Name
5.1
?
Number and
Operations—5.3.H, 5.3.K
MATHEMATICAL PROCESSES
5.1.C
Addition with Unequal
Denominators
Essential Question
How can you use models to add fractions that have
unequal denominators?
Hands
On
Investigate
Investigate
Hilary is using red fabric to make a tote bag. She uses one piece that
is 1_2 yard long. She uses another piece that is 1_4 yard long. How much
red fabric does she use?
Materials ■ fraction strips ■ MathBoard
A. Find 1_2 + 1_4 . Place a 1_2 strip and a 1_4 strip under the 1-whole strip
on your MathBoard.
B. Find fraction strips, all with the same denominator, that are
equivalent to 1_2 and 1_4 and fit exactly under the sum 1_2 + 1_4 .
Record the addends, using equal denominators.
VXP
+
C. Record the sum in simplest form. 1_2 + 1_4 = _
Math Talk
So, Hilary uses _ yard of fabric.
Draw Conclusions
Mathematical Processes
How can you tell if the sum of
the fractions is less than 1?
1. Describe how you would determine what fraction strips, all with the
© Houghton Mifflin Harcourt Publishing Company
same denominator, would fit exactly under 1_2 + 1_3 . What are they?
2.
Explain the difference between finding fraction strips
with the same denominator for 1_2 + 1_3 and 1_2 + 1_4 .
Module 5
195
Make
Make Connections
Connections
Sometimes, the sum of two fractions is greater than 1. When adding fractions
with unequal denominators, you can use the 1-whole strip to help determine
if a sum is greater than 1 or less than 1.
Hands
On
Use fraction strips to solve. 3_5 + _12
STEP 1
Work with another student. Place
three 1_5 fraction strips under the
1-whole strip on your MathBoard.
Then place a 1_2 fraction strip beside
the three 1_5 strips.
STEP 2
Find fraction strips, all with the same
denominator, that are equivalent to
3
_ and 1_ . Place the fraction strips under
5
2
the sum. At the right, draw a picture
of the model and write the equivalent
fractions.
STEP 3
Add the fractions with equal
denominators. Use the 1-whole strip
to rename the sum in simplest form.
Think: How many fraction strips with the
same denominator are equal to 1 whole?
3=
__
5
_
1
__ =
2 _
3
__ + 1
__ =
+
5 2 _ _
= _ , or _
Math Talk
Mathematical Processes
In what step did you find out
that the answer is greater
than 1? Explain.
Share
Share and
and Show
Show
Use fraction strips to find the sum. Write your answer in simplest form.
2.
1+3
__
__ =
+
=
2 8 _ _ _
196
3 + 1__ =
__
+
=
4 3 _ _ _
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1.
Name
Use fraction strips to find the sum. Write your answer
in simplest form.
3 =
__ + ___
3. 2
5
10
_
1 =
__ + ___
4. 1
4
12
_
3 =
__ + ___
5. 1
2
10
_
Problem
Problem Solving
Solving
6.
Multi-Step Maya makes trail mix by combining
cup of mixed nuts, 1_4 cup of dried fruit, and 1_6 cup of chocolate
morsels. What is the total amount of ingredients in her trail mix?
1_
3
7.
Pose a Problem Write a new problem using
different amounts for ingredients Maya used. Each amount should
be a fraction with a denominator of 2, 3, or 4.
Write Math
Show Your Work
8. Use Diagrams Solve the problem you wrote. Draw a picture of the
fractions strips you use to solve your problem.
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9. Explain why you chose the amounts you did for your problem.
10.
Write Math
Explain how using fraction strips with
equal denominators makes it possible to add fractions with
unequal denominators.
Module 5 • Lesson 1
197
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
7
11. In a garden, bluebonnets occupy __
10 of the garden. After winter, the
bluebonnets spread to cover another 1_5 of the garden. What fraction of
the garden is now covered in bluebonnets?
A
1
_
5
C
8
__
B
1
_
2
D
9
__
10
10
7
12. Ling is using fraction strips to add 2_3 and __
12 . The sum is one whole,
plus how many twelfths?
A
1
B
2
C
3
D
4
13. Multi-Step Juan uses 1_5 liter to water a small plant, and he uses
_1
2
2
liter to water a large plant. Now he has __
10 liter left in the pitcher.
How much water did Juan have in the beginning?
A
3
_L
5
B
9 L
__
C
10
1 L
__
10
D
3 L
__
10
TEXAS Test Prep
14. Wilhelm is making a pie. He uses 1_2 cup of blueberries and 32_ cup of
198
A
3_ cup
5
B
2_ cup
6
C
7_ cups
6
D
3_ cup
6
© Houghton Mifflin Harcourt Publishing Company
raspberries. What is the total amount of berries in Wilhelm’s pie?
Number and Operations—5.3.H,
5.3.K
MATHEMATICAL PROCESSES 5.1.C
H o mewo rk
and Practice
5.1
Name
Addition with Unequal Denominators
Use fraction strips to find the sum. Write your answer in simplest form.
1.
2.
1__ + 1__ =
+
=
3 6 _ _ _
2__ + 3__ =
+
=
3 4 _ _ _
__ + 3
__ =
3. 1
_
__ + 1
__ =
4. 5
_
__ + 2
__ =
5. 1
_
__ + 2
__ =
6. 1
_
__ + 5
__ =
7. 1
_
3 =
__ + ___
8. 3
_
__ + 3
__ =
9. 1
_
7 + 1__ =
10. ___
_
1 =
__ + ___
11. 5
_
6
4
8
4
3
4
6
3
10
2
6
2
2
5
6
5
10
12
Problem
Problem Solving
Solving
12. Cooper is grating cheese for the family taco
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_1
2
dinner. He grates cup of cheddar cheese and
3_ cup of monterey jack cheese. How much
4
cheese does Cooper grate?
13. Jasmine has to mix 3_4 cup of flour and 3_8 cup of
cornmeal. She has a container that holds 1 cup.
Can Jasmine mix the flour and cornmeal in the
container? Explain.
Module 5 • Lesson 1
199
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
1 of his weekly allowance on a set
14. Julio spent __
10
2_
5
of markers and of it on a book. What fraction
of Julio’s allowance is this altogether?
B
C
D
1
__
2
3
___
10
3__
5
1__
5
16. Which fraction correctly completes the
6__ + ■
___ = 1
8 ■
B
C
D
D
200
2
C
5
D
8
17. An apple was cut into 8 equal-size pieces.
C
D
_5
6
her poodle mile on Saturday and mile on
Sunday. Fiona walked her beagle 1_3 mile on
Saturday and 1_2 mile on Sunday. How much
farther did the poodle walk last weekend than
the beagle?
C
B
B
_2
3
B
1
A
1__
2
1__
8
3__
8
1__
4
18. Multi-Step Last weekend, Beatrice walked
A
A
Stacy ate 1_4 of the apple. Tony ate 3_8 of the apple.
What part of the apple did Stacy and Tony eat
in all?
equation?
A
She uses one whole strip to represent the
sum. How many fifths strips does she need to
complete the sum?
1 mile
__
2
11__ miles
3
2__ mile
3
11__ miles
2
1
__
2
5__
8
3__
4
1__
4
19. Multi-Step Rick worked in his garden on
Friday. He pulled weeds for 5_6 hour, planted
seeds for 1_2 hour, and watered for 1_6 hour.
How much time did Rick spend working in his
garden on Friday?
A
1__ hour
2
B
1 hour
C
11__ hours
3
11__ hours
2
D
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A
4 and 4_ .
15. Kate is using fraction strips to add __
10
5