Name
5.6
?
Number and
Operations—5.3.K
MATHEMATICAL PROCESSES
5.1.A
Add and Subtract Mixed
Numbers
Essential Question
How can you add and subtract mixed numbers with
unequal denominators?
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___
Add. 14
5
10
To find the sum of mixed numbers with unequal
denominators, you can use a common denominator.
STEP 1
Estimate the sum.
___
__ =
14
5
STEP 2
STEP 3
Find a common denominator. Use the
common denominator to write equivalent
fractions with equal denominators.
1 =+
+ 2 ___
10
Add the fractions. Then add the whole
numbers. Write the answer in simplest form.
Math Talk
So, Denise mixed _ ounces of paint.
Mathematical Processes
Did you use the least common
denominator? Explain.
© Houghton Mifflin Harcourt Publishing Company
1. Explain how you know whether your answer is reasonable.
2. What other common denominator could you have used?
Module 5
225
Example
__ − 2 3
__
Subtract. 4 5
6
4
You can also use a common denominator to find the
difference of mixed numbers with unequal denominators.
STEP 1
__ =
45
Estimate the difference. ___
6
STEP 2
STEP 3
Find a common denominator. Use the
common denominator to write equivalent
fractions with equal denominators.
__ = –
– 23
4
Subtract the fractions. Subtract the whole
numbers. Write the answer in simplest form.
3. Explain how you know whether your answer is reasonable.
Share
Share and
and Show
Show
1. Use a common denominator to write equivalent fractions with
equal denominators and then find the sum. Write your answer in
simplest form.
__ =
72
5
__ = +
+ 43
4
3
2. 2 3_ + 3 __
4
10
226
3. 5 3_ + 1 1_
4
3
3
4. 3 4_ + 2 __
5
10
© Houghton Mifflin Harcourt Publishing Company
Find the sum. Write your answer in simplest form.
Name
Problem
Problem Solving
Solving
Practice: Copy and Solve Find the sum or difference. Write your
answer in simplest form.
5 + 41
_
5. 1 __
12
6
6. 8 1_ + 6 3_
5
2
9. 3 2_ − 1 1_
3
6
10. 5 6_ − 1__2
7
3
5
8. 3 5_ + __
8 12
7. 2 1_ + 4 5_
6
9
1
11. 2 7_ − _2
8
7 − 12
_
12. 4 __
12
9
13. Communicate Why do you need to write equivalent fractions with
__ ? Explain.
common denominators to add 4 5_6 and 11
8
Problem
Problem Solving
Solving
Use the table to solve 14–15.
14.
Multi-Step Gavin needs to make 2 batches
of Mango paint. Explain how you could find the total
amount of paint Gavin mixed.
Paint Gavin Uses
(in ounces)
© Houghton Mifflin Harcourt Publishing Company
15.
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?
Explain your answer.
Red
Yellow
Shade
2 58
3 14
Sunrise
Orange
9
3 10
2 38
Tangerine
5 56
5 56
Mango
Module 5 • Lesson 6
227
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
16. Dr. Whether-or-Not collects two hailstones during a storm in California.
One hailstone weighs 2 3_8 pounds, and the other hailstone weighs
3
1 __
10 pounds. How much heavier is the larger hailstone than the
smaller hailstone?
A
3 pounds
__
C
__ pounds
127
B
3 pounds
1__
D
__ pounds
327
40
40
40
40
17. Apply Jason is making a fruit salad. He mixes in 3 1_4 cups of orange
melon and 2 2_3 cups of green melon. How many cups of melon does
Jason put in the fruit salad?
A
51_4 cups
C
7 cups
5__
B
5 1_3 cups
D
__ cups
511
12
12
18. Multi-Step 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?
A
61_ fluid ounces
B
63_ fluid ounces
C
__ fluid ounces
611
D
__ fluid ounces
617
8
8
24
24
TEXAS Test Prep
6
1_
19. Yolanda walked 3 __
10 miles. Then she walked 4 2 more miles.
228
A
1 miles
7__
B
7 miles
8__
C
1 miles
8__
D
7 miles
7__
10
10
10
10
© Houghton Mifflin Harcourt Publishing Company
How many miles did Yolanda walk?
Number and Operations—5.3.K
MATHEMATICAL PROCESSES 5.1.A
H o mewo rk
and Practice
5.6
Name
Add and Subtract Mixed Numbers
Find the sum or difference. Write your answer in simplest form.
__ + 22
__
1. 11
4
3
__ + 42
__
5. 55
6
9
__ − 11
__
9. 24
5
2
__ − 21
__
13. 41
3
4
_
_
_
_
5
__ + 4___
2. 33
4
12
__ + 32
__
6. 71
4
5
__ − 11
__
10. 53
8
4
__ − 11
__
14. 31
4
6
_
_
_
_
__ + 21
__
3. 11
3
6
__ + 81
__
7. 32
7
3
__ − 31
__
11. 41
3
6
_
4
__ + 3__
4. 41
5
_
_
1
__ + 3__
8. 43
2
_
_
7
__ − 5__
12. 65
9
_
1
__ − 2__
16. 73
_
5
__ − 2___
15. 63
4
16
_
2
7
6
5
4
1.
17. Use two mixed numbers to write an equation with a sum of 4__
4
Problem
Problem Solving
Solving
18. Lucas says his twin baby brothers have a total
weight of 15 1_8
pounds. Jackson weighs 6 1_4 pounds,
and Jeremy weighs 8 7_8 pounds. Explain how you
© Houghton Mifflin Harcourt Publishing Company
can use estimation to tell if the total weight is
reasonable.
19. The gas tank in Rebecca’s old car held 14 1_5
gallons. The gas tank in Rebecca’s new car
holds 18 1_2 gallons. How many more gallons
will the tank in Rebecca’s new car hold than
her old car?
Module 5 • Lesson 6
229
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
Use the table for 20−21.
Four students made paper chains to decorate the
community center. The table at the right shows the
lengths of the paper chains.
Length of Paper Chains
Student
20. If Ioana attaches her chain to the end of
Gabrielle’s chain, what will be the length of the
combined chain?
B
C
D
133__ feet
4
131__ feet
4
121__ feet
4
121__ feet
2
21. How much longer is Oksana’s chain than
Gabrielle’s chain?
A
B
C
D
7 feet
15___
12
1 feet
14___
12
41__ feet
4
1 feet
4___
12
23. Multi-Step Mr. Carter owned a ranch with
7 _14
acres. Last year, he bought 3 _15
acres of land
from his neighbor. Then he sold 2 1_4 acres. How
many acres does Mr. Carter own now?
A
B
C
D
230
9 acres
10___
20
81__ acres
5
7 acres
12___
10
3 acres
6___
10
Skye
1
8 __
12
Ioana
7 1_2
Gabrielle
5 3_4
Oksana
9 5_6
22. Mia hiked 2 1_2 miles farther than Jacob. Which
could be the two distances each person hiked?
A
B
C
D
Mia: 2__1 miles; Jacob: 1__1 miles
2
4
Mia: 2__1 miles; Jacob: 7__1 miles
2
2
9 miles
Mia: 3__2 miles; Jacob: 5___
5
10
9 miles; Jacob: 3__2 miles
Mia: 5___
10
5
24. Multi-Step 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?
A
B
C
D
1 hours
2___
12
5 hours
8___
12
___ hours
1811
12
51__ hours
3
© Houghton Mifflin Harcourt Publishing Company
A
Length (in feet)