Download 18 = ⋅ 32 = 8 ⋅ 56 = 18 2 6 3 4 5 3 ⋅ 6 = 18 4 ⋅ 12 = 48 ⋅ 6 = 2

Name
3-1
Date
Solve. Write a multiplication equation for each problem.
Miguel swam 6 lengths of the pool. Po Lan swam 3 times as far
1
as far as Miguel.
as Miguel. Lionel swam __
3
1. How many lengths did Po Lan swim?
18
3 ⋅ 6 = 18
Write the equation.
2. How many lengths did Lionel swim?
1
__
⋅6=2
3
Write the equation.
2
Chris cut a length of rope that was 12 feet long. Dayna cut
a rope 4 times as long as Chris’s rope. Benita cut a rope
1
__
as long as Chris’s rope.
4
48 ft
3. How long is Dayna’s rope?
Write the equation.
4 ⋅ 12 = 48
3 ft
4. How long is Benita’s rope?
1
__
⋅ 12 = 3
4
Write the equation.
Write two statements for each pair of treats. Use the word times.
5. Compare cookies and drinks.
There are 3 times as many cookies as drinks.
1
There are __
times as many drinks as cookies.
Treat
Number
© Houghton Mifflin Harcourt Publishing Company
3
24
6. Compare drinks and pizzas.
There are 4 times as many drinks as pizzas.
1
times as many pizzas as drinks.
There are __
8
4
7. Compare cookies and pizzas.
2
There are 12 times as many cookies as pizzas.
1
times as many pizzas as cookies.
There are ___
12
Solve.
1
⋅ 18 =
8. __
6
1
11. __
of 27 =
9
UNIT 3 LESSON 1
3
1 of 12 =
9. __
3
3
1
12. __
⋅ 56 =
8
1
10. __
⋅ 32 =
4
8
4
7
1
13. __
of 15 =
5
3
Basic Multiplication Concepts
47
Name
3-1
Date
Use the number lines to complete Exercises 1–3.
Thirds
0
3
1
3
2
3
3
3
Sixths
0
6
1
6
2
6
3
6
4
6
5
6
6
6
Twelfths
0 1 2 3 4 5 6 7 8 9 10 11 12
12 12 12 12 12 12 12 12 12 12 12 12 12
2
1. If you run __
mile, how many sixths have you run?
3
4
__
6
5
2. If you measure __
meter, how many twelfths have you measured?
6
10
___
12
8
3. If you have ___
of a pizza, how many thirds do you have?
12
2
__
3
Write each fraction as a decimal.
76 = 0.076
4. _____
1,000
7 =
5. ___
10
0.7
49 = 0.49
6. ____
100
32 = 0.032
7. _____
1,000
0.71
8. 0.28 + 0.43 =
0.74
9. 0.7 + 0.04 =
5.85
10. 7.8 - 1.95 =
1
times 30 equals 6.
11. Stretch Your Thinking Draw a diagram that shows __
Possible answer:
48
UNIT 3 LESSON 1
5
Basic Multiplication Concepts
© Houghton Mifflin Harcourt Publishing Company
Add or subtract.
Name
3-2
Date
Multiply.
2
⋅ 15 =
1. __
10
2
4. __
⋅ 27 =
6
2
7. __
⋅ 21 =
14
4
10. __
⋅ 45 =
20
7
13. __
⋅ 18 =
14
3
2. __
⋅8=
6
3
5. __
⋅ 56 =
21
4
8. __
⋅ 35 =
28
4
3
9
12
5
9. __
⋅ 28 =
20
7
5 ⋅
11. ___
24 =
10
5
14. __
⋅ 80 =
50
12
9
3
6. __
⋅ 16 =
4
5
9
28
8
8
3
7
3. __
⋅ 32 =
9 ⋅
12. ___
70 =
63
4
15. ___
⋅ 45 =
12
10
15
8
Show your work.
Solve.
16. Rebecca has 21 math problems to solve. She has solved
2
__
of them. How many problems has she solved?
7
© Houghton Mifflin Harcourt Publishing Company
6 problems
17. Tessa shot 36 free throws. She made 27 of them.
What fraction of her free throws did Tessa make?
3
__
4
3
18. A carousel has 56 horses. __
of them are white. How
8
many horses are not white?
35 horses
19. Nathan works at a hardware store. Today he sold
5
of the tools he sold were hammers. How
48 tools. __
6
many hammers did Nathan sell today?
40 hammers
UNIT 3 LESSON 2
Multiplication with Non-Unit Fractions
49
Name
3-2
Date
Complete each exercise about the pairs of fraction bars.
3 __
__
,6
1. What equivalent fractions are shown? 4 8
2
2. Identify the multiplier.
12 __
___
,4
3. What equivalent fractions are shown? 18 6
3
4. Identify the divisor.
Write each amount as a decimal number.
84
5. _____
0.084
1,000
31564
6. _____
1,000 31.564
1176
7. ____
100 11.76
876
8. _____
1,000 0.876
Solve. Write a multiplication equation for each problem.
Jonas has 8 sponsors for the school walk-a-thon.
Maura has 3 times as many sponsors as Jonas.
1
as many sponsors as Jonas.
Trenton has __
4
9. How many sponsors does Maura have?
Write the equation.
24
8 ⋅ 3 = 24
10. How many sponsors does Trenton have?
1
__
⋅8=2
4
Write the equation.
2
Jo has driven farther. Jo has 10 miles to go. Hannah
as 24 miles to go.
50
UNIT 3 LESSON 2
Multiplication with Non-Unit Fractions
© Houghton Mifflin Harcourt Publishing Company
11. Stretch Your Thinking Hannah and Jo are driving
separately to a restaurant that is 60 miles away
3
of the distance
from their town. Hannah drives __
5
5
__
and Jo drives of the distance before stopping for
6
gasoline. Who has driven farther? How many
more miles does each driver need to drive to
reach the restaurant?
5
1
⋅ 60 = 5 ⋅ (__
of 60) = 5 ⋅ 10 = 50 miles.
Jo has driven __
6
6
3
1
⋅ 60 = 3 ⋅ (__
⋅ 60) = 3 ⋅ 12 = 36 miles.
Hannah has driven __
5
5
Name
3-3
Date
The campers in each cabin at Bear Claw Camp held a contest
to see who could walk the farthest in one day. Use the sign to
answer the questions. Write your answers as fractions.
1
of the way to Otter
1. The campers in Cabin A walked __
4
Ridge. How many miles did they walk?
13
___
miles
4
2
2. The campers in Cabin B walked __
of the way to Silver
3
Stream. How many miles did they walk?
16
___
miles
3
3
3. The campers in Cabin C walked __
of the way to Fossil Cave.
5
How many miles did they walk?
27
___
miles
5
1
4. The campers in Cabin D walked __
of the way to Mammoth
6
Mountain. How many miles did they walk?
25
___
miles
6
5. Which group of campers walked the farthest that day?
Cabin C
2
6. Show __
of 4 on the number line.
© Houghton Mifflin Harcourt Publishing Company
3
0
1
2
7. Write __
of 4 as a fraction.
8
__
2
4
3
3
__
8. Write 2 of 4 as a mixed number.
3
2
2__
3
Multiply. Write your answers as fractions.
8
__
2
2
⋅
4=
10. __
⋅8=
9. __
7
7
3
40
___
2
7
12. __
⋅
20 =
13. __
⋅2=
9
9
9
26
___
5
2
15. __
⋅
13 =
16. ___
⋅ 18 =
3
3
12
UNIT 3 LESSON 3
3
16
___
3
14
___
9
90
___
12
5
11. __
⋅4=
6
3
14. __
⋅5=
8
5
17. __
⋅ 12 =
9
20
___
6
15
___
8
60
___
9
Multiplication with Fractional Solutions
51
Name
3-3
Date
Compare.
5 > __
5
1. __
7
1 < __
1
2. __
4
8 > __
6
3. ___
6 < __
7
4. __
3
2 < __
5. __
8 > __
6
6. __
8. 0.207 < 0.342
9. 0.5 > 0.47
6
7
5
8
3
10
4
9
8
7
Compare.
7. 0.54 < 0.65
10. 0.76 > 0.67
12. 0.6 > 0.06
11. 0.22 < 0.41
Multiply.
16
2 ⋅
14. __
21 =
14
5 ⋅
15. __
24 =
15
1 ⋅
16. __
36 =
4
3 ⋅
17. __
16 =
12
2 ⋅
18. __
14 =
4
3 ⋅
21. __
45 =
15
5
9
3 ⋅
19. ___
24 =
12
6
3
4
8 ⋅
20. ___
80 =
10
8
7
64
9
22. Stretch Your Thinking Write a multiplication equation
using one whole number and one fraction that have
18
.
a product of ___
8
3 = ___
18
Possible answer: 6 ⋅ __
8
8
52
UNIT 3 LESSON 3
Multiplication with Fractional Solutions
© Houghton Mifflin Harcourt Publishing Company
4 ⋅
20 =
13. __
Name
3-4
Date
3 __
Tanith is using a number line to find __
⋅ 2 . This is her work so far:
4
5
0
1
–
5
2
–
5
3
–
5
4
–
5
1
0
1
–
5
2
–
5
3
–
5
4
–
5
1
0
—
20
1
—
20
2
—
20
3
—
20
4
—
20
5
—
20
6
—
20
7
—
20
8
—
20
9
—
20
10
—
20
11
—
20
12
—
20
13
—
20
14
—
20
15
—
20
16
—
20
17
—
20
18
—
20
19
—
20
20
—
20
1. Explain Tanith’s work so far to someone at home.
3
of each
2. Finish Tanith’s work by circling __
4
circled fifth. How many 20ths did you circle altogether?
6
3
3 __
2 ___ or ___
What is __
⋅
? 20
10
4 5
2 __
3. Use the number line to find __
⋅ 5.
3 6
Label all the parts above and below.
1
–
6
0
0
—
18
1
—
18
2
—
18
3
—
18
2
–
6
4
—
18
5
—
18
6
—
18
10
___
18
3
–
6
7
—
18
8
—
18
6
9
—
18
4
–
6
10
—
18
11
—
18
5
–
6
12
—
18
13
—
18
14
—
18
16
—
18
17
—
18
18
—
18
Show your work.
Solve.
© Houghton Mifflin Harcourt Publishing Company
15
—
18
1
3
of a bag of popcorn.
4. Four friends at a party popped __
4
They ate half of what was popped. What fraction of the
3
__
popcorn in the bag did they eat?
8
7
5. Ashley brought __
gallon of lemonade to the party.
8
2
of it. How many gallons of
Her friends drank __
3
7
___
gallon
lemonade did they drink?
12
Multiply. You do not need to simplify.
2
___
2 __
1 =
4 __
⋅
7. __
⋅2=
6. __
21
7 3
9 9
24
___
2
4 __
9. __
⋅
12 =
10. __
⋅2=
7
7
5 3
9
___
9 __
5
1 =
12. ___
⋅
13. ___
⋅3=
20
10 2
12
UNIT 3 LESSON 4
8
___
81
8
___
15
15
___
12
1 __
8. __
⋅5=
8
6
1 __
11. __
⋅3=
7
5
5 __
14. __
⋅1=
6
6
5
___
48
3
___
35
5
___
36
Multiply a Fraction by a Fraction
53
Name
3-4
Date
Name the mixed number shown by the shaded parts.
