Name
5.5
?
Add and Subtract Fractions
Essential Question
Number and
Operations—5.3.K
MATHEMATICAL PROCESSES
5.1.C
How can you use a common denominator to add and
subtract fractions with unequal denominators?
Connect You can use what you have learned about common
denominators to add or subtract fractions with unequal denominators.
Hands
On
Unlock
Unlock the
the Problem
Problem
Malia bought shell beads and glass beads to
weave into designs in her baskets. She bought
1_ pound of shell beads and 3_ pound of glass
4
8
beads. How many pounds of beads did she buy?
• Underline the question you need to answer.
• Draw a circle around the information
you will use.
1+3
__ Write your answer in simplest form.
Add. __
4
8
One Way
Another Way
Find a common denominator by multiplying
the denominators.
Find the least common denominator.
4×8=_
common denominator
Use the common denominator to write equivalent
fractions with equal denominators. Then add, and
write your answer in simplest form.
1
__ =
4
The least common denominator
of 1_4 and 3_8 is _.
1×
______
=
1×
1 = ______
__
=
4 4×
4×
3
×
______
+ __
=
+
=+
8
3
__
+3
8×
8
+
© Houghton Mifflin Harcourt Publishing Company
=
So, Malia bought _ pound of beads.
1. Explain how you know whether your answer is reasonable.
Module 5
219
Example
When subtracting two fractions with unequal denominators, follow the same
steps you follow when adding two fractions. However, instead of adding the
fractions, subtract.
9 −2
__ Write your answer in
Subtract. ___
5
10
simplest form.
Describe the steps you took to solve
the problem.
9 =
___
10
2
− __
5 =
2. Explain how you know whether your answer is reasonable.
Share
Share and
and Show
Show
5 +1
_
1. __
12 3
2. 2_ + 3_
5 7
3. 1_ + 3_
6 4
4. _3 − 1_
4 8
5. _1 − 1_
4 7
9 − 1_
6. __
10 4
Math Talk
Mathematical Processes
Explain why it is important
to check your answer for
reasonableness.
220
© Houghton Mifflin Harcourt Publishing Company
Find the sum or difference. 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.
__ + 1
__
8. 3
4
__ + ___
7. 1
3
5
18
11. _1 − 3_
2 8
3
12. _5 − 2_
7 3
3 + 1__
9. ___
10
__ + 4
__
10. 1
6
2
9
7
11 − __
14. __
12 15
13. _4 − 1_
9 6
Algebra Find the unknown number.
9 −
15. __
10
■ = 1_5
5 + ■ = 1_
16. __
2
12
■=_
■=_
Problem
Problem Solving
Solving
Use the picture for 17–18.
17. Sara is making a key chain using the bead design shown.
What fraction of the beads in her design are either
blue or red?
18.
© Houghton Mifflin Harcourt Publishing Company
19.
Multi-Step In making the key chain, Sara
uses the pattern of beads 3 times. After the key chain
is complete, what fraction of the beads in the key chain
are either white or blue?
Write Math
Jamie had 4_5 of a spool of twine. He
then used 1_2 of a spool of twine to make friendship
3
knots. He claims to have __
10 of the original spool of
twine left over. Explain how you know whether
Jamie’s claim is reasonable.
Write Math
Show Your Work
Module 5 • Lesson 5
221
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
20. Apply Students are voting for a new school mascot. So far, the results
3
1_
show that __
10 of the students voted for “Fightin’ Titan,” 2 of the students
voted for “Nifty Knight,” and the rest of the students have not voted yet.
What fraction of the student population has not voted yet?
A
3
__
C
2_
5
B
1
_
5
D
4
_
5
10
21. Tina spent 3_5 of her paycheck on a trip to the beach. She spent 3_8 of her
paycheck on new clothes for the trip. What fraction of her paycheck did
Tina spend on the trip and clothes together?
