Lesson 6.7
Name
Subtraction with Renaming
Number and Operations—
Fractions—5.NF.A.1 Also 5.NF.A.2
MATHEMATICAL PRACTICES
MP1, MP2
Essential Question How can you use renaming to find the difference of
two mixed numbers?
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the Problem
Problem
To practice for a race, Kara is running 2 1_2 miles.
When she reaches the end of her street, she
knows that she has already run 1 5_6 miles. How
many miles does Kara have left to run?
• Underline the sentence that tells you
what you need to find.
• What operation should you use to solve
the problem?
One Way Rename the first mixed number.
1 − 15
__
Subtract. 2__
2
6
STEP 1
Estimate the difference. __
STEP 2
Find a common denominator. Use the
common denominator to write equivalent
fractions with like denominators.
STEP 3
6
as a mixed number with a
Rename 2__
12
fraction greater than 1.
6 =
__ = 2___
21
2
12
__ = –110
___ = – 110
___
–15
6
12
12
=
6 5 1 1 1 1 ___
6 5 1 1 12
6 5 118
___
___ 1 ___
___
Think: 212
12
12
12
12
6 =
2___
12
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STEP 4
_
Find the difference of the fractions.
Then find the difference of the whole
numbers. Write the answer in simplest
form. Check to make sure your answer
is reasonable.
So, Kara has _ mile left to run.
•
MATHEMATICAL
PRACTICE
6 Explain why it is important to write equivalent fractions before renaming.
Chapter 6
389
Another Way
Rename both mixed numbers as
fractions greater than 1.
Subtract. 2 1_2 − 1 5_6
STEP 1
Write equivalent fractions,
using a common denominator.
A common denominator of 1_2 and 5_6 is 6.
__
21
2
__
15
6
STEP 2
Rename both mixed numbers
as fractions greater than 1.
__ =
23
Think: __6 1 __6 1 6
__ =
15
Think: __66 1 5__6
6
6
6
STEP 3
Find the difference of the
fractions. Then write the
answer in simplest form.
–
6
3
__
=
=
2 1_2 − 1 5_6 = _
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MATH
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Estimate. Then find the difference and write it in simplest form.
41_ 2 34_
2
5
2. Estimate: __
91_ – 23_4
6
Math
Talk
MATHEMATICAL PRACTICES 5
Communicate Explain the
strategy you could use to
solve 3 1_9 – 2 1_3 .
390
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1. Estimate: __
Name
On
On Your
Your Own
Own
Estimate. Then find the difference and write it in simplest form.
3. Estimate: __
4. Estimate: __
11
32_ 2 1___
3
5. Estimate: __
41_4 2 21_
12
52_ 2 11_
5
3
2
Practice: Copy and Solve Find the difference and write it in simplest form.
6. 111_ − 32_
9
14.
15.
9. 91_ − 35_
12. 122_ − 53_4
13. 73_ − 27_
2
10. 11_ − 1_
5
8. 43_ − 31_
7. 6 − 31_
3
8
11. 131_ − 34_
2
6
5
6
5
8
8
9
DEEPER
Three commercials are played in a row between songs on
the radio. The three commercials fill exactly 3 minutes of time. If the first
commercial uses 1 1_6 minutes, and the second uses 3_5 minute, how long is the
third commercial?
SMARTER
Four students made videos for
an art project. The table shows the length of each video.
Match each pair of videos with the correct difference
between their times.
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2
Art in Nature
Video
Time (in hours)
1
43_
Video 1 and Video 3
•
•
Video 2 and Video 3
•
• 1 __109 hours
3
Video 2 and Video 4
•
• 1 11__12 hours
4
17
1 __
30
hours
2
4
42_
5
25_
6
2 1_2
Chapter 6 • Lesson 7 391
Summarize
An amusement park in Sandusky, Ohio, offers 17 amazing roller
coasters for visitors to ride. One of the roller coasters runs at
60 miles per hour and has 3,900 feet of twisting track. This
coaster also has 3 trains with 8 rows per train. Riders stand in
rows of 4, for a total of 32 riders per train.
The operators of the coaster recorded the number of riders on
each train during a run. On the first train, the operators reported
that 7 1_4 rows were filled. On the second train, all 8 rows were
filled, and on the third train, 5 1_2 rows were filled. How many more
rows were filled on the first train than on the third train?
When you summarize, you restate the most important
information in a shortened form to more easily understand
what you have read.
16.
MATHEMATICAL
PRACTICE
1 Analyze Identify and summarize the important
information given in the problem.
Use the summary from item 16 to solve.
17. Solve the problem above.
18.
392
SMARTER
How many rows were empty on the first train?
How many additional riders would it take to fill the empty rows?
Explain your answer.
Math t Show Your Work
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WRITE
Practice and Homework
Name
Lesson 6.7
Subtraction with Renaming
Estimate. Then find the difference and write it in simplest form.
1. Estimate: ___
61_ − 12_
3
41_ − 35_
5
_
61
3
_
− 12
5
2
3. Estimate: ___
9 − 37_
6
8
20
5 5
__
6
15
6
− 1 __
15
__
4 14
15
4. Estimate: ___
21_ − 12_
6
2. Estimate: ___
COMMON CORE STANDARD—5.NF.A.1
Use equivalent fractions as a strategy to add
and subtract fractions.
5. Estimate: ___
91_ − 32_
8 − 61_
7
6. Estimate: ___
4
9
3
Problem
Problem Solving
Solving
1 yards of ribbon to decorate a
7. Carlene bought 8 __
16
shirt. She only used 5 1_2 yards. How much ribbon
does she have left over?
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_______
9.
WRITE
8. During his first vet visit, Pedro’s puppy weighed
6 1_8 pounds. On his second visit, he weighed
1 pounds. How much weight did he gain
9 __
16
between visits?
_______
Math Write a subtraction problem that has mixed numbers
and requires renaming. Draw a model illustrating the steps you take to
solve the problem.
Chapter 6
393
Lesson Check (5.NF.A.1)
1. Natalia picked 7 1_6 bushels of apples today and
4 5_8 bushels yesterday. How many more bushels
did she pick today?
2. Max needs 10 1_4 cups of flour to make a batch
of pizza dough for the pizzeria. He only has
4 1_2 cups of flour. How much more flour does
he need to make the dough?
Spiral Review (5.NBT.A.1, 5.NBT.A.2, 5.NBT.B.6, 5.NBT.B.7)
3. The accountant charged $35 for the first hour
of work and $23 for each hour after that. He
earned a total of $127. How many hours did
he work?
4. The soccer league needs to transport all
133 players to the tournament. If 4 players can
ride in one car, how many cars are needed?
5. What is five hundred million, one hundred
fifteen written in standard form?
6. Find the quotient.
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6.39 ÷ 0.3
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