1
5__
2
1.
5
1__
7
2.
1
1__
3
3.
Add.
81.46
5. 80.55 + 0.91=
454.65
4. 454 + 0.65 =
37.98 m
6. 31.78 m + 6.2 m =
1
7. Show __
of 7 on the number line.
3
0
1
2
3
4
5
6
7
7
__
1
of 7 as a fraction.
8. Write __
3
3
1
2__
3
3
5
6
10. Stretch Your Thinking Solve for the unknown fraction.
Then divide and shade an area model to show the
2 ⋅ = ___
? 10 .
equation. __
5
2
5
30
5
__
6
54
UNIT 3 LESSON 4
Multiply a Fraction by a Fraction
© Houghton Mifflin Harcourt Publishing Company
1
9. Write __
of 7 as a mixed number.
Name
3-5
Date
Multiply. Simplify first if you can.
12
___
2 __
1. __
⋅6=
5
7
5 ___
3. ___
⋅ 8 =
3 24
15 3
1
1
5 35
1
12 3
9
6
1
1
7 __
12. __
⋅2=
21
49 7
25
5 __
10. __
⋅7=
2
___
2
1
816
15
7 ___
11. __
⋅ 6 =
3
1
1
___
1
4 ___
9. ___
⋅ 7 =
8
5 ___
8. ___
⋅ 2 5=
5
31
1
7
1
__
1
1
5 __
6. __
⋅3=
25
3 ⋅ __
2 =
7. ___
5 10
17
9
___
⋅
4 25
12 =
___
82
2 __
4. ___
⋅8=
9
3
3
5. __
9
1
__
1
1
1
4 __
2. __
⋅1=
35
4
8
3
1
___
18
16
___
17
15
___
56
1
___
40
35
___
6
7
___
12
13. Which fraction is not equivalent to the others?
3
___
2
___
1
__
9
___
10
___
6
___
7
___
100
____
15
10
5
45
50
40
35
500
Solve.
Show your work
© Houghton Mifflin Harcourt Publishing Company
3
of the animals are birds. Of the
14. In the town zoo, ___
28
4
___
are birds of prey. What fraction of the
birds,
15
animals at the zoo are birds of prey?
1
___
35
5
15. Tuesday at the zoo, ___
of the visitors were adults. Of these
12
3
___
were men. What fraction of the people who
adults,
10
visited the zoo on Tuesday were men?
1
__
8
14
16. On Tuesday, ___
of the souvenirs purchased at the zoo gift
25
shop were stuffed animals. Of the stuffed animals purchased,
10
___
were bears. What fraction of the souvenirs purchased at
21
the zoo gift shop on Tuesday were stuffed bears?
4
___
15
UNIT 3 LESSON 5
Multiplication Strategies
55
Name
3-5
Date
Add or subtract.
1 + __
2. 5__
35
4 + __
1. 1__
52
5
5
6
1
7__
3
3 + __
5
4. __
4
2
3
1
1__
9
5
4
2 - __
1
3. 1__
6
3
8 - __
35
5. 7__
9
9
3
1
__
4 or 4__
9
3
1
6. 6 - 4__
8. 132.76 - 87.24 =
9. 968.29 - 217.5 =
2
1
1__
2
Subtract.
7. 31,763 - 6.51 =
45.52
31,756.49
750.79
3 __
10. Use the number line to find __
⋅ 2 . Label all the parts
4 5
above and below.
⋅ __2 =
4 5
3
__
6
___
20
1
5
0
1
20
2
20
3
20
4
20
5
20
6
20
7
20
8
20
1
9
20
10
20
11
20
12
20
13
20
14
20
15
20
16
20
17
20
18
20
19
20
20
20
11. Stretch Your Thinking Write a word problem that will
2 ___
⋅ 8 = x in order to solve. Then
use the equation __
6
10
simplify and multiply to solve.
8
of the basketball team’s points in
Possible answer: Jacob scored ___
10
Saturday’s basketball game. Two sixths of the points Jacob scored were
from free throws. What fraction of the team’s points did Jacob score
2 ___
1 __
4
from free throws? __
⋅ 8 = __
⋅ 4 = ___
6
56
UNIT 3 LESSON 5
10
3
5
15
Multiplication Strategies
© Houghton Mifflin Harcourt Publishing Company
0
20
2
5
Name
3-6
Date
Find each product by first rewriting each mixed number
as a fraction.
3
⋅ 2__1 =
1. __
7
2
2
3. 2__
⋅ 4__1 =
5
3
3 __
15 = ___
__
⋅ 5 = ___
11
7
2
2
5
3
7
2. 1___
⋅5=
14
10
5
5
5 __
7
__
⋅ 7 = __
9
5
1
7. 3__
⋅ 3__1 =
14
8 ___
56 =
1
__
⋅ 21 = ___
11__
5
5. __
⋅ 1__2 =
9
2
5
2
4
3
8
3 =
6. 12 ⋅ 2__
9
4
49 =
7 __
1
__
⋅ 7 = ___
12__
2
1 __
4. 5__
⋅3=
4
9 =
1
8. __
⋅ 3___
9
10
Solve.
17 __
17 = __
___
⋅ 5 = ___
81
1
10
2
2
16 __
___
⋅3=2
3
8
12 ___
___
⋅ 11 = 33
1
4
13
1 ___
__
⋅ 39 = ___
9
10
30
Show your work.
© Houghton Mifflin Harcourt Publishing Company
9. The bottom of Zeyda’s jewelry box is a rectangle with
3
1
inches and width 3__
inches. What is the area
length 5__
4
8
of the bottom of the jewelry box?
15
17___
square inches
32
10. The Patel family went apple picking. The number of
2
times the number of
red apples they picked was 2__
9
green apples they picked. If they picked 45 green
apples, how many red apples did they pick?
100 red apples
1
11. The art museum is 8__
miles from Alison’s house.
2
2
of the way there so far.
Alison has ridden her bike __
3
How far has she gone?
2
miles
5__
3
UNIT 3 LESSON 6
Multiply Mixed Numbers
57
Name
3-6
Date
Add.
3 + __
1
1. __
8
3
1 + __
2. __
5
6
5 + __
1
3. __
4
6
8
13
___
19
___
23
___
24
20
24
1 + __
2
4. __
2 + __
1
5. __
7
3
3
4 + ___
1
6. __
5
9
10
13
___
7
__
9
___
21
9
10
Use the Commutative Property to solve for n.
7. 55,207 + 87,331 = 87,331 + n
n = 55,207
8. 48.76 + 20.08 = 20.08 + n
n = 48.76
Multiply. Simplify first if you can.
1
__
3 =
2 __
7 __
⋅
10. ___
⋅6=
9. __
2
3 4
10 7
6
25
2
__
1 __
⋅4=
13. __
5
2
7
5
2
__
7
3 __
11. __
⋅5=
5
6
2 __
14. __
⋅3=
9
8
1
__
2
1
___
12
15. Stretch Your Thinking Complete the mixed number equation
that is represented by the area model.
⋅
2
1
__
58
2
1__
3
=
UNIT 3 LESSON 6
5
__
6
Multiply Mixed Numbers
© Houghton Mifflin Harcourt Publishing Company
5 ___
⋅ 12 =
12. __
3
__
3-7
Name
Date
Solve.
3 __
⋅1
1. __
4 8
3
___
32
2 - __
1
2. __
2
4. __
⋅ 12
7
24 = __
___
33
7
7
1 + __
2
5. __
5 __
7. __
⋅5
7 6
25
___
42
11 +
8. ___
3
1 __
10. __
⋅1
3 8
1
___
24
3
1 + __
1
3. ___
9
10
5
__
3
___
9
10
5
5
3
1 + __
6. __
4
3
8
5
__
8
13
___
15
4 - __
2
9. __
12
9
11
3___
9
2
__
12
9
1
12. 10 - __
9
89 = __
___
98
9
9
7 __
11. __
⋅3
8 4
21
___
32
Show your work.
Solve.
7
gallon of water. It is
13. Rodrigo’s fish bowl holds __
8
1
now __ full. How much water is in it?
2
7
___
gallon
16
© Houghton Mifflin Harcourt Publishing Company
1
14. Kenya jumped 7__
feet. Janet jumped
6
How much farther did Kenya jump?
5
__
foot
6
1
6__
feet.
3
7
15. A group of hikers walked 8___
miles to Caribou Cave
10
1
__
and then 5 miles to Silver Stream. How far did they
5
walk altogether?
9
13___
miles
10
3
16. A recipe calls for __
cup of flour. Estevan wants to make
4
1
__
of the recipe. How much flour will he need?
3
1
__
cup
4
1
17. A truck was carrying 2__
tons of sand. When it arrived,
8
1
only 1__ tons of sand were left. How much sand was
2
lost along the way?
5
__
ton
8
UNIT 3 LESSON 7
Relate Fraction Operations
59
Name
3-7
Date
Subtract.
3 - __
1
1. __
4
2 - ___
1
2. __
6
9
10
7 - __
1
3. __
4
8
7
___
11
___
5
__
12
90
8
6 - __
1
4. __
7
4 - __
2
5. __
5
3
3
1 - __
1
6. __
2
8
11
___
2
___
3
__
21
15
8
Sample estimates shown; accept
reasonable estimates.
8. $44.25 - $21.76 $22
9. 14.6 + 2.4 17
Estimate each sum or difference.
7. 6.759 + 2.099
9
Find each product by first rewriting each mixed
number as a fraction.
5 ___
25 = ___
__
⋅ 10 = ___
21
5
1 =
⋅
3__
10. __
8 3
12
12
8
3
3
11. 4__
⋅5=
5
2
12. 1__
⋅ 3__4 =
5
9
5
8
5
1
1
7 ___
217 = ___
__
⋅ 31 = ___
4 37
5
9
45
45
© Houghton Mifflin Harcourt Publishing Company
1 __
13. 6__
⋅5=
23 __
23 =
___
⋅ 5 = ___
23
31 __
31 = __
___
⋅ 5 = ___
37
5
8
8
8
14. Stretch Your Thinking Give an example that shows
how to use the Distributive Property to multiply a
number by a sum. All of the numbers you use should
be mixed numbers or fractions.
5 = __
2
1 + __
1 + __
2 __
Possible answer: __
⋅ (2__
) 2 ⋅ 2__
⋅5=
4
4
3
6
3
3 6
3 + __
5 = ___
37 = ___
2 __
2 __
__
⋅ 9 + __
⋅ 5 = __
21
3 4
3 6
2
9
18
18
60
UNIT 3 LESSON 7
Relate Fraction Operations
Name
3-8
Date
Complete each fraction box.
1.
3
7
__
and __
>
+
-
⋅
8
3
6
7 > __
7 > __
__
or __
4
8
8
8
7
__
8
7
__
8
7
__
8
2.