A
9
__
B
3
_
4
C
7
_
8
D
39
__
40
40
22. Multi-Step On Friday, 1_6 of band practice was spent trying on uniforms.
The band spent 1_4 of practice on marching. What fraction of practice time
was left for playing music?
A
5
__
C
1_
2
B
7
__
D
1
_
4
12
12
TEXAS Test Prep
A
B
C
D
222
1 1
_
+ _ = 3_
2 4 4
1
_+1
_=3
_
4 8 8
1 _
_
+ 1 = _5
2 8 8
3
_+2
_=1
4 8
© Houghton Mifflin Harcourt Publishing Company
23. Which equation represents the fraction of beads that are green or yellow?
Number and Operations—5.3.K
MATHEMATICAL PROCESSES 5.1.C
H o mewo rk
and Practice
5.5
Name
Add and Subtract Fractions
Find the sum or difference. Write your answer in simplest form.
__ + 1
__
1. 1
5
2
__ + 1
__
5. 2
9
3
3
__ − 1
__
13. 5
9
6
3
_
_
6
__ + 2
__
6. 1
_
6 − 1__
9. ___
12
__ + 1
__
2. 2
_
2
6
__ − 1
__
10. 3
4
6
__ − 1
__
14. 2
3
4
_
_
_
_
__ + 2
__
3. 1
4
3
3 + 1__
7. ___
10
3
__ − 1
__
11. 5
7
2
4
7
8
_
4 + 2__
8. ___
_
18
6
__ − 2
__
12. 8
_
7 − 2__
15. ___
14
__ + 1
__
4. 3
_
9
3
__ − 3
__
16. 5
_
6
4
_
_
_
Find the unknown number.
7 − ■ = __1
17. ___
12
6
5 + ■ = __1
18. ___
18
■ = __
7 − ■ = __2
19. ___
10
5
■ = __
2
■ = __
20.
■ + 1__9 = __31
■ = __
Problem
Problem Solving
Solving
© Houghton Mifflin Harcourt Publishing Company
21. There are 12 students in the pep squad. Three
students are wearing white shirts. Six students
are wearing blue shirts. What fraction of the
students in the pep squad are wearing either
white or blue shirts?
22. Tiffany ran 5_6 mile. Shayne ran 3_4 mile. Who ran
farther? How much farther?
Module 5 • Lesson 5
223
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
23. Mr. Benson spent 2_5 of the monthly budget
3 of the budget on food. What
on rent and __
10
fraction of Mr. Benson’s budget was spent on
rent and food?
A
B
C
D
1__
3
3
___
10
7
___
10
1__
2
__ pound of confetti
24. The Ortega family made 15
16
for the annual Fiesta celebration in San
Antonio. They used 1_4 pound to make confetti
filled eggs. How much confetti is left to use
next year?
A
B
C
D
11 pound
___
16
9 pound
___
16
4__ pound
5
3__ pound
4
Use the recipe for 25–26.
25. If Rory measures the lemon juice and the
A
B
C
D
5 teaspoon
__
8
1__ teaspoon
5
1__ teaspoon
4
3__ teaspoon
8
26. Multi-Step Rory has 5_8 cup of milk. How
much milk does she have left after she doubles
the recipe for the smoothie?
A
B
C
D
224
3__ cup
8
1__ cup
8
3__ cup
4
1__ cup
2
Berry Smoothie
2 cups strawberries
1 cup blueberries
1 cup milk
__
4
1 Tbsp sugar
1__ tsp lemon juice
2
1 tsp vanilla extract
__
8
27. Multi-Step Tom has 7_8 cup of olive oil. He
uses 1_2 cup to make salad dressing and 1_4 cup to
make tomato sauce. How much olive oil does
Tom have left?
A
B
C
D
5 cups
__
4
5__ cup
8
3__ cup
8
1__ cup
8
© Houghton Mifflin Harcourt Publishing Company
vanilla extract into one spoon before adding
them to the blender, how much liquid will be
in the spoon?