use the number line to find __
2 __
⋅ 4. 3 5 8
___
Label all the parts above and below. 15

1 2 3 4
0 5 5 5 5 1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15

Write an equation to solve the problem. Use mental math

or estimation to show that your answer is reasonable.
Equations and estimates may vary.
8 Terrell runs two timed drills at practice. The first drill
takes 33.5 seconds and the second drill takes 28.2 seconds.
How much time does it take him to complete both drills?

Equation: 61.7 seconds; 33.5

+ 28.2 = n
© Houghton Mifflin Harcourt Publishing Company
Estimate: Possible answer: Round 33.5 to 30 and 28.2
to 30, then add; my answer is reasonable because
my estimate is 30 + 30 or about 60 seconds.
3
9 Stretch Your Thinking Maverick has a 12__ -foot-long
4
streamer to decorate a hallway at his school. He cuts off
3
__ of a foot from each end to make it fit the hallway.
8
His principal asks him to make another streamer that is
5
__ as long. How long is the new streamer?
6
10 feet

138 UNIT 6 LESSON 5 Language of Comparison Problems

 6-6 Name Date
Homework

Solve. Draw a model if you will find it helpful.

Equations and models may vary.
9
1 A flagpole flying the Ohio state flag is ___ the height of a
10
30-foot-tall flagpole that is flying the U.S. flag. What is the
height (h) in feet of the flagpole flying the Ohio state flag?
9
27 feet; h = ___ ⋅ 30
10

2 The number of students in the Period 7 study hall at Jin’s

school is 4 times the number of students in Jin’s home room.
How many students (s) are in the study hall if there are
16 students in Jin’s home room?
64 students; s = 16 ⋅ 4

3 The enrollment at Roosevelt High School is 1,045 students,

which is 5 times the enrollment of Truman Middle
School. How many students (s) are enrolled at Truman
Middle School?
209 students; s = 1,045 ÷ 5

4 A truck weighs 5,400 pounds. An open-wheel race car

weighs __
1
as much. How much does the race car weigh?
4
1,350 lb; n = __
1
⋅ 5,400
4

5 Owen and Maya each studied for a test. Owen studied for
90 minutes and Maya studied for 0.5 times that length of
time. Who studied more? Multiply to check your prediction.
© Houghton Mifflin Harcourt Publishing Company

Prediction:
Owen; 90 × 0.5 = 45, and 45 < 90

6 Sonia’s family has 2 children, which is __

2
the number of
3
children in Zeke’s family. Which family has more children?
Divide to check your prediction.
Zeke’s family; __2
⋅ f = 2 or f = 2 ÷ __2 = __
⋅ 3 = __
2 __ 6 =
3
Prediction: 3 3 1 2 2

UNIT 6 LESSON 6 Multiplicative Comparison Situations 139

 6-6 Name Date
Remembering

Copy each exercise. Then add or subtract

5.09 6.95 3.77

1 22.09 - 17 = 2 7 - 0.05 = 3 4.07 - 0.3 =

49.06 0.87 0.86

4 44 + 5.06 = 5 0.07 + 0.8 = 6 0.55 + 0.31 =

Solve.

0.02 0.21 0.014

7 0.5 × 0.04 = 8 0.3 × 0.7 = 9 0.07 × 0.2 =

10 0.46 11 0.06 12 3.2

× 80
__ × 0.8
__ × 9
_
36.8 0.048 28.8

Solve each problem. Show your work.

13 A soccer team has 35 soccer balls. One fifth of the balls
are made of leather. How many of the balls are leather?
7 balls are leather.

14 There are 56 fifth graders who play basketball. That is

7 times the number of fifth graders who play tennis. © Houghton Mifflin Harcourt Publishing Company

How many fifth graders play tennis?

8 fifth graders play tennis.

15 Stretch Your Thinking Samantha draws a hopscotch

diagram on the sidewalk in front of her house.
The diagram is 10 feet long. Her neighbor asks her
to draw a 4-foot hopscotch diagram on a canvas mat.
In simplest form, what fraction of the length of
Samantha’s diagram is her neighbor’s diagram?
__
2
5

140 UNIT 6 LESSON 6 Multiplicative Comparison Situations

 6-7 Name Date
Homework

Write an equation and use it to solve the problem. Draw a

model it you need to. Equations and models may vary. Show your work.
1 The Yukon River is 1,980 miles long, and twice as long as the
Platte River. How many miles long (l) is the Platte River?
l = 1,980 ÷ 2; l = 990 miles

2 The height of the Empire State Building in New York City

is 1,250 feet, and 364 fewer feet than the height of the
World Financial Center building in Shanghai, China. What is
the height (h) of the World Financial Center building?
h = 1,250 + 364; h = 1,614 feet