3
1
__
and __
3 = __
6 = ___
13 = __
7 + __
+ __
15
4
8
8
8
8
3 = __
6 = __
7 - __
1
- __
4
8
8
8
3 = ___
21
⋅ __
4
32
5
2
4
>
+
-
⋅
3 > __
6 > ___
5
1
__
or ___
5
2
10
3 = ___
5 +
1 + __
__
5
2
10
3 - __
6 1 = ___
__
5
2
10
3
1 __
__
⋅ 3 = ___
2 5
10
10
6 =
___
10
5 =
___
10
11 = ___
___
11
10
1
___
10
10
Show your work.
Solve.
7
ton of
3. The Eagle Trucking Company must deliver __
8
5
__
cement blocks and ton of bricks to one place.
8
How much will this load weigh?
1
1__
tons
2
© Houghton Mifflin Harcourt Publishing Company
1
1
4. A truck carried 3__
tons of sand, but lost __
ton along
4
3
the way. How many tons of sand were delivered?
1
3___
tons
12
2
5. The trucking company also needs to deliver 1__
tons of
3
7
___
oak logs and 1 tons of maple logs. Which load
12
weighs more?
oak logs
3
1
6. In a load of __
ton of steel rods, __
of them are bent.
4
8
How many tons of steel rods are bent?
3
___
ton
32
3
7. The company delivered 1__
tons of bricks to one building site.
5
1
__
They delivered 2 times this much to a second site. What was
2
the weight of the load the company delivered to
the second site?
4 tons
UNIT 3 LESSON 8
Solve Real World Problems
61
Name
3-8
Date
Multiply.
1.
2.
2,548
×
__5
3.
945
12,740
4.
21
×
45
_
5.
33
×
_4
132
3,015
×
__6
18,090
65
×
87
_
6.
215
×
__9
1,935
5,655
Find each product by first rewriting each mixed number as a fraction.
40 __
320 =
23
___
⋅ 8 = ___
11___
4
2 =
7. 4__
⋅
2__
9 3
27
27
9
3
5
9. 3__
6
23
___
12 =
___
6
⋅ 13
1
8. 6__
⋅ 10 =
13
5
5
46 = ___
12 = ___
⋅ ___
37
13
31 ___
62 =
___
⋅ 10 = ___
62
1
10. 5__
13
3
16
___
3 =
__
3
⋅5
1
1
3 = ___
16 = __
⋅ __
31
5
5
5
Solve.
6 - __
2
11. __
7
7
4
__
7
4 + __
2
12. __
9
3
1
1__
9
2 ___
13. __
⋅ 9
3 10
3
__
5
3 __
⋅5
14. __
1
15. 8 - __
3
1 + __
16. __
5
7
8
6
55 = __
___
76
7
7
8
13
___
24
© Houghton Mifflin Harcourt Publishing Company
3
__
8
17. Stretch Your Thinking Write and solve a word problem
that requires multiplying two mixed numbers.
5
Possible answer: Taylor worked 6__
hours doing yard
6
work one weekend. The next weekend, he worked
1
1__
times as long as he did the previous weekend.
2
How many hours did Taylor work on the second
1
weekend? 10__
hours
4
62
UNIT 3 LESSON 8
Solve Real World Problems
Name
3-9
Date
Predict whether the product will be greater than, less than,
or equal to the second factor. Then compute the product. Predictions may vary.
4
1. __
⋅6=x
1
2. 1__
⋅6=x
5
Predict: x < 6
4
4__
5
Compute: x =
2 __
4. __
⋅5=x
2
10
3. ___
⋅6=x
9
10
Predict: x > 6
2
6__
3
Compute: x =
5 __
5. __
⋅5=x
6
6
5
Predict: x = __
6 __
5
Compute: x =
6
Compute: x =
6
Compute: x =
1 __
6. 1__
⋅5=x
6
Predict: x <
Predict: x = 6
3
5
__
6 ___
25
36
6
5
Predict: x > __
6
Compute: x =
1
1__
9
Show your work.
Solve.
3
times as tall as his brother. His brother
7. James is 1__
7
1
__
is 3 feet tall.
2
1
feet?
Is James’s height more or less than 3__
2
© Houghton Mifflin Harcourt Publishing Company
more
How tall is James?
5 feet
8. South Middle School has 750 students. North Middle
13
times as many students as South.
School has ___
15
Does North Middle School have more or fewer than
750 students?
fewer
How many students attend North Middle School?
650 students
UNIT 3 LESSON 9
Make Generalizations
63
Name
Date
Perry measured the foot length of four
friends for a science fair experiment. Then,
he made a bar graph to display his results.
Foot length (in.)
Foot Length
1. How much longer is Brennen’s foot than
Clara’s foot?
0.7 inch
2. What is the difference between the
longest foot and the shortest
foot?
9
8.8
8.6
8.4
8.2
8
7.8
7.6
7.4
n
a
Ch
Br
en
ne
ar
Cl
ey
0.9 inch
ne
Ty
e
0
en
3-9
Student Name
Solve.
7
7 __
3. __
⋅ 4 ___
8 9 18
1
3
4. 11 - __
10__
4
4
1
9 - ___
5 __
6. ___
12
12 3
7 + __
2
7. ___
15
3
15 = __
4 + ___
7 ___
5. __
11
5
10 10
2
17 = ___
___
12
15
15
15
5 ___
⋅ 9 ___
8. __
6 11 22
Complete each fraction box.
5
7
___
and __
12
4
2
__
and __
6
5
+
−
⋅
6
12
12
5
10
7
__ + ___ = ___ +
6
12
12
5 - ___
10 −
7 = ___
__
6
12
12
5
35
7
__ ⋅ ___ = ___
6 12
72
12
7
___ =
12
7 =
___
12
>
17 = ___
___
15
12
12
3 = __
1
___
4
12
+
−
⋅
3
10
4 > __
2
12 > ___
__
or ___
5
15
3
4 + __
2 = ___
12 +
__
5
15
3
4 − __
2 = ___
12 −
__
5
15
3
8
4 __
__
⋅ 2 = ___
5 3
15
15
10
___ =
15
10 =
___
15
22 = ___
___
17
15
15
2
___
15
9. Stretch Your Thinking Write two multiplication equations
using fractions and mixed numbers. Write one equation
that will have a product greater than the first factor.
Then write another equation that will have a product
less than the first factor.
3 = ___
25 = ___
4
1 __
⋅ 2__
3 31 ; 3__
⋅ 2 = ___
21
Possible answer: 1__
9
8
72 8 3
12
12
64
UNIT 3 LESSON 9
Making Generalizations
© Houghton Mifflin Harcourt Publishing Company
5 > ___
10 > ___
7
7
> __
or ___
Name
3-10
Date
Divide
5
__
1. 5 ÷ 6 =
3. 33 ÷ 30 =
5. 3 ÷ 10 =
1 =
7. 100 ÷ __
6
1 ÷ =
9. __
8
5
1 ÷ =
11. __
9
2
6
10
3
___
10
600
1
___
40
1
___
18
45
1 =
4. 8 ÷ __
48
1 =
6. 4 ÷ __
36
5
11 = ___
___
11
10
1 =
2. 9 ÷ __
6
9
1
___
8. 1 ÷ 100 =
100
1
___
1 ÷ =
10. __
7
56
8
1
___
1 ÷ =
12. __
5
15
3
Show your work.
Solve.
13. Alexander is dividing oranges into eighths. He has 5 oranges.
How many eighths will he have?
40 eighths
© Houghton Mifflin Harcourt Publishing Company
14. Carrie has 32 ounces of ice cream to divide equally among
10 people. How much ice cream will each person get?
1
3__
ounces
5
15. Nayati wants to swim 50 miles this school year. She plans to
swim _1_ mile each day. How many days will it take her to
4
swim 50 miles?
200 days
1
16. Eric has __
of a watermelon to share equally with 3 friends.
3
How much will each person get?
1
___
watermelon
12
17. A gardener needs to pack 16 pounds of beans into 20 bags.
He wants all the bags to weigh about the same. About how
much will each bag weigh?
_4_ pound
5
UNIT 3 LESSON 10
When Dividing Is Also Multiplying
65
Name
3-10
Add or subtract.
3
1. 2__
Date
2.
4
5
- 1__
_8
1
1__
5.
1
- 2__
_6
5
4__
12
8.
5
6
__
and __
7
6
7
10
2
14 > ___
> __
or ___
7
35
35
10
2
14
__
___
___
+ =
+
=
7
35
35
10 =
2 = ___
14 − ___
− __
7
35
35
2 = ___
4
__
⋅
7
35
3
3
+ 1__
_4
1
10___
30
2
__
5
2
__
5
2
__
5
2
__
5
1
8__
6.
7
8___
5
⋅
10
5
5
+ 4__
_6
Complete each fraction box.
7.
2
2
__
and __
−
7
6___
2
3__
6
+
2
6__
2
4
- 3__
_5
9
7
>
1
3. 10__
3
5
+ 1__
_9
8
4.
2
4__
6 > __
5
36 > ___
35
__
or ___
>
24
___
35
4
___
35
7
6
42
42
6
5
36
35
__ + __ = ___ + ___ =
7
6
42
42
6 − __
5 = ___
36 − ___
35 =
__
7
6
42
42
6
5
30
5
__ ⋅ __ = ___ = __
7 6
7
42
+
−
⋅
71 = ___
___
1 29
42
42
1
___
42
Predict whether the product will be greater than, less than,
or equal to the second factor. Then compute the product. Predictions may vary.
3
2
1
⋅5=x
10. __
⋅5=x
11. 1__
⋅5=x
9. __
3
Compute: x =
1
3__
3
6
Predict: x > 5
Predict: x = 5
Compute: x =
5
Compute: x =
5
5__
6
12. Stretch Your Thinking Draw a diagram to show how many
twelfths there are in 3. Describe a situation in which you
would need to know how many twelfths there are in 3.
1
of a foot, so the
Possible answer: An inch is ___
12
number of inches in 3 feet is the number of
twelfths in 3.
66
UNIT 3 LESSON 10
When Dividing Is Also Multiplying
© Houghton Mifflin Harcourt Publishing Company
Predict: x < 5
3
3-11
Name
Date
1 ÷
1. Consider the division problem __
3.
2
Describe a situation this division could represent.
Situations will vary.
Draw a diagram to represent the division. Then find the solution.
1
__
; Diagrams will vary. Check students’ work.
6
Write an equation. Then solve. Equations may vary.
Show your work.
2. A rectangle has an area of 12 square feet and a length of
5 feet. What is its width?
2
5 ⋅ w = 12; 2__
feet
5
© Houghton Mifflin Harcourt Publishing Company
1
3. A tortoise must walk ___
mile to visit a friend. He plans to
12
break the journey into four equal parts with breaks in between.
How long will each part of his journey be?
1 ÷
1
4; ___
mile
x = ___
12
48
1
4. Harry worked 7 hours last week. This is __
as many hours as
3
Aidan worked. How many hours did Aidan work?
