Name
6.4
?
Number and
Operations—5.3.J, 5.3.L
MATHEMATICAL PROCESSES
5.1.C, 5.1.F
Divide Fractions and
Whole Numbers
Essential Question
How do you divide a whole number by a fraction
and divide a fraction by a whole number?
Hands
On
Investigate
Investigate
Materials ■ fraction strips
A. Mia walks a 2-mile fitness trail. She stops to exercise
every 1_5 mile. How many times does Mia stop to exercise?
• Draw a number line from 0 to 2. Divide the number line
into fifths. Label each fifth on your number line.
0
1
2
• Skip count by fifths from 0 to 2 to find 2 ÷ 1_5 .
There are _ one-fifths in 2 wholes.
You can use the relationship between multiplication and
division to explain and check your solution.
• Record and check the quotient.
2 ÷ 1_ = _ because _ × 1_ = 2.
5
5
So, Mia stops to exercise _ times.
B. Roger has 2 yards of string. He cuts the string into pieces that
are 1_3 yard long. How many pieces of string does Roger have?
• Model 2 using 2 whole fraction strips.
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• Then place enough 1_3 strips to fit exactly under the
2 wholes. There are _ one-third-size pieces in 2 wholes.
• Record and check the quotient.
2 ÷ 1_ = _ because _ × 1_ = 2.
3
3
So, Roger has _ pieces of string.
Module 6
263
Make
Make Connections
Connections
You can use fraction strips to divide a fraction by a
whole number.
Hands
On
Calia shares half of a package of clay equally among
herself and each of 2 friends. What fraction of the
whole package of clay will each friend get?
STEP 1 Place a 1_2 strip under a 1-whole strip to
show the 1_2 package of clay.
STEP 2 Find 3 fraction strips, all with the same
denominator, that fit exactly under the
1
_ strip.
2
? ? ?
Think: How much of the whole is each piece
Each piece is _ of the whole.
when 1_2 is divided into 3 equal pieces?
STEP 3 Record and check the quotient.
1÷3=
__
2
_ because _ × 3 = 1__2.
Math Talk
So, each friend will get _ of the whole package of clay.
Mathematical Processes
When you divide a fraction
by a whole number, how does
the quotient compare to the
dividend? Explain.
Share
Share and
and Show
Show
Divide and check the quotient.
1.
3 ÷ 1_ = _ because _ × 1_ = 3.
3
3
2.
3.
1
2
3
Think: What label should I write for each
tick mark?
3 ÷ 1_ = _ because
1 ÷ 2 = _ because
_
4
_ × 1_6 = 3.
_ × 2 = 1_4.
6
264
© Houghton Mifflin Harcourt Publishing Company
0
Name
Problem
Problem Solving
Solving
Sense or Nonsense?
4. Emilio and Julia used different ways to find 1_2 ÷ 4. Emilio used a model
to find the quotient. Julia used a related multiplication equation to find
the quotient. Whose answer makes sense? Whose answer is nonsense?
Explain your reasoning.
Emilio’s Work
Julia’s Work
If _1 ÷ 4 = ■, then ■ × 4 = 1_.
2
2
I know that 1_ × 4 = 1_.
8
2
So, 1_ ÷ 4 = 1_ because 1_ × 4 = 1_.
2
8
8
2
1_ ÷ 4 = 1
_
4
2
5. For the answer that is nonsense, describe how to find the
correct answer.
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6.
Multi-Step If you were going to find 2_1 ÷ 5, explain how you would
find the quotient using fraction strips. Write an equation to show the quotient.
Module 6 • Lesson 4
265
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
7. Ants are lined up along the edges of your sandwich at a picnic.
If the sandwich is 9 inches around and each ant is 1_6 of an inch,
how many ants are lined up around the sandwich?
A
15 ants
B
16 ants
C
27 ants
D
54 ants
8. Use Tools Which is the division problem modeled by the picture?
A
1
4 ÷ __
12
B
3 ÷ 1_4
C
3 ÷ 1_3
D
12 ÷ 1_3
9. Multi-Step Maddie divided 6 by 1_2 , and then divided that answer by 1_3 .
What was her final answer?
A
9
C
12
B
1
D
36
TEXAS Test Prep
10. Reid has 4 bags of soil. He uses 1_3 of a bag to fill each planter. How many
266
A
11_
B
12
C
32_
D
41_
3
3
3
© Houghton Mifflin Harcourt Publishing Company
planters can Reid fill with the bags of soil?
Number and Operations—5.3.J,
5.3.L
MATHEMATICAL PROCESSES 5.1.C, 5.1.F
H o mewo rk
and Practice
6.4
Name
Divide Fractions and Whole Numbers
Divide and check the quotient.
1.
4 ÷ 1_4 = _ because
_ × 1_4 = 4.
3.
2.
0
1
2
2 ÷ 1_ = _ because _ × 1__ = 2.
6
6
1÷2=
__
3
4.
_ because _ × 2 = __31.
5.
0
1
2
3
3 ÷ 1__ = _ because _ × 1__ = 3.
5
5
1 ÷ 2 = _ because _ × 2 = __
1.
__
5
5
© Houghton Mifflin Harcourt Publishing Company
Problem
Problem Solving
Solving
6. Julie buys a board that is 6 feet long. She wants to
_1
2
cut it into pieces that are foot each. How many
pieces will Julie have after she cuts the board?
7. Mr. Morales makes four batches of cookies for
family math night. He divides half of a pound of
butter equally into 4 mixing bowls. How much
butter is in each bowl?
Module 6 • Lesson 4 267
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
8. Which is the division problem modeled by
the picture?
0
A
A
B
C
D
B
1÷6
__
2
1__ ÷ 12
6
1__ ÷ 2
6
1 ÷2
___
12
C
D
10. Evan brings 8 liters of juice to be served
_1
5
at family math night. He pours liter into
each glass. How many glasses of juice can
be served?
B
40
C
13
B
D
10
C
A
D
cup flour into a small bowl. Then he divides
the amount in the small bowl into 4 empty
mixing bowls. What amount of dry ingredients
is in each mixing bowl?
A
B
C
D
268
1 cup
___
16
1__ cup
2
1__ cup
8
2 cups
3
3 ÷ __1
8
24 ÷ __1
4
1
3 ÷ ___
24
8 ÷ __1
3
walls. She marks off 1_4 of the wall. Then she
divides the marked section into 3 equal
parts and paints one part blue. What fraction
of the whole wall is blue?
8
_1
4
2
11. Marissa is painting one of her bedroom
A
12. Multi-Step Rex combines 1_4 cup sugar and
1
1
__
3
1__
4
1__
7
1
___
12
13. Multi-Step Jamie divided 8 by 1_2 , and then
multiplied that answer by 1_4 . What was her
final answer?
A
4
B
1
C
64
D
32
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the picture?
9. Which is the division problem modeled by