3 Olivia is 48 inches tall, and __

2
as tall as her brother Cameron.
3
In inches, how tall (t) is Cameron?
t = 48 ÷ __ 2
; t = 72 inches
3

4 Sydney is shopping for a new television. The cost of a 32-inch

LCD flat screen is $149.95. The cost of 46-inch LED flat screen
is $280.04 more. What is the cost (c) of the 46-inch LED flat
screen television?
c = $149.95 + $280.04; c = $429.99

5 After arriving home from school, Luis read for __

1
of an hour.
3
__
1
If he reads for 1 hours after dinner, how many hours (h)
6
will Luis have read altogether?
h = __1 + __
1 1 ; h = 1__
1
© Houghton Mifflin Harcourt Publishing Company

hours
3 6 2

6 Each morning, Jared needs 60 minutes to get ready for school.

Kiara needs ___
7
as much time as Jared. How many minutes
12
does Kiara need each morning to get ready for school?
t = ___
7
⋅ 60; t = 35 minutes
12

7 When compared to Tasha, Liam spent 20 additional minutes

doing homework. Liam took 45 minutes to complete his
homework. How long did it take Tasha?
t = 45 - 20; t = 25 minutes

UNIT 6 LESSON 7 Types of Comparison Problems 141

 6-7 Name Date
Remembering

Solve.
1 6.9 2 7.3 3 5.8
× 4.2
__ × 0.90
__ × 0.54
__
28.98 6.57 3.132

4 5.3 5 0.7 6 9.4

× 0.08
__ × 6.25
__ × 1.7
__
0.424 4.375 15.98

Divide.
_90 _ 5 _ 58
7 ⟌
0.05 4.5 8 0.3⟌ 1.5 9 ⟌
0.04 2.32

_ 7.7 9.05
_ _ 54
10 0.64⟌ 4.928 11 0.6⟌ 5.43 12 0.08⟌ 4.32

Solve. Draw a model if you will find it helpful.

Equations and models may vary.
5
13 The gymnasium at Audubon Middle School is __ the
6
height of a 30-foot-tall building that is next to the
gymnasium. What is the height (h) in feet of the
gymnasium?
h = __5 ⋅ 30; 25 feet
6
© Houghton Mifflin Harcourt Publishing Company
14 Amiee’s karate instructor has 595 students. That is
5 times the number of students that her dance instructor
has. How many students does her dance instructor have?
s = 595 ÷ 5; 119 students
3 =
15 Stretch Your Thinking Draw a model that shows 5 ⋅ __ 3.
5
Possible answer:

142 UNIT 6 LESSON 7 Types of Comparison Problems

 6-8 Name Date
Homework

Solve each problem if possible. If a problem does not

have enough information, write the information that is
needed to solve the problem. Show your work.
1 At the school bookstore, Quinn purchased a binder
for $4.75 and 4 pens for $0.79 each. What was
Quinn’s total cost (c)?
c = $4.75 + (4 ⋅ $0.79); $7.91

2 A school bus has 12 rows of seats, and 4 students can be

seated in each row. How many students (s) are riding the
bus if 11 rows are filled with students, and 2 students are
riding in the twelfth row?
s = (11 ⋅ 4) + 2; 46 students

3 A group of 16 friends visited an amusement park. When

3
they arrived, __ of the friends wanted to ride the fastest
4
roller coaster first. How many friends (f) wanted to ride?
3
f = (16 ⋅ __ ); 12 friends
4

4 Zeke is shipping clerk for a large business. Today he

spent 90 minutes preparing boxes for shipping. One box
weighed 10 pounds and 7 boxes each weighed 3__ 1
pounds.
2
What is the total weight (w) of the boxes?
w = 10 + (7 ⋅ 3__ 1
); 34__
1
pounds
2 2
© Houghton Mifflin Harcourt Publishing Company

5 A middle school faculty parking lot has 3 rows of parking

spaces with 13 spaces in each row, and 1 row of 7 spaces.
How many vehicles (v) can be parked in the faculty lot?
v = (3 ⋅ 13) + 7; 46 vehicles

6 Rochelle’s homework always consists of worksheets. Last

night, the average amount of time she needed to complete
each worksheet was 15 minutes. How much time (t) did
Rochelle spend completing worksheets last night?
To solve the problem, the number of worksheets
must be known.

UNIT 6 LESSON 8 Equations and Parentheses 143

 6-8 Name Date
Remembering

Multiply.