1
__
⋅ a = 7; 21 hours
3
5. Lin is a camp counselor. She is making small bags of trail mix
for campers to take on a hike. She has 2 pounds of raisins and
1
pound in each bag. How many bags can she fill
is putting __
8
before she runs out of raisins?
1
; 16 bags
x = 2 ÷ __
8
1
6. Mr. Ramirez bought __
pounds of cashews. He divided the
4
cashews equally among his three children. How much did
each child get?
1 ÷
1
3; ___
pound
x = __
4
12
UNIT 3 LESSON 11
Solve Division Problems
67
Name
3-11
Date
Add or subtract.
1.
1
1__
2.
8
2
+ 4__
_3
19
5___
4.
1
6__
3.
4
5
– 4__
_6
12
4
5.
7
11
+ 5___
14
__
6.
2
– 2__
_5
3
1__
5
1
11___
14
3
8
+ 7__
_9
2
17__
5
1___
24
2
5__
1
9__
9
5
6__
8
1
+ 3__
_2
1
10__
8
Predict whether the product will be greater than, less than, or
equal to the second factor. Then compute the product. Predictions may vary.
5
⋅9=x
7. __
7
8. __
⋅9=x
5
Predict: x = 9
5
Predict: x < 9
9
Compute: x =
1 __
10. 1__
⋅4=x
2
3
9. 1__
⋅9=x
8
7
7__
8
Compute: x =
6 __
11. __
⋅4=x
5
6
4
Predict: x > __
5
Compute: x =
1
1__
5
Predict: x > 9
2
14__
5
Compute: x =
2 __
12. __
⋅4=x
5
5
4
Predict: x = __
5
Compute: x =
4
__
5
5
4
Predict: x < __
5
8
___
25
Compute: x =
Divide.
4
1 =
16. 200 ÷ __
4
24
800
14. 2 ÷ 3 =
1 ÷ =
17. __
8
4
2
__
3
1
___
32
15. 10 ÷ 3 =
1 ÷ =
18. __
6
7
1
3__
3
1
___
42
19. Stretch Your Thinking Harrison is playing a board game that
1
of the
has a path of 100 spaces. After his first turn, he is __
5
1
fewer
way along the spaces. On his second turn, he moves __
4
spaces than he moved on his first turn. On his third turn, he
1
times as many spaces than he moved on his first
moves 1__
4
turn. What space is he on after three turns?
60
68
UNIT 3 LESSON 11
Solve Division Problems
© Houghton Mifflin Harcourt Publishing Company
1 =
13. 6 ÷ __
Name
3-12
Date
Solve.
1 =
1. 5 ⋅ __
3
1 ÷ =
3. __
2
8
1 =
5. 5 ÷ ____
100
3 ___
7. __
⋅ 10 =
5
27
1 ÷
9. __
10 =
5
1
11. __
⋅ 14 =
8
5
__
3
1 =
2. 5 ÷ __
3
1
___
16
4. 27 ÷ 10 =
500
1 =
6. 12 ⋅ __
2
__
9
1
___
50
3
1__
4
15
7
2___
10
1
1__
9
3
1 =
8. 16 ÷ __
64
1 =
10. 10 ÷ __
50
4
5
12. 18 ÷ 20 =
Tell whether you need to multiply or divide. Then solve.
Equations will vary. Possible equations are given.
9
___
10
Show your work.
1
ounce. Jody has 1 pound
13. A dime weighs about ___
12
(16 ounces) of dimes. About many dimes does she have?
Divide; 192 dimes
1
14. Maddie has 180 coins. Of these coins, ___
are dimes.
12
About how many dimes does she have?
© Houghton Mifflin Harcourt Publishing Company
Multiply; 15 dimes
1
15. A rectangle has length 3 feet and width __
foot. What is the
4
area of the rectangle?
3
square foot
Multiply; __
4
1
16. A rectangle has area 3 square feet and width __
foot.
2
What is the length of the rectangle?
Divide; 6 feet
17. Nisha wants to study 5 hours for the spelling bee. If she
1
hour per night, how many nights will she
studies __
3
have to study?
Divide; 15 nights
UNIT 3 LESSON 12
Distinguishing Multiplication from Division
69
Name
3-12
Date
Multiply.
1. 134 ⋅ 5 =
670
4. 4,507 ⋅ 3 = 13,521
2. 44 ⋅ 21 =
924
3. 7 ⋅ 57 =
399
5. 36 ⋅ 76 = 2,736
6. 1,928 ⋅ 6 = 11,568
1 =
8. 100 ÷ __
1 ÷ =
9. __
4
Divide.
1 ÷ =
7. __
2
9
10. 4 ÷ 5 =
1
___
18
4
__
5
3
11. 12 ÷ 5 =
300
2
2__
5
5
1 =
12. 8 ÷ __
7
1
___
20
56
Show your work.
Write an equation. Then solve. Equations may vary.
14. Stretch Your Thinking Using a whole number and a fraction
as factors, write a multiplication equation with a product
less than the whole number factor. Draw a picture to show
how the product is less than the whole number factor.
9
7
Possible answer: ___
⋅ 3 = 2___
10
10
70
UNIT 3 LESSON 12
Distinguishing Multiplication from Division
© Houghton Mifflin Harcourt Publishing Company
13. Marc is running 5 kilometers at track practice. He decides
to break the run into 3 equal lengths. How long will each
length be?
2
x = 5 ÷ 3; 1__
km
3
Name
3-13
Date
Show your work.
Solve.
1. Dan’s Ice Cream comes in cartons of two sizes. The large
3
1
pounds. The small carton holds 1__
pounds
carton holds 4__
4
2
less. How much ice cream does the small carton hold?
3
2__
pounds
4
2. Mac picked four baskets of blueberries. The weights of the
berries in pounds are given below. Order the weights from
lightest to heaviest.
5
__
9
___
4
__
13
___
4
10
5
20
13 __
9 __
___
, 4 , ___
,5
20 5 10 4
1
3. Four cones of Dan’s Ice Cream hold __
pound. How much
2
ice cream does each cone hold?
1
__
pound
8
1
4. If a dish of ice cream holds __
pound, how many dishes can
4
1
__
you get from a 4 -pound carton of Dan’s Ice Cream?
18 dishes
2
© Houghton Mifflin Harcourt Publishing Company
Solve. Give your answer in simplest form.
1 =
5. 3 ÷ __
5
9
7. ___
⋅ 2__1 =
14
3 =
1 + __
9. __
5
3
1 ÷ =
11. __
4
8
5 - __
13. 3__
11 =
7
2
UNIT 3 LESSON 13
4
1
1__
2
3
7
2___
3 + ___
11 =
6. 1__
15
14
___
3
8. 2__
⋅6=
6
1
___
9
2 - ___
1 =
12. __
32
5
3
2___
14
3
15__
5
5
5 + __
8 =
10. __
15
16
16
10
7 __
14. __
⋅2=
8
7
13
1___
18
3
___
10
1
__
4
Review Operations with Fractions
71
Name
3-13
Date
1
Use benchmarks of 0, __
, and 1 to estimate the sum or
2
difference. Then find the actual sum or difference.
5 + __
4
1. ___
10
13 – __
3
2. ___
14
9
1
Estimate:
85
17
___
or ___
Sum: 90
18
1
__
Estimate:
2
1
__
2
Difference:
8 – __
7
3. __
9
7
13 + __
3
4. ___
8
14
0
1
___
Estimate:
2
Estimate:
72
Difference:
4
Sum:
19
1___
28
Show your work.
Write an equation. Then solve. Equations may vary.
5. A rectangle has an area of 20 square feet and a length of
6 feet. What is its width?
1
6 ⋅ w = 20; 3 __
feet
3
6. Bailey attends gymnastics practice for 8 hours each week.
1
the number of hours that the gym is open for
This is __
4
practice. How many hours is the gym open for practice?
1
__
⋅ a = 8; 32 hours
4
Solve.
1 ÷ =
7. __
3
4
1
___
12
1
8. __
⋅3=
4
3
__
4
1 =
9. 14 ⋅ __
6
1
2 __
3
© Houghton Mifflin Harcourt Publishing Company
1 ÷
5 different
10. Stretch Your Thinking How is solving __
8
1
from solving __ ⋅ 5?
8
1 ÷
1
5, multiply __
by
Possible answer: To solve __
8
8
1 __
1.
1
the reciprocal of 5: __
⋅ 1 = ___
To solve __
⋅ 5, first
8 5
40
8
5.
rewrite 5 as __
Then, multiply the two fractions:
1
5.
1 __
__
⋅ 5 = __
8 1
8
72
UNIT 3 LESSON 13
Review Operations with Fractions
Name
3-14
Date
These graphs show the instruments in two different high school
marching bands.
Carter School Marching Band
Reagan School Marching Band
1
–
3
1
–
3
percussion
2
–
5
brass
1
–
6
percussion
woodwind
1
–
2
brass
4
—
15
woodwind
Show your work.
Solve. Use the circle graphs.
1. The Reagan School Marching Band has three percussion
musicians. How many musicians altogether are in the
band?
18 musicians
2. There are 30 musicians in the Carter School
Marching Band. How many of them play brass
instruments?
© Houghton Mifflin Harcourt Publishing Company
12 musicians
Suppose both bands decide to combine and perform as one band.
3. What fraction of the band members will play a brass
instrument?
7
___
16
4. What fraction of the band members will play a percussion
instrument?
13
___
48
5. What fraction of the band members will play a
woodwind instrument?
7
___
24
UNIT 3 LESSON 14
Focus on Mathematical Practices
73
Name
3-14
Date
Show your work.
Solve. Explain how you know your answer is reasonable.
Explanations may vary.
1
feet and a width
1. James’s garden has a length of 12__
4
2
of 9__ feet. What length of fencing will he need to
3
surround his garden?
5
feet
43__
6
Answer:
Why is the answer reasonable?
1
2
12__
rounds to 12. 9__
rounds to 10. The answer
4
3
should be about 12 + 12 + 10 + 10, or 44
Solve.
1 ÷ =
2. ___
3
11
1 ÷ =
5. ___
5
12
1
___
33
1
___
60
1 =
3. 6 ÷ __
3
1 =
6. 7 ⋅ __
8
18
7
__
8
2 __
4. __
⋅5=
3
7
1
7. __
⋅ 12 =
5
10
___
21
2
2__
5
Show your work.
Solve.
1
pound altogether. What
8. Kayla packs 4 boxes that weigh __
6
does each box weigh?
1
___
pound
24
© Houghton Mifflin Harcourt Publishing Company
2
9. Mrs. Blackwell put 4__
grams on the scale during a lab in
3
5
grams to the scale. How
science class. Then, she added 2__
6
many grams are on the scale in all?
1
7__
grams
2
10. Stretch Your Thinking If you start with 1 and repeatedly
1
, will you reach 0? Explain why or why not.
multiply by __
2
No. Possible explanation: Each fraction has twice
the denominator as the fraction preceding
1 __
1 ___
, 1 , __
, 1 , . . . The fraction will get closer
it: 1, __
2 4 8 16
and closer to zero without ever reaching zero.
