Lesson 6.7
Name
Compare Fractions
Number and Operations—
Fractions—4.NF.A.2
MATHEMATICAL PRACTICES
MP2, MP4, MP6
Essential Question How can you compare fractions?
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the Problem
Problem
Every year, Avery’s school has a fair. This year, 3_8 of the
booths had face painting and 1_4 of the booths had sand art.
Were there more booths with face painting or sand art?
Compare 3_8 and 1_4 .
One Way Use a common denominator.
When two fractions have the same denominator, they have
equal-size parts. You can compare the number of parts.
THINK
Think: 8 is a multiple of both 4 and 8.
Use 8 as a common denominator.
MODEL AND RECORD
Shade the model. Then compare.
1=1
×
__
_________
= _____
4 4×
8
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_3
8
already has 8 as a denominator.
●
3
__
8
2
__
8
Another Way Use a common numerator.
When two fractions have the same numerator, they represent the
same number of parts. You can compare the size of the parts.
THINK
Think: 3 is a multiple of both 3 and 1.
Use 3 as a common numerator.
_3
8
MODEL AND RECORD
Shade the model. Then compare.
already has 3 as a numerator.
3
1=1
×
__
_________
= _____
4
Since 3_8
●
4×
_1 , there were more booths with
4
3
__
8
__ .
●
Math
Talk
3
___
12
MATHEMATICAL PRACTICES 2
Reason Abstractly Why
can you not use 1_2 as a
benchmark to compare _38
and 1_4 ?
Chapter 6
365
Try This! Compare the fractions. Explain your reasoning.
__
A 3
● 31
__
__
B 3
● 83
__
C 3
● 87
__
D 4
● 32
4
4
__
5
5
__
__
8 and 3_ ? Explain.
2. Can you use simplest form to compare __
10
5
366
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__ and 5_ , a common
1. Which would you use to compare 11
12
6
numerator or a common denominator? Explain.
Name
MATH
M
Share
hhow
Share and
and Show
Sh
BOARD
B
1.
1. Compare 2_5 and __
10
6 and 3_ .
__
2. Compare 10
4
Think: Use _ as a common denominator.
Think: Use _ as a common numerator.
×
2__ = __________
= ____
5
×
6
___
10
×
3__ = __________
= ____
4
×
1
___
10
Think: 4 tenth-size parts
2__
5
● 101
●
1 tenth-size part.
Think: A tenth-size part
6
___
___
10
Compare. Write <, >, or =.
2__
5
__
3. 7
4. ___
8
8
12
●
● 63
__
4
5. ___
10
● 34
●
an eighth-size part.
__
● 46
6
6. ___
__
12
Math
Talk
On
On Your
Your Own
Own
● 42
__
MATHEMATICAL PRACTICES 2
Use Reasoning How can
using a common numerator
or a common denominator
help you compare fractions?
Compare. Write <, >, or =.
__
7. 1
3
● 14
__
__
8. 4
5
● 108
___
__
9. 3
4
● 26
__
__
10. 1
2
● 58
__
Reason Quantitatively Algebra Find a number that
makes the statement true.
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MATHEMATICAL
PRACTICE
2
__ > ____
11. 1
2
15.
3
3 < ____
12. ___
10
5
5 < ____
13. ___
12
3
4
__ > ____
14. 2
3
DEEPER
Students cut a pepperoni pizza into 12 equal
slices and ate 5 slices. They cut a veggie pizza into
6 equal slices and ate 4 slices. Use fractions to compare
the amounts of each pizza that were eaten.
Chapter 6 • Lesson 7 367
MATHEMATICAL PRACTICES
ANALYZEt-00,'034536$563&t13&$*4*0/
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the Problem
Problem
16.
SMARTER
Jerry is making a strawberry
smoothie. Which measure is greatest, the
amount of milk, cottage cheese, or
strawberries?
Strawberry Smoothie
3 ice cubes
_3 cup milk
4
2
_ cup cottage cheese
6
8
__
12 cup strawberries
_1 teaspoon vanilla
4
1
_ teaspoon sugar
8
a. What do you need to find?
b. How will you find the answer?
c. Show your work.
WRITE
M t Show Your Work
Math
d. Jerry needs more ___ than the other two ingredients.
DEEPER
Angie, Blake, Carlos, and
Daisy went running. Angie ran 1_3 mile,
7 mile, and
Blake ran 3_5 mile, Carlos ran __
10
Daisy ran 1_2 mile. Which runner ran the
shortest distance? Who ran the greatest
distance?
18.
Elaine bought 5_8 pound
of potato salad and 4_6 pound of macaroni
salad for a picnic. Use the numbers to
compare the amounts of potato salad and
macaroni salad Elaine bought.
SMARTER
4
_______
<
_______
5
6
8
368
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17.
Practice and Homework
Name
Lesson 6.7
Compare Fractions
COMMON CORE STANDARD—4.NF.A.2
Extend understanding of fraction equivalence
and ordering.
Compare. Write ,, ., or 5.
1. _3 < _5
4
6
2. _1
5
2
__
10
3. _2
4
_2
5
Think: 12 is a common
denominator.
3×3
3 = _____
9
_
= __
4×3
4
12
5×2
5
10
_ = _____
= __
6×2
6
12
9 , __
10
__
12
4. _3
5
12
7
__
10
4
5. __
12
_1
6
6. _2
6
_1
3
7. _1
3
_2
4
Problem
Problem Solving
Solving
8. A recipe uses 3_2 cup of flour and 8_5 cup of
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blueberries. Is there more flour or more
blueberries in the recipe?
10.
9. Peggy completed 6_5 of the math homework
and Al completed 5_4 of the math homework.
Did Peggy or Al complete more of the math
homework?
Math Give an example of fractions that you would
compare by finding common denominators, and an example of
fractions you would compare by finding common numerators.
WRITE
Chapter 6
369
Lesson Check (4.NF.A.2)
1. Pedro fills a glass 2_4 full with orange juice.
Write a fraction with a denominator of
6 that is greater than 2_4 .
7
2. Today Ian wants to run less than __
12 mile.
Write a fraction with a denominator of
4 to respresent a distance that is less than
7
__
12 mile.
Spiral Review (4.OA.B.4, 4.NBT.A.1, 4.NBT.B.5, 4.NF.A.1)
year on business. What is the value
of 6 in 372,645?
5. Sam has 12 black-and-white photos and
18 color photos. He wants to put the
photos in equal rows so each row has
either black-and-white photos only or
color photos only. In how many rows
can Sam arrange the photos?
4. One section of an auditorium has
12 rows of seats. Each row has 13 seats.
What is the total number of seats in
that section?
10
__ on the board. Write
6. The teacher writes 12
this fraction in simplest form.
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3. Ms. Davis traveled 372,645 miles last
FOR MORE PRACTICE
GO TO THE
370
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