1 56 2 256 3 3,801 4 4,239

× 3
_ × 7
__ ×
__ 6 ×
__ 9
168 1,792 22,806 38,151

5 84 6 67 7 88 8 42
× 23
_ × 18
_ × 39
_ × 45
_
1,932 1,206 3,432 1,890

Multiply or divide.

_ 750 _
4,500
9 0.67⟌ 502.5 10 0.21⟌ 945 11 0.55 12 32.5
× 0.30
__ × 6.3
__
0.165 204.75

Write an equation and use it to solve the problem.

Draw a model it you need to. Equations and models may vary.

13 Lindsay is shopping for a new CD player. The cost of

one CD player she is considering is $56.55. The cost of
a higher priced CD player is $14.25 more. What is the
cost (c) of the higher priced CD player?
c = $56.55 + $14.25; c = $70.80
© Houghton Mifflin Harcourt Publishing Company
14 Stretch Your Thinking Use the equation below to write a
word problem. Leave out one piece of information that is
needed to solve the problem and describe the information
that should have been included. b = (5 ⋅ 6) + 10
Possible answer: Bailey has ten more than 6 times
the number of baseball cards that Tim has. How
many baseball cards does Bailey have? The missing
information is the number of baseball cards Tim
has, which is 5. So, Bailey has 40 baseball cards.

144 UNIT 6 LESSON 8 Equations and Parentheses

 6-9 Name Date
Homework

Solve each problem. Equations may vary. Show your work.

1 After a deposit of $100, a withdrawal of $125, and a deposit
of $24, the balance in a savings account was $27.28. What
was the balance (b) before the deposits and withdrawal?
b = 27.28 − 24 + 125 − 100; b = $28.28

2 The charge for a plumbing repair was $29.60 for parts,

1__
1
hours for labor at $56 per hour, and a $40 for the
4
service call. What was the total cost (c) of the repair?
c = 29.60 + (1__ 1
⋅ 56) + 40; c = $139.60
4

3 Ebi, Jose, Derell, and Asami measured their heights. Ebi’s

height was 2.5 cm greater than Jose’s height. Jose’s height
was 3.1 cm greater than Derell’s height. Derell’s height was
0.4 cm less than Asami’s height. Ebi is 162.5 cm tall. How
tall (t) is Asami?
t = 162.5 − 2.5 − 3.1 + 0.4; t = 157.3 cm

4 A school bus has 22 rows of seats, and 4 students can be

seated in each row. Students riding in the bus have filled
19 rows of seats, and __
1
of the remaining seats. How many
2
seats on the bus are empty (e)?
e = __
1
⋅ 4(22 − 19); e = 6 seats
2

5 Rosa is 13 years and 6 months old and her brother Malcolm

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is 11 years and 6 months old. Their great grandfather is

89 years old. How many years (y) older is the great grandfather
than the combined ages of Rosa and Malcolm?
y = 89 − (13.5 + 11.5); y = 64 years older

6 A riverfront business offers raft trips. The capacity of each

raft is 4 people. Suppose 29 adults and 22 children would
like to raft. If each raft is filled to capacity, how many
people (p) will be aboard the last raft?
p = the remainder of (29 + 22) ÷ 4; p = 3 people

UNIT 6 LESSON 9 Multistep Word Problems 145

 6-9 Name Date
Remembering

Solve.

1 500 2 500 3 900

× 60
__ × 50
__ × 40
__
30,000 25,000 36,000

4 30 5 200 6 300
× 10
_ × 70
__ × 80
__
300 14,000 24,000

Complete each division. Check your answer.

_ 493 _ 538 R3 _ 515 R2
7 7⟌ 3,451 8 4⟌ 2,155 9 8⟌ 4,122

_ 248 R2 _ 704 R2 _ 642

10 5⟌ 1,242 11 3⟌ 2,114 12 9⟌ 5,778

Write and solve an equation to solve the problem. If the

problem does not have enough information, write the
information that is needed to solve the problem.
Equations may vary.
13 Danny has $14.75, Jason has $22.10, and Trey has $87.45. Show your work.
How much more money (m) does Trey have than the
combined amounts of the other two boys?
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m = $87.45 - ($14.75 + $22.10); m = $50.60 more

14 Stretch Your Thinking Write a multistep word problem in

which the remainder is the solution. Write an equation
that will solve it.
Possible answer: Forty-two girls and 60 boys show up
to play in a volleyball tournament. If the tournament
director forms 5 equal teams, how many players would
be left over after the teams are formed? p = the
remainder of (42 + 60) ÷ 5; p = 2 players
146 UNIT 6 LESSON 9 Multistep Word Problems
 6-10 Name Date
Homework

Solve each problem. Equations may vary. Show your work.