74
UNIT 3 LESSON 14
Focus on Mathematical Practices
Name
3-1
Date
Solve. Write a multiplication equation for each problem.
Miguel swam 6 lengths of the pool. Po Lan swam 3 times as far
1
as far as Miguel.
as Miguel. Lionel swam __
3
1. How many lengths did Po Lan swim?
18
3 ⋅ 6 = 18
Write the equation.
2. How many lengths did Lionel swim?
1
__
⋅6=2
3
Write the equation.
2
Chris cut a length of rope that was 12 feet long. Dayna cut
a rope 4 times as long as Chris’s rope. Benita cut a rope
1
__
as long as Chris’s rope.
4
48 ft
3. How long is Dayna’s rope?
Write the equation.
4 ⋅ 12 = 48
3 ft
4. How long is Benita’s rope?
1
__
⋅ 12 = 3
4
Write the equation.
Write two statements for each pair of treats. Use the word times.
5. Compare cookies and drinks.
There are 3 times as many cookies as drinks.
1
There are __
times as many drinks as cookies.
Treat
Number
© Houghton Mifflin Harcourt Publishing Company
3
24
6. Compare drinks and pizzas.
There are 4 times as many drinks as pizzas.
1
times as many pizzas as drinks.
There are __
8
4
7. Compare cookies and pizzas.
2
There are 12 times as many cookies as pizzas.
1
times as many pizzas as cookies.
There are ___
12
Solve.
1
⋅ 18 =
8. __
6
1
11. __
of 27 =
9
UNIT 3 LESSON 1
3
1 of 12 =
9. __
3
3
1
12. __
⋅ 56 =
8
1
10. __
⋅ 32 =
4
8
4
7
1
13. __
of 15 =
5
3
Basic Multiplication Concepts
47
Name
3-1
Date
Use the number lines to complete Exercises 1–3.
Thirds
0
3
1
3
2
3
3
3
Sixths
0
6
1
6
2
6
3
6
4
6
5
6
6
6
Twelfths
0 1 2 3 4 5 6 7 8 9 10 11 12
12 12 12 12 12 12 12 12 12 12 12 12 12
2
1. If you run __
mile, how many sixths have you run?
3
4
__
6
5
2. If you measure __
meter, how many twelfths have you measured?
6
10
___
12
8
3. If you have ___
of a pizza, how many thirds do you have?
12
2
__
3
Write each fraction as a decimal.
76 = 0.076
4. _____
1,000
7 =
5. ___
10
0.7
49 = 0.49
6. ____
100
32 = 0.032
7. _____
1,000
0.71
8. 0.28 + 0.43 =
0.74
9. 0.7 + 0.04 =
5.85
10. 7.8 - 1.95 =
1
times 30 equals 6.
11. Stretch Your Thinking Draw a diagram that shows __
Possible answer:
48
UNIT 3 LESSON 1
5
Basic Multiplication Concepts
© Houghton Mifflin Harcourt Publishing Company
Add or subtract.
Name
3-2
Date
Multiply.
2
⋅ 15 =
1. __
10
2
4. __
⋅ 27 =
6
2
7. __
⋅ 21 =
14
4
10. __
⋅ 45 =
20
7
13. __
⋅ 18 =
14
3
2. __
⋅8=
6
3
5. __
⋅ 56 =
21
4
8. __
⋅ 35 =
28
4
3
9
12
5
9. __
⋅ 28 =
20
7
5 ⋅
11. ___
24 =
10
5
14. __
⋅ 80 =
50
12
9
3
6. __
⋅ 16 =
4
5
9
28
8
8
3
7
3. __
⋅ 32 =
9 ⋅
12. ___
70 =
63
4
15. ___
⋅ 45 =
12
10
15
8
Show your work.
Solve.
16. Rebecca has 21 math problems to solve. She has solved
2
__
of them. How many problems has she solved?
7
© Houghton Mifflin Harcourt Publishing Company
6 problems
17. Tessa shot 36 free throws. She made 27 of them.
What fraction of her free throws did Tessa make?
3
__
4
3
18. A carousel has 56 horses. __
of them are white. How
8
many horses are not white?
35 horses
19. Nathan works at a hardware store. Today he sold
5
of the tools he sold were hammers. How
48 tools. __
6
many hammers did Nathan sell today?
40 hammers
UNIT 3 LESSON 2
Multiplication with Non-Unit Fractions
49
Name
3-2
Date
Complete each exercise about the pairs of fraction bars.
3 __
__
,6
1. What equivalent fractions are shown? 4 8
2
2. Identify the multiplier.
12 __
___
,4
3. What equivalent fractions are shown? 18 6
3
4. Identify the divisor.
Write each amount as a decimal number.
84
5. _____
0.084
1,000
31564
6. _____
1,000 31.564
1176
7. ____
100 11.76
876
8. _____
1,000 0.876
Solve. Write a multiplication equation for each problem.
Jonas has 8 sponsors for the school walk-a-thon.
Maura has 3 times as many sponsors as Jonas.
1
as many sponsors as Jonas.
Trenton has __
4
9. How many sponsors does Maura have?
Write the equation.
24
8 ⋅ 3 = 24
10. How many sponsors does Trenton have?
1
__
⋅8=2
4
Write the equation.
2
Jo has driven farther. Jo has 10 miles to go. Hannah
as 24 miles to go.
50
UNIT 3 LESSON 2
Multiplication with Non-Unit Fractions
© Houghton Mifflin Harcourt Publishing Company
11. Stretch Your Thinking Hannah and Jo are driving
separately to a restaurant that is 60 miles away
3
of the distance
from their town. Hannah drives __
5
5
__
and Jo drives of the distance before stopping for
6
gasoline. Who has driven farther? How many
more miles does each driver need to drive to
reach the restaurant?
5
1
⋅ 60 = 5 ⋅ (__
of 60) = 5 ⋅ 10 = 50 miles.
Jo has driven __
6
6
3
1
⋅ 60 = 3 ⋅ (__
⋅ 60) = 3 ⋅ 12 = 36 miles.
Hannah has driven __
5
5
Name
3-3
Date
The campers in each cabin at Bear Claw Camp held a contest
to see who could walk the farthest in one day. Use the sign to
answer the questions. Write your answers as fractions.
1
of the way to Otter
1. The campers in Cabin A walked __
4
Ridge. How many miles did they walk?
13
___
miles
4
2
2. The campers in Cabin B walked __
of the way to Silver
3
Stream. How many miles did they walk?
16
___
miles
3
3
3. The campers in Cabin C walked __
of the way to Fossil Cave.
5
How many miles did they walk?
27
___
miles
5
1
4. The campers in Cabin D walked __
of the way to Mammoth
6
Mountain. How many miles did they walk?
25
___
miles
6
5. Which group of campers walked the farthest that day?
Cabin C
2
6. Show __
of 4 on the number line.
© Houghton Mifflin Harcourt Publishing Company
3
0
1
2
7. Write __
of 4 as a fraction.
8
__
2
4
3
3
__
8. Write 2 of 4 as a mixed number.
3
2
2__
3
Multiply. Write your answers as fractions.
8
__
2
2
⋅
4=
10. __
⋅8=
9. __
7
7
3
40
___
2
7
12. __
⋅
20 =
13. __
⋅2=
9
9
9
26
___
5
2
15. __
⋅
13 =
16. ___
⋅ 18 =
3
3
12
UNIT 3 LESSON 3
3
16
___
3
14
___
9
90
___
12
5
11. __
⋅4=
6
3
14. __
⋅5=
8
5
17. __
⋅ 12 =
9
20
___
6
15
___
8
60
___
9
Multiplication with Fractional Solutions
51
Name
3-3
Date
Compare.
5 > __
5
1. __
7
1 < __
1
2. __
4
8 > __
6
3. ___
6 < __
7
4. __
3
2 < __
5. __
8 > __
6
6. __
8. 0.207 < 0.342
9. 0.5 > 0.47
6
7
5
8
3
10
4
9
8
7
Compare.
7. 0.54 < 0.65
10. 0.76 > 0.67
12. 0.6 > 0.06
11. 0.22 < 0.41
Multiply.
16
2 ⋅
14. __
21 =
14
5 ⋅
15. __
24 =
15
1 ⋅
16. __
36 =
4
3 ⋅
17. __
16 =
12
2 ⋅
18. __
14 =
4
3 ⋅
21. __
45 =
15
5
9
3 ⋅
19. ___
24 =
12
6
3
4
8 ⋅
20. ___
80 =
10
8
7
64
9
22. Stretch Your Thinking Write a multiplication equation
using one whole number and one fraction that have
18
.
a product of ___
8
3 = ___
18
Possible answer: 6 ⋅ __
8
8
52
UNIT 3 LESSON 3
Multiplication with Fractional Solutions
© Houghton Mifflin Harcourt Publishing Company
4 ⋅
20 =
13. __
Name
3-4
Date
3 __
Tanith is using a number line to find __
⋅ 2 . This is her work so far:
4
5
0
1
–
5
2
–
5
3
–
5
4
–
5
1
0
1
–
5
2
–
5
3
–
5
4
–
5
1
0
—
20
1
—
20
2
—
20
3
—
20
4
—
20
5
—
20
6
—
20
7
—
20
8
—
20
9
—
20
10
—
20
11
—
20
12
—
20
13
—
20
14
—
20
15
—
20
16
—
20
17
—
20
18
—
20
19
—
20
20
—
20
1. Explain Tanith’s work so far to someone at home.
3
of each
2. Finish Tanith’s work by circling __
4
circled fifth. How many 20ths did you circle altogether?
6
3
3 __
2 ___ or ___
What is __
⋅
? 20
10
4 5
2 __
3. Use the number line to find __
⋅ 5.
3 6
Label all the parts above and below.
1
–
6
0
0
—
18
1
—
18
2
—
18
3
—
18
2
–
6
4
—
18
5
—
18
6
—
18
10
___
18
3
–
6
7
—
18
8
—
18
6
9
—
18
4
–
6
10
—
18
11
—
18
5
–
6
12
—
18
13
—
18
14
—
18
16
—
18
17
—
18
18
—
18
Show your work.
Solve.
© Houghton Mifflin Harcourt Publishing Company
15
—
18
1
3
of a bag of popcorn.
4. Four friends at a party popped __
4
They ate half of what was popped. What fraction of the
3
__
popcorn in the bag did they eat?
8
7
5. Ashley brought __
gallon of lemonade to the party.
8
2
of it. How many gallons of
Her friends drank __
3
7
___
gallon
lemonade did they drink?
12
Multiply. You do not need to simplify.
2
___
2 __
1 =
4 __
⋅
7. __
⋅2=
6. __
21
7 3
9 9
24
___
2
4 __
9. __
⋅
12 =
10. __
⋅2=
7
7
5 3
9
___
9 __
5
1 =
12. ___
⋅
13. ___
⋅3=
20
10 2
12
UNIT 3 LESSON 4
8
___
81
8
___
15
15
___
12
1 __
8. __
⋅5=
8
6
1 __
11. __
⋅3=
7
5
5 __
14. __
⋅1=
6
6
5
___
48
3
___
35
5
___
36
Multiply a Fraction by a Fraction
53
Name
3-4
Date
Name the mixed number shown by the shaded parts.
