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```Lesson 6.6
Name
Essential Question How can you add and subtract mixed numbers with
unlike denominators?
Number and Operations—
Fractions—5.NF.A.1 Also 5.NF.A.2
MATHEMATICAL PRACTICES
MP1, MP2, MP6
Unlock
Unlock the
the Problem
Problem
Denise mixed 1 4_5 ounces of blue paint with
1
2 __
10 ounces of yellow paint. How many
ounces of paint did Denise mix?
• What operation should you use to solve
the problem?
• Do the fractions have the same denominator?
1
__ + 2___
5
10
To find the sum of mixed numbers with unlike denominators, you can
use a common denominator.
STEP 1
Estimate the sum. ___
STEP 2
Find a common denominator. Use the
common denominator to write equivalent
fractions with like denominators.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (l) ©Andrew Paterson/Alamy
STEP 3
numbers. Write the answer in simplest form.
So, Denise mixed _ ounces of paint.
1.
MATHEMATICAL
PRACTICE
__ =
14
5
1 = +
+ 2 ___
10
Math
Talk
MATHEMATICAL PRACTICES 2
Connect Symbols and Words
Did you use the least
common denominator?
Explain.
1 Evaluate Reasonableness Explain how you know whether your answer is reasonable.
2. What other common denominator could you have used?
Chapter 6
383
Example
5 − 23
__
Subtract. 4 __
6
4
You can also use a common denominator to find the difference of
mixed numbers with unlike denominators.
STEP 1
Estimate the difference. __
STEP 2
Find a common denominator. Use the
common denominator to write equivalent
fractions with like denominators.
STEP 3
3.
__ =
45
6
__ = –
– 23
4
Subtract the fractions. Subtract the whole
numbers. Write the answer in simplest form.
MATHEMATICAL
PRACTICE
1 Evaluate Reasonableness Explain how you know whether
Share
hhow
Share and
and Show
Sh
MATH
M
BOARD
B
1. Use a common denominator to write equivalent fractions with like
denominators and then find the sum. Write your answer in simplest form.
__ =
72
5
__ = +
+ 43
3
2. 2 3_4 + 3 __
10
384
3. 5 3_4 + 1 1_
3
3
4. 3 4_ + 2 __
5
10
© Houghton Mifflin Harcourt Publishing Company
4
Name
5. 9 5_ − 2 1_
6
6. 10 5_ − 9 1_
3
9
7. 7 _2 − 3 1_
6
3
Math
Talk
On
On Your
Own
3 + 22
_
8. 1 __
5
9. 8 1_ + 7 3_
11. 12 3_4 − 6 1_
6
12. 2 5_ − 1 1_4
10
6
6
MATHEMATICAL PRACTICES 6
Explain why you need to
write equivalent fractions
with common denominators
to add 4 5_6 and 1 1_8 .
10. 2 1_ + 2 1_
8
2
3
7 − 5 1_
13. 14 __
4
8
12
Practice: Copy and Solve Find the sum or difference. Write your
15. 8 1_ + 6 3_
16. 2 1_ + 4 5_
17. 3 5_ + __
12
18. 3 2_ − 1 1_
19. 5 6_7 − 1__2
3
20. 2 7_ − 1_2
7 − 12
_
21. 4 __
12
3
22.
© Houghton Mifflin Harcourt Publishing Company
5
5 + 41
_
14. 1 __
23.
6
6
2
5
6
9
8
8
12
9
DEEPER
Dakota makes a salad dressing by combining 6 1_3 fluid ounces of oil
and 2 3_8 fluid ounces of vinegar in a jar. She then pours 2 1_4 fluid ounces of the
dressing onto her salad. How much dressing remains in the jar?
DEEPER
This week, Maddie worked 2 1_2 hours on Monday, 2 2_3 hours on
Tuesday, and 3 1_4 hours on Wednesday. How many more hours will Maddie
need to work this week to make her goal of 10 1_2 hours a week?
Chapter 6 • Lesson 6 385
MATHEMATICAL PRACTICES .0%&-t3&"40/tM",&4&/4&
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OqnakdlRnkuhmf¤@ookhb`shnmr
Use the table to solve 24–25.
24.
2 Reason Quantitatively Gavin plans to mix a batch
3 ounces of paint
of Tangerine paint. He expects to have a total of 5 __
MATHEMATICAL
PRACTICE
10
after he mixes the amounts of red and yellow. Explain how you can
tell if Gavin’s expectation is reasonable.
Paint Gavin Uses
(in ounces)
Red
25.
SMARTER
Gavin mixes the amount of red
from one shade of paint with the amount of
yellow from a different shade of paint. He mixes
the batch so he will have the greatest possible
amount of paint. What amounts of red and yellow
from which shades are used in the mixture?
SMARTER
26.
Yellow
1
Sunrise
Orange
3
Tangerine
5
Mango
28
5
34
3 10
9
28
5
56
56
Martin won first place in the 100-meter dash with a time of
23
7
__
14 ___
100 seconds. Samuel came in second place with a time of 15 10 seconds.
26a.
A common denominator of the mixed
numbers is 100.
True
False
26b.
To find the difference between the
runners’ times, Samuel’s time needs
to be rewritten.
True
False
26c.
Samuel’s time written with a denominator
70
of 100 is 15 ___
100 .
True
False
True
False
__ second.
26d. Martin beat Samuel by 21
25
386
© Houghton Mifflin Harcourt Publishing Company
For 26a–26d, select True or False for each statement.
Practice and Homework
Name
Lesson 6.6
COMMON CORE STANDARD—5.NF.A.1
Use equivalent fractions as a strategy to add
and subtract fractions.
1. 31_ − 11_
2
2. 21_ + 13_
5
3
_
31
5
3__
_
−11
2
−1__
2
8
3
4. 51_ + 61_
3
6
10
5
10
3
2__
10
__
5. 2 1_ + 12_
4
3. 41_ + 21_
4
__
__ − 22
_
6. 5 17
5
18
__
3
__
__
7. 6 3_ − 15_
4
8
__
__
8. 53_ − 21_
7
5
__
Problem
Problem Solving
Solving
9. Jacobi bought 7 1_2 pounds of meatballs. He
decided to cook 1 1_4 pounds and freeze the rest.
How many pounds did he freeze?
© Houghton Mifflin Harcourt Publishing Company
_______
11.
WRITE
10. Jill walked 8 1_8 miles to a park and then
7 2_5 miles home. How many miles did
she walk?
_______
Math Write your own story problem using mixed numbers.
Show the solution.
Chapter 6
387
Lesson Check (5.NF.A.1)
1. Ming has a goal to jog 4 1_2 miles each day. On
9 miles. By how much did
Monday she jogged 5 __
16
she exceed her goal for that day?
2. At the deli, Ricardo ordered 3 1_5 pounds of
cheddar cheese and 2 3_4 pounds of mozzarella
cheese. How many pounds of cheese did
he order all together?
3. The theater has 175 seats. There are 7 seats in
each row. How many rows are there?
4. During the first 14 days, 2,744 people visited a
new store. The same number of people visited
the store each day. About how many people
visited the store each day?
5. What number is 100 times as great as 0.3?
6. Mark said that the product of 0.02 and 0.7
is 14. Mark is wrong. What is the product?
FOR MORE PRACTICE
GO TO THE
388
Personal Math Trainer
© Houghton Mifflin Harcourt Publishing Company
Spiral Review (5.NBT.A.2, 5.NBT.A.3b, 5.NBT.B.6, 5.NBT.B.7)
```
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