1 A savings account balance was $135.10 before a withdrawal
of $60, a deposit of $22.50, and a withdrawal of $45. What
was the balance (b) after the withdrawals and deposit?
b = 135.10 − 60 + 22.50 − 45; b = $52.60

2 The charge for a bicycle repair was $9.28 for parts, __

1
hour
4
of labor at $18 per hour, and a $2 shop fee. What was the
total cost (c) of the repair?
c = 9.28 + (__ 1
⋅ 18) + 2; c = $15.78
4

3 While shopping at the school bookstore, Ric purchased

4 book covers for $1.25 each, and a pen that cost __
2
as much
5
as a book cover. What amount of change (c) did Ric receive
if he paid for his purchase with a $10 bill?
c = 10 − (4 ⋅ 1.25) − (__ 2
⋅ 1.25); c = $4.50
5

4 A junior baseball team plays 16 games each summer. Last

summer the team scored an average of 3.25 runs per game
during the first half of the season. The team scored a total of
29 runs during the second half of the season. How many
runs (r) were scored by the team last season?
r = (16 ⋅ __
1
) ⋅ 3.25 + 29; r = 55 runs
2
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5 Four family members compared their ages. Terell is 3 years

younger than Danny. Danny is 1 year younger than Pablo.
Pablo’s age is __
1
Shaniqua’s age. How old is Terell (t) if
3
Shaniqua is 36 years old?
t = (__
1
⋅ 36) − 1 − 3; t = 8 years old
3

6 Twenty-four soccer players, four coaches, and one equipment

manager are traveling to a game in minivans. The capacity
each minivan is 6 people. How many people (p) are riding in
the last minivan if the other minivans are filled to capacity?
t = the remainder of (24 + 4 + 1) ÷ 6; t = 5 people

UNIT 6 LESSON 10 Practice Problem Solving 147

 6-10 Name Date
Remembering

Multiply.

1 495 2 126 3 2,689 4 3,249

× 7
__ × 6
__ ×
__ 3 ×
__ 8
3,465 756 8,067 25,992

5 78 6 68 7 41 8 92
×
_ 21 ×
_ 55 ×
_ 33 × 89
_
1,638 3,740 1,353 8,188

Divide.
_70 _600 _ 2
9 ⟌
0.7 49 10 ⟌
0.03 18 11 ⟌
0.4 0.8

300
_ _345 _140
12 0.09⟌ 27 13 ⟌
0.5 172.5 14 ⟌
0.06 8.4

Write an equation to solve the problem.

Equations may vary.
15 After a deposit of $250, a withdrawal of $312, and a
deposit of $15, the balance in a savings account is
$67.50. What was the balance (b) before the deposits
and withdrawal?
b = 67.50 - 15 + 312 - 250; b = $114.50

16 Stretch Your Thinking Write an equation that is © Houghton Mifflin Harcourt Publishing Company

represented by the following diagram.

Equations may vary.

r = the remainder of (15 + 7 + 1) ÷ 5

148 UNIT 6 LESSON 10 Practice Problem Solving

 6-11 Name Date
Homework

The data below represent typical weights for five

different breeds of adult male dogs. Make a bar
graph to display the data. Choose an appropriate
scale based on the weights of the dogs.
Check students’ graphs.

Adult Weight
Type of Dog
(in pounds)
Labrador retriever 65.25
German shepherd __
1
75 4
golden retriever 72.8
boxer __
1
70 2
standard poodle 64.3
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UNIT 6 LESSON 11 Focus on Problem Solving 149

 6-11 Name Date
Remembering

Compare. Write > (greater than) or < (less than).

1
●
0.05 < 0.5 2 0.61 ●
> 0.6 3 0.77 ●
> 0.7

4 0.34 ●
< 0.43 5 0.28 ●
< 0.29 6 0.981 ●
> 0.978

Solve the problem. Equations may vary.

1
7 The charge for skating is $6.35 for skate rental, 1__ hours
3
of skating at $18 per hour, and an additional $1 fee.
What is the total cost (c) for skating?
c = 6.35 + (1__ 1
⋅ 18) + 1; c = $31.35
3

8 Stretch Your Thinking Make a table that lists the

data from the bar graph. Tables and data may vary.

Long Jump Lengths

16.5
16
15.5
Jump Length (ft)

15
14.5
14
13.5
13
12.5
12
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0
n
na

on
l
ae

de
aw

nt
ich

Ai
e
Sh

Tr
M

Student Name

Long Jump Length

Student Name Shawna Michael Trenton Aiden

3
Jump Length (ft) 14 __
3
16.5 13__ 15.4
5 4

150 UNIT 6 LESSON 11 Focus on Problem Solving