1
5__
2
1.
5
1__
7
2.
1
1__
3
3.
Add.
81.46
5. 80.55 + 0.91=
454.65
4. 454 + 0.65 =
37.98 m
6. 31.78 m + 6.2 m =
1
7. Show __
of 7 on the number line.
3
0
1
2
3
4
5
6
7
7
__
1
of 7 as a fraction.
8. Write __
3
3
1
2__
3
3
5
6
10. Stretch Your Thinking Solve for the unknown fraction.
Then divide and shade an area model to show the
2 ⋅ = ___
? 10 .
equation. __
5
2
5
30
5
__
6
54
UNIT 3 LESSON 4
Multiply a Fraction by a Fraction
© Houghton Mifflin Harcourt Publishing Company
1
9. Write __
of 7 as a mixed number.
Name
3-5
Date
Multiply. Simplify first if you can.
12
___
2 __
1. __
⋅6=
5
7
5 ___
3. ___
⋅ 8 =
3 24
15 3
1
1
5 35
1
12 3
9
6
1
1
7 __
12. __
⋅2=
21
49 7
25
5 __
10. __
⋅7=
2
___
2
1
816
15
7 ___
11. __
⋅ 6 =
3
1
1
___
1
4 ___
9. ___
⋅ 7 =
8
5 ___
8. ___
⋅ 2 5=
5
31
1
7
1
__
1
1
5 __
6. __
⋅3=
25
3 ⋅ __
2 =
7. ___
5 10
17
9
___
⋅
4 25
12 =
___
82
2 __
4. ___
⋅8=
9
3
3
5. __
9
1
__
1
1
1
4 __
2. __
⋅1=
35
4
8
3
1
___
18
16
___
17
15
___
56
1
___
40
35
___
6
7
___
12
13. Which fraction is not equivalent to the others?
3
___
2
___
1
__
9
___
10
___
6
___
7
___
100
____
15
10
5
45
50
40
35
500
Solve.
Show your work
© Houghton Mifflin Harcourt Publishing Company
3
of the animals are birds. Of the
14. In the town zoo, ___
28
4
___
are birds of prey. What fraction of the
birds,
15
animals at the zoo are birds of prey?
1
___
35
5
15. Tuesday at the zoo, ___
of the visitors were adults. Of these
12
3
___
were men. What fraction of the people who
adults,
10
visited the zoo on Tuesday were men?
1
__
8
14
16. On Tuesday, ___
of the souvenirs purchased at the zoo gift
25
shop were stuffed animals. Of the stuffed animals purchased,
10
___
were bears. What fraction of the souvenirs purchased at
21
the zoo gift shop on Tuesday were stuffed bears?
4
___
15
UNIT 3 LESSON 5
Multiplication Strategies
55
Name
3-5
Date
Add or subtract.
1 + __
2. 5__
35
4 + __
1. 1__
52
5
5
6
1
7__
3
3 + __
5
4. __
4
2
3
1
1__
9
5
4
2 - __
1
3. 1__
6
3
8 - __
35
5. 7__
9
9
3
1
__
4 or 4__
9
3
1
6. 6 - 4__
8. 132.76 - 87.24 =
9. 968.29 - 217.5 =
2
1
1__
2
Subtract.
7. 31,763 - 6.51 =
45.52
31,756.49
750.79
3 __
10. Use the number line to find __
⋅ 2 . Label all the parts
4 5
above and below.
⋅ __2 =
4 5
3
__
6
___
20
1
5
0
1
20
2
20
3
20
4
20
5
20
6
20
7
20
8
20
1
9
20
10
20
11
20
12
20
13
20
14
20
15
20
16
20
17
20
18
20
19
20
20
20
11. Stretch Your Thinking Write a word problem that will
2 ___
⋅ 8 = x in order to solve. Then
use the equation __
6
10
simplify and multiply to solve.
8
of the basketball team’s points in
Possible answer: Jacob scored ___
10
Saturday’s basketball game. Two sixths of the points Jacob scored were
from free throws. What fraction of the team’s points did Jacob score
2 ___
1 __
4
from free throws? __
⋅ 8 = __
⋅ 4 = ___
6
56
UNIT 3 LESSON 5
10
3
5
15
Multiplication Strategies
© Houghton Mifflin Harcourt Publishing Company
0
20
2
5
Name
3-6
Date
Find each product by first rewriting each mixed number
as a fraction.
3
⋅ 2__1 =
1. __
7
2
2
3. 2__
⋅ 4__1 =
5
3
3 __
15 = ___
__
⋅ 5 = ___
11
7
2
2
5
3
7
2. 1___
⋅5=
14
10
5
5
5 __
7
__
⋅ 7 = __
9
5
1
7. 3__
⋅ 3__1 =
14
8 ___
56 =
1
__
⋅ 21 = ___
11__
5
5. __
⋅ 1__2 =
9
2
5
2
4
3
8
3 =
6. 12 ⋅ 2__
9
4
49 =
7 __
1
__
⋅ 7 = ___
12__
2
1 __
4. 5__
⋅3=
4
9 =
1
8. __
⋅ 3___
9
10
Solve.
17 __
17 = __
___
⋅ 5 = ___
81
1
10
2
2
16 __
___
⋅3=2
3
8
12 ___
___
⋅ 11 = 33
1
4
13
1 ___
__
⋅ 39 = ___
9
10
30
Show your work.
© Houghton Mifflin Harcourt Publishing Company
9. The bottom of Zeyda’s jewelry box is a rectangle with
3
1
inches and width 3__
inches. What is the area
length 5__
4
8
of the bottom of the jewelry box?
15
17___
square inches
32
10. The Patel family went apple picking. The number of
2
times the number of
red apples they picked was 2__
9
green apples they picked. If they picked 45 green
apples, how many red apples did they pick?
100 red apples
1
11. The art museum is 8__
miles from Alison’s house.
2
2
of the way there so far.
Alison has ridden her bike __
3
How far has she gone?
2
miles
5__
3
UNIT 3 LESSON 6
Multiply Mixed Numbers
57
Name
3-6
Date
Add.
3 + __
1
1. __
8
3
1 + __
2. __
5
6
5 + __
1
3. __
4
6
8
13
___
19
___
23
___
24
20
24
1 + __
2
4. __
2 + __
1
5. __
7
3
3
4 + ___
1
6. __
5
9
10
13
___
7
__
9
___
21
9
10
Use the Commutative Property to solve for n.
7. 55,207 + 87,331 = 87,331 + n
n = 55,207
8. 48.76 + 20.08 = 20.08 + n
n = 48.76
Multiply. Simplify first if you can.
1
__
3 =
2 __
7 __
⋅
10. ___
⋅6=
9. __
2
3 4
10 7
6
25
2
__
1 __
⋅4=
13. __
5
2
7
5
2
__
7
3 __
11. __
⋅5=
5
6
2 __
14. __
⋅3=
9
8
1
__
2
1
___
12
15. Stretch Your Thinking Complete the mixed number equation
that is represented by the area model.
⋅
2
1
__
58
2
1__
3
=
UNIT 3 LESSON 6
5
__
6
Multiply Mixed Numbers
© Houghton Mifflin Harcourt Publishing Company
5 ___
⋅ 12 =
12. __
3
__
3-7
Name
Date
Solve.
3 __
⋅1
1. __
4 8
3
___
32
2 - __
1
2. __
2
4. __
⋅ 12
7
24 = __
___
33
7
7
1 + __
2
5. __
5 __
7. __
⋅5
7 6
25
___
42
11 +
8. ___
3
1 __
10. __
⋅1
3 8
1
___
24
3
1 + __
1
3. ___
9
10
5
__
3
___
9
10
5
5
3
1 + __
6. __
4
3
8
5
__
8
13
___
15
4 - __
2
9. __
12
9
11
3___
9
2
__
12
9
1
12. 10 - __
9
89 = __
___
98
9
9
7 __
11. __
⋅3
8 4
21
___
32
Show your work.
Solve.
7
gallon of water. It is
13. Rodrigo’s fish bowl holds __
8
1
now __ full. How much water is in it?
2
7
___
gallon
16
© Houghton Mifflin Harcourt Publishing Company
1
14. Kenya jumped 7__
feet. Janet jumped
6
How much farther did Kenya jump?
5
__
foot
6
1
6__
feet.
3
7
15. A group of hikers walked 8___
miles to Caribou Cave
10
1
__
and then 5 miles to Silver Stream. How far did they
5
walk altogether?
9
13___
miles
10
3
16. A recipe calls for __
cup of flour. Estevan wants to make
4
1
__
of the recipe. How much flour will he need?
3
1
__
cup
4
1
17. A truck was carrying 2__
tons of sand. When it arrived,
8
1
only 1__ tons of sand were left. How much sand was
2
lost along the way?
5
__
ton
8
UNIT 3 LESSON 7
Relate Fraction Operations
59
Name
3-7
Date
Subtract.
3 - __
1
1. __
4
2 - ___
1
2. __
6
9
10
7 - __
1
3. __
4
8
7
___
11
___
5
__
12
90
8
6 - __
1
4. __
7
4 - __
2
5. __
5
3
3
1 - __
1
6. __
2
8
11
___
2
___
3
__
21
15
8
Sample estimates shown; accept
reasonable estimates.
8. $44.25 - $21.76 $22
9. 14.6 + 2.4 17
Estimate each sum or difference.
7. 6.759 + 2.099
9
Find each product by first rewriting each mixed
number as a fraction.
5 ___
25 = ___
__
⋅ 10 = ___
21
5
1 =
⋅
3__
10. __
8 3
12
12
8
3
3
11. 4__
⋅5=
5
2
12. 1__
⋅ 3__4 =
5
9
5
8
5
1
1
7 ___
217 = ___
__
⋅ 31 = ___
4 37
5
9
45
45
© Houghton Mifflin Harcourt Publishing Company
1 __
13. 6__
⋅5=
23 __
23 =
___
⋅ 5 = ___
23
31 __
31 = __
___
⋅ 5 = ___
37
5
8
8
8
14. Stretch Your Thinking Give an example that shows
how to use the Distributive Property to multiply a
number by a sum. All of the numbers you use should
be mixed numbers or fractions.
5 = __
2
1 + __
1 + __
2 __
Possible answer: __
⋅ (2__
) 2 ⋅ 2__
⋅5=
4
4
3
6
3
3 6
3 + __
5 = ___
37 = ___
2 __
2 __
__
⋅ 9 + __
⋅ 5 = __
21
3 4
3 6
2
9
18
18
60
UNIT 3 LESSON 7
Relate Fraction Operations
Name
3-8
Date
Complete each fraction box.
1.
3
7
__
and __
>
+
-
⋅
8
3
6
7 > __
7 > __
__
or __
4
8
8
8
7
__
8
7
__
8
7
__
8
2.
3
1
__
and __
3 = __
6 = ___
13 = __
7 + __
+ __
15
4
8
8
8
8
3 = __
6 = __
7 - __
1
- __
4
8
8
8
3 = ___
21
⋅ __
4
32
5
2
4
>
+
-
⋅
3 > __
6 > ___
5
1
__
or ___
5
2
10
3 = ___
5 +
1 + __
__
5
2
10
3 - __
6 1 = ___
__
5
2
10
3
1 __
__
⋅ 3 = ___
2 5
10
10
6 =
___
10
5 =
___
10
11 = ___
___
11
10
1
___
10
10
Show your work.
Solve.
7
ton of
3. The Eagle Trucking Company must deliver __
8
5
__
cement blocks and ton of bricks to one place.
8
How much will this load weigh?
1
1__
tons
2
© Houghton Mifflin Harcourt Publishing Company
1
1
4. A truck carried 3__
tons of sand, but lost __
ton along
4
3
the way. How many tons of sand were delivered?
1
3___
tons
12
2
5. The trucking company also needs to deliver 1__
tons of
3
7
___
oak logs and 1 tons of maple logs. Which load
12
weighs more?
oak logs
3
1
6. In a load of __
ton of steel rods, __
of them are bent.
4
8
How many tons of steel rods are bent?
3
___
ton
32
3
7. The company delivered 1__
tons of bricks to one building site.
5
1
__
They delivered 2 times this much to a second site. What was
2
the weight of the load the company delivered to
the second site?
4 tons
UNIT 3 LESSON 8
Solve Real World Problems
61
Name
3-8
Date
Multiply.
1.
2.
2,548
×
__5
3.
945
12,740
4.
21
×
45
_
5.
33
×
_4
132
3,015
×
__6
18,090
65
×
87
_
6.
215
×
__9
1,935
5,655
Find each product by first rewriting each mixed number as a fraction.
40 __
320 =
23
___
⋅ 8 = ___
11___
4
2 =
7. 4__
⋅
2__
9 3
27
27
9
3
5
9. 3__
6
23
___
12 =
___
6
⋅ 13
1
8. 6__
⋅ 10 =
13
5
5
46 = ___
12 = ___
⋅ ___
37
13
31 ___
62 =
___
⋅ 10 = ___
62
1
10. 5__
13
3
16
___
3 =
__
3
⋅5
1
1
3 = ___
16 = __
⋅ __
31
5
5
5
Solve.
6 - __
2
11. __
7
7
4
__
7
4 + __
2
12. __
9
3
1
1__
9
2 ___
13. __
⋅ 9
3 10
3
__
5
3 __
⋅5
14. __
1
15. 8 - __
3
1 + __
16. __
5
7
8
6
55 = __
___
76
7
7
8
13
___
24
© Houghton Mifflin Harcourt Publishing Company
3
__
8
17. Stretch Your Thinking Write and solve a word problem
that requires multiplying two mixed numbers.
5
Possible answer: Taylor worked 6__
hours doing yard
6
work one weekend. The next weekend, he worked
1
1__
times as long as he did the previous weekend.
2
How many hours did Taylor work on the second
1
weekend? 10__
hours
4
62
UNIT 3 LESSON 8
Solve Real World Problems
Name
3-9
Date
Predict whether the product will be greater than, less than,
or equal to the second factor. Then compute the product. Predictions may vary.
4
1. __
⋅6=x
1
2. 1__
⋅6=x
5
Predict: x < 6
4
4__
5
Compute: x =
2 __
4. __
⋅5=x
2
10
3. ___
⋅6=x
9
10
Predict: x > 6
2
6__
3
Compute: x =
5 __
5. __
⋅5=x
6
6
5
Predict: x = __
6 __
5
Compute: x =
6
Compute: x =
6
Compute: x =
1 __
6. 1__
⋅5=x
6
Predict: x <
Predict: x = 6
3
5
__
6 ___
25
36
6
5
Predict: x > __
6
Compute: x =
1
1__
9
Show your work.
Solve.
3
times as tall as his brother. His brother
7. James is 1__
7
1
__
is 3 feet tall.
2
1
feet?
Is James’s height more or less than 3__
2
© Houghton Mifflin Harcourt Publishing Company
more
How tall is James?
5 feet
8. South Middle School has 750 students. North Middle
13
times as many students as South.
School has ___
15
Does North Middle School have more or fewer than
750 students?
fewer
How many students attend North Middle School?
650 students
UNIT 3 LESSON 9
Make Generalizations
63
Name
Date
Perry measured the foot length of four
friends for a science fair experiment. Then,
he made a bar graph to display his results.
Foot length (in.)
Foot Length
1. How much longer is Brennen’s foot than
Clara’s foot?
0.7 inch
2. What is the difference between the
longest foot and the shortest
foot?
9
8.8
8.6
8.4
8.2
8
7.8
7.6
7.4
n
a
Ch
Br
en
ne
ar
Cl
ey
0.9 inch
ne
Ty
e
0
en
3-9
Student Name
Solve.
7
7 __
3. __
⋅ 4 ___
8 9 18
1
3
4. 11 - __
10__
4
4
1
9 - ___
5 __
6. ___
12
12 3
7 + __
2
7. ___
15
3
15 = __
4 + ___
7 ___
5. __
11
5
10 10
2
17 = ___
___
12
15
15
15
5 ___
⋅ 9 ___
8. __
6 11 22
Complete each fraction box.
5
7
___
and __
12
4
2
__
and __
6
5
+
−
⋅
6
12
12
5
10
7
__ + ___ = ___ +
6
12
12
5 - ___
10 −
7 = ___
__
6
12
12
5
35
7
__ ⋅ ___ = ___
6 12
72
12
7
___ =
12
7 =
___
12
>
17 = ___
___
15
12
12
3 = __
1
___
4
12
+
−
⋅
3
10
4 > __
2
12 > ___
__
or ___
5
15
3
4 + __
2 = ___
12 +
__
5
15
3
4 − __
2 = ___
12 −
__
5
15
3
8
4 __
__
⋅ 2 = ___
5 3
15
15
10
___ =
15
10 =
___
15
22 = ___
___
17
15
15
2
___
15
9. Stretch Your Thinking Write two multiplication equations
using fractions and mixed numbers. Write one equation
that will have a product greater than the first factor.
Then write another equation that will have a product
less than the first factor.
3 = ___
25 = ___
4
1 __
⋅ 2__
3 31 ; 3__
⋅ 2 = ___
21
Possible answer: 1__
9
8
72 8 3
12
12
64
UNIT 3 LESSON 9
Making Generalizations
© Houghton Mifflin Harcourt Publishing Company
5 > ___
10 > ___
7
7
> __
or ___
Name
3-10
Date
Divide
5
__
1. 5 ÷ 6 =
3. 33 ÷ 30 =
5. 3 ÷ 10 =
1 =
7. 100 ÷ __
6
1 ÷ =
9. __
8
5
1 ÷ =
11. __
9
2
6
10
3
___
10
600
1
___
40
1
___
18
45
1 =
4. 8 ÷ __
48
1 =
6. 4 ÷ __
36
5
11 = ___
___
11
10
1 =
2. 9 ÷ __
6
9
1
___
8. 1 ÷ 100 =
100
1
___
1 ÷ =
10. __
7
56
8
1
___
1 ÷ =
12. __
5
15
3
Show your work.
Solve.
13. Alexander is dividing oranges into eighths. He has 5 oranges.
How many eighths will he have?
40 eighths
© Houghton Mifflin Harcourt Publishing Company
14. Carrie has 32 ounces of ice cream to divide equally among
10 people. How much ice cream will each person get?
1
3__
ounces
5
15. Nayati wants to swim 50 miles this school year. She plans to
swim _1_ mile each day. How many days will it take her to
4
swim 50 miles?
200 days
1
16. Eric has __
of a watermelon to share equally with 3 friends.
3
How much will each person get?
1
___
watermelon
12
17. A gardener needs to pack 16 pounds of beans into 20 bags.
He wants all the bags to weigh about the same. About how
much will each bag weigh?
_4_ pound
5
UNIT 3 LESSON 10
When Dividing Is Also Multiplying
65
Name
3-10
Add or subtract.
3
1. 2__
Date
2.
4
5
- 1__
_8
1
1__
5.
1
- 2__
_6
5
4__
12
8.
5
6
__
and __
7
6
7
10
2
14 > ___
> __
or ___
7
35
35
10
2
14
__
___
___
+ =
+
=
7
35
35
10 =
2 = ___
14 − ___
− __
7
35
35
2 = ___
4
__
⋅
7
35
3
3
+ 1__
_4
1
10___
30
2
__
5
2
__
5
2
__
5
2
__
5
1
8__
6.
7
8___
5
⋅
10
5
5
+ 4__
_6
Complete each fraction box.
7.
2
2
__
and __
−
7
6___
2
3__
6
+
2
6__
2
4
- 3__
_5
9
7
>
1
3. 10__
3
5
+ 1__
_9
8
4.
2
4__
6 > __
5
36 > ___
35
__
or ___
>
24
___
35
4
___
35
7
6
42
42
6
5
36
35
__ + __ = ___ + ___ =
7
6
42
42
6 − __
5 = ___
36 − ___
35 =
__
7
6
42
42
6
5
30
5
__ ⋅ __ = ___ = __
7 6
7
42
+
−
⋅
71 = ___
___
1 29
42
42
1
___
42
Predict whether the product will be greater than, less than,
or equal to the second factor. Then compute the product. Predictions may vary.
3
2
1
⋅5=x
10. __
⋅5=x
11. 1__
⋅5=x
9. __
3
Compute: x =
1
3__
3
6
Predict: x > 5
Predict: x = 5
Compute: x =
5
Compute: x =
5
5__
6
12. Stretch Your Thinking Draw a diagram to show how many
twelfths there are in 3. Describe a situation in which you
would need to know how many twelfths there are in 3.
1
of a foot, so the
Possible answer: An inch is ___
12
number of inches in 3 feet is the number of
twelfths in 3.
66
UNIT 3 LESSON 10
When Dividing Is Also Multiplying
© Houghton Mifflin Harcourt Publishing Company
Predict: x < 5
3
3-11
Name
Date
1 ÷
1. Consider the division problem __
3.
2
Describe a situation this division could represent.
Situations will vary.
Draw a diagram to represent the division. Then find the solution.
1
__
; Diagrams will vary. Check students’ work.
6
Write an equation. Then solve. Equations may vary.
Show your work.
2. A rectangle has an area of 12 square feet and a length of
5 feet. What is its width?
2
5 ⋅ w = 12; 2__
feet
5
© Houghton Mifflin Harcourt Publishing Company
1
3. A tortoise must walk ___
mile to visit a friend. He plans to
12
break the journey into four equal parts with breaks in between.
How long will each part of his journey be?
1 ÷
1
4; ___
mile
x = ___
12
48
1
4. Harry worked 7 hours last week. This is __
as many hours as
3
Aidan worked. How many hours did Aidan work?
1
__
⋅ a = 7; 21 hours
3
5. Lin is a camp counselor. She is making small bags of trail mix
for campers to take on a hike. She has 2 pounds of raisins and
1
pound in each bag. How many bags can she fill
is putting __
8
before she runs out of raisins?
1
; 16 bags
x = 2 ÷ __
8
1
6. Mr. Ramirez bought __
pounds of cashews. He divided the
4
cashews equally among his three children. How much did
each child get?
1 ÷
1
3; ___
pound
x = __
4
12
UNIT 3 LESSON 11
Solve Division Problems
67
Name
3-11
Date
Add or subtract.
1.
1
1__
2.
8
2
+ 4__
_3
19
5___
4.
1
6__
3.
4
5
– 4__
_6
12
4
5.
7
11
+ 5___
14
__
6.
2
– 2__
_5
3
1__
5
1
11___
14
3
8
+ 7__
_9
2
17__
5
1___
24
2
5__
1
9__
9
5
6__
8
1
+ 3__
_2
1
10__
8
Predict whether the product will be greater than, less than, or
equal to the second factor. Then compute the product. Predictions may vary.
5
⋅9=x
7. __
7
8. __
⋅9=x
5
Predict: x = 9
5
Predict: x < 9
9
Compute: x =
1 __
10. 1__
⋅4=x
2
3
9. 1__
⋅9=x
8
7
7__
8
Compute: x =
6 __
11. __
⋅4=x
5
6
4
Predict: x > __
5
Compute: x =
1
1__
5
Predict: x > 9
2
14__
5
Compute: x =
2 __
12. __
⋅4=x
5
5
4
Predict: x = __
5
Compute: x =
4
__
5
5
4
Predict: x < __
5
8
___
25
Compute: x =
Divide.
4
1 =
16. 200 ÷ __
4
24
800
14. 2 ÷ 3 =
1 ÷ =
17. __
8
4
2
__
3
1
___
32
15. 10 ÷ 3 =
1 ÷ =
18. __
6
7
1
3__
3
1
___
42
19. Stretch Your Thinking Harrison is playing a board game that
1
of the
has a path of 100 spaces. After his first turn, he is __
5
1
fewer
way along the spaces. On his second turn, he moves __
4
spaces than he moved on his first turn. On his third turn, he
1
times as many spaces than he moved on his first
moves 1__
4
turn. What space is he on after three turns?
60
68
UNIT 3 LESSON 11
Solve Division Problems
© Houghton Mifflin Harcourt Publishing Company
1 =
13. 6 ÷ __
Name
3-12
Date
Solve.
1 =
1. 5 ⋅ __
3
1 ÷ =
3. __
2
8
1 =
5. 5 ÷ ____
100
3 ___
7. __
⋅ 10 =
5
27
1 ÷
9. __
10 =
5
1
11. __
⋅ 14 =
8
5
__
3
1 =
2. 5 ÷ __
3
1
___
16
4. 27 ÷ 10 =
500
1 =
6. 12 ⋅ __
2
__
9
1
___
50
3
1__
4
15
7
2___
10
1
1__
9
3
1 =
8. 16 ÷ __
64
1 =
10. 10 ÷ __
50
4
5
12. 18 ÷ 20 =
Tell whether you need to multiply or divide. Then solve.
Equations will vary. Possible equations are given.
9
___
10
Show your work.
1
ounce. Jody has 1 pound
13. A dime weighs about ___
12
(16 ounces) of dimes. About many dimes does she have?
Divide; 192 dimes
1
14. Maddie has 180 coins. Of these coins, ___
are dimes.
12
About how many dimes does she have?
© Houghton Mifflin Harcourt Publishing Company
Multiply; 15 dimes
1
15. A rectangle has length 3 feet and width __
foot. What is the
4
area of the rectangle?
3
square foot
Multiply; __
4
1
16. A rectangle has area 3 square feet and width __
foot.
2
What is the length of the rectangle?
Divide; 6 feet
17. Nisha wants to study 5 hours for the spelling bee. If she
1
hour per night, how many nights will she
studies __
3
have to study?
Divide; 15 nights
UNIT 3 LESSON 12
Distinguishing Multiplication from Division
69
Name
3-12
Date
Multiply.
1. 134 ⋅ 5 =
670
4. 4,507 ⋅ 3 = 13,521
2. 44 ⋅ 21 =
924
3. 7 ⋅ 57 =
399
5. 36 ⋅ 76 = 2,736
6. 1,928 ⋅ 6 = 11,568
1 =
8. 100 ÷ __
1 ÷ =
9. __
4
Divide.
1 ÷ =
7. __
2
9
10. 4 ÷ 5 =
1
___
18
4
__
5
3
11. 12 ÷ 5 =
300
2
2__
5
5
1 =
12. 8 ÷ __
7
1
___
20
56
Show your work.
Write an equation. Then solve. Equations may vary.
14. Stretch Your Thinking Using a whole number and a fraction
as factors, write a multiplication equation with a product
less than the whole number factor. Draw a picture to show
how the product is less than the whole number factor.
9
7
Possible answer: ___
⋅ 3 = 2___
10
10
70
UNIT 3 LESSON 12
Distinguishing Multiplication from Division
© Houghton Mifflin Harcourt Publishing Company
13. Marc is running 5 kilometers at track practice. He decides
to break the run into 3 equal lengths. How long will each
length be?
2
x = 5 ÷ 3; 1__
km
3
Name
3-13
Date
Show your work.
Solve.
1. Dan’s Ice Cream comes in cartons of two sizes. The large
3
1
pounds. The small carton holds 1__
pounds
carton holds 4__
4
2
less. How much ice cream does the small carton hold?
3
2__
pounds
4
2. Mac picked four baskets of blueberries. The weights of the
berries in pounds are given below. Order the weights from
lightest to heaviest.
5
__
9
___
4
__
13
___
4
10
5
20
13 __
9 __
___
, 4 , ___
,5
20 5 10 4
1
3. Four cones of Dan’s Ice Cream hold __
pound. How much
2
ice cream does each cone hold?
1
__
pound
8
1
4. If a dish of ice cream holds __
pound, how many dishes can
4
1
__
you get from a 4 -pound carton of Dan’s Ice Cream?
18 dishes
2
© Houghton Mifflin Harcourt Publishing Company
Solve. Give your answer in simplest form.
1 =
5. 3 ÷ __
5
9
7. ___
⋅ 2__1 =
14
3 =
1 + __
9. __
5
3
1 ÷ =
11. __
4
8
5 - __
13. 3__
11 =
7
2
UNIT 3 LESSON 13
4
1
1__
2
3
7
2___
3 + ___
11 =
6. 1__
15
14
___
3
8. 2__
⋅6=
6
1
___
9
2 - ___
1 =
12. __
32
5
3
2___
14
3
15__
5
5
5 + __
8 =
10. __
15
16
16
10
7 __
14. __
⋅2=
8
7
13
1___
18
3
___
10
1
__
4
Review Operations with Fractions
71
Name
3-13
Date
1
Use benchmarks of 0, __
, and 1 to estimate the sum or
2
difference. Then find the actual sum or difference.
5 + __
4
1. ___
10
13 – __
3
2. ___
14
9
1
Estimate:
85
17
___
or ___
Sum: 90
18
1
__
Estimate:
2
1
__
2
Difference:
8 – __
7
3. __
9
7
13 + __
3
4. ___
8
14
0
1
___
Estimate:
2
Estimate:
72
Difference:
4
Sum:
19
1___
28
Show your work.
Write an equation. Then solve. Equations may vary.
5. A rectangle has an area of 20 square feet and a length of
6 feet. What is its width?
1
6 ⋅ w = 20; 3 __
feet
3
6. Bailey attends gymnastics practice for 8 hours each week.
1
the number of hours that the gym is open for
This is __
4
practice. How many hours is the gym open for practice?
1
__
⋅ a = 8; 32 hours
4
Solve.
1 ÷ =
7. __
3
4
1
___
12
1
8. __
⋅3=
4
3
__
4
1 =
9. 14 ⋅ __
6
1
2 __
3
© Houghton Mifflin Harcourt Publishing Company
1 ÷
5 different
10. Stretch Your Thinking How is solving __
8
1
from solving __ ⋅ 5?
8
1 ÷
1
5, multiply __
by
Possible answer: To solve __
8
8
1 __
1.
1
the reciprocal of 5: __
⋅ 1 = ___
To solve __
⋅ 5, first
8 5
40
8
5.
rewrite 5 as __
Then, multiply the two fractions:
1
5.
1 __
__
⋅ 5 = __
8 1
8
72
UNIT 3 LESSON 13
Review Operations with Fractions
Name
3-14
Date
These graphs show the instruments in two different high school
marching bands.
Carter School Marching Band
Reagan School Marching Band
1
–
3
1
–
3
percussion
2
–
5
brass
1
–
6
percussion
woodwind
1
–
2
brass
4
—
15
woodwind
Show your work.
Solve. Use the circle graphs.
1. The Reagan School Marching Band has three percussion
musicians. How many musicians altogether are in the
band?
18 musicians
2. There are 30 musicians in the Carter School
Marching Band. How many of them play brass
instruments?
© Houghton Mifflin Harcourt Publishing Company
12 musicians
Suppose both bands decide to combine and perform as one band.
3. What fraction of the band members will play a brass
instrument?
7
___
16
4. What fraction of the band members will play a percussion
instrument?
13
___
48
5. What fraction of the band members will play a
woodwind instrument?
7
___
24
UNIT 3 LESSON 14
Focus on Mathematical Practices
73
Name
3-14
Date
Show your work.
Solve. Explain how you know your answer is reasonable.
Explanations may vary.
1
feet and a width
1. James’s garden has a length of 12__
4
2
of 9__ feet. What length of fencing will he need to
3
surround his garden?
5
feet
43__
6
Answer:
Why is the answer reasonable?
1
2
12__
rounds to 12. 9__
rounds to 10. The answer
4
3
should be about 12 + 12 + 10 + 10, or 44
Solve.
1 ÷ =
2. ___
3
11
1 ÷ =
5. ___
5
12
1
___
33
1
___
60
1 =
3. 6 ÷ __
3
1 =
6. 7 ⋅ __
8
18
7
__
8
2 __
4. __
⋅5=
3
7
1
7. __
⋅ 12 =
5
10
___
21
2
2__
5
Show your work.
Solve.
1
pound altogether. What
8. Kayla packs 4 boxes that weigh __
6
does each box weigh?
1
___
pound
24
© Houghton Mifflin Harcourt Publishing Company
2
9. Mrs. Blackwell put 4__
grams on the scale during a lab in
3
5
grams to the scale. How
science class. Then, she added 2__
6
many grams are on the scale in all?
1
7__
grams
2
10. Stretch Your Thinking If you start with 1 and repeatedly
1
, will you reach 0? Explain why or why not.
multiply by __
2
No. Possible explanation: Each fraction has twice
the denominator as the fraction preceding
1 __
1 ___
, 1 , __
, 1 , . . . The fraction will get closer
it: 1, __
2 4 8 16
and closer to zero without ever reaching zero.
74
UNIT 3 LESSON 14
Focus on Mathematical Practices