Lesson 6.8
Name
Compare and Order Fractions
Number and Operations—
Fractions—4.NF.A.2
MATHEMATICAL PRACTICES
MP2, MP4, MP6
Essential Question How can you order fractions?
Unlock
Unlock the
the Problem
Problem
Jody has equal-size bins for the recycling center.
1
She filled 3_5 of a bin with plastics, __
12 of a bin with
9
paper, and __
10 of a bin with glass. Which bin is the
most full?
• Underline what you need to find.
• Circle the fractions you will compare.
Example 1 Locate and label 3_5, __121 , and __109 on the
number line.
0
1
1
2
STEP 1 Compare each fraction to 1_2 .
3
__
5
_
_
● 12
and
__
_
1
___
12
● 12
__
Sometimes it is not reasonable
to find the exact location of
a point on a number line.
Benchmarks can help you find
approximate locations.
9
___
10
9
STEP 2 Compare 3_5 and __
10 .
● 12
__
Think: Use 10 as a common denominator.
×
3
__ = _____________
= _____
5
×
are both greater than 1_2 .
is less than 1_2 .
1
Label __
12 on the number line above.
6
Since __
10
●
9
3
__
_
10 , you know that 5
●
9.
__
10
9
Label 3_5 and __
10 on the number line above.
The fraction the greatest distance from 0 has the greatest value.
The fraction with the greatest value is _.
© Houghton Mifflin Harcourt Publishing Company
So, the bin with __ is the most full.
Math
Talk
• Compare the distance between 3_5 and 0 and the distance
9
between __
10 and 0. What can you conclude about the
9
relationship between 3_5 and __
10 ? Explain.
MATHEMATICAL PRACTICES 4
Use Models How do you
__ on the
know you located 3
5
number line correctly?
Chapter 6
371
Example 2 Write __107 , 1_3, __127 , and __108 in order from least to greatest.
0
1
2
1
STEP 1 Compare each fraction to 1_2 .
List fractions that are less than 1_2 : ___
List fractions that are greater than 1_2 : ___
The fraction with the least value is _ .
Locate and label 1_3 on the number line above.
7
7
8
__
__
STEP 2 Compare __
10 to 12 and 10 .
7
7
__
Think: __
10 and 12 have a common
numerator.
7
___
10
● 127
___
7
8
__
Think: __
10 and 10 have a common
denominator.
7
___
10
● 108
___
7 __
7
8
__
Locate and label __
10 , 12 , and 10 on the number line above.
The fractions in order from least to greatest are ___ .
So, _ < _ < _ < _ .
2
Try This! Write 3_4 , 3_6 , 1_3 , and __
12 in order from least to greatest.
© Houghton Mifflin Harcourt Publishing Company
_<_<_<_
372
Name
Share
hhow
Share and
and Show
Sh
MATH
M
BOARD
B
1. Locate and label points on the number line to help you write
3 __
11
__
_5
10 , 12 , and 8 in order from least to greatest.
0
1
2
1
Write the fraction with the greatest value.
7 , __1 , ___
9
2. ___
7 , ___
7
__ , ___
3. 5
10 5 10
1 , __2 , __2
__ , __
4. 2
6 12 10
8 8 4 6
Write the fractions in order from least to greatest.
3, 1__
__ , __
5. 1
2 , ___
3 , __4
__ , __
6. 3
4 6 8
7 , ___
5
__ , ___
7. 3
5 3 10 5
4 12 12
Math
Talk
On
On Your
Your Own
Own
MATHEMATICAL PRACTICES 2
Use Reasoning How can
benchmarks help you
order fractions?
Write the fractions in order from least to greatest.
1 , __5
__ , __
8. 2
5 , __1
__ , ___
9. 4
© Houghton Mifflin Harcourt Publishing Company
5 3 6
MATHEMATICAL
PRACTICE
7 , ___
9 , __4
10. ____
8 12 6
100 10 5
2
Reason Quantitatively Algebra Write a numerator that makes
the statement true.
__ < ____ < 4
__
11. 1
2
10
5
5 < ____
__ < ___
12. 1
4
12
6
7
__ < __
13. ____ < 3
8
4
8
Chapter 6 • Lesson 8 373
MATHEMATICAL PRACTICES .0%&-t3&"40/tM",&4&/4&
Unlock
Unlock the
the Problem
Problem
14.
SMARTER
Nancy, Lionel, and Mavis ran in a
5-kilometer race. The table shows their finish times. In
what order did Nancy, Lionel, and Mavis finish the race?
a. What do you need to find?
5-Kilometer
Race Results
b. What information do you need to solve the problem?
Name
Time
Nancy
_2 hour
3
7
__
12 hour
3_
4 hour
Lionel
c. What information is not necessary?
Mavis
d. How will you solve the problem?
WRITE
e. Show the steps to solve the problem.
M t Show Your Work
Math
f. Complete the sentences.
The runner who finished first is _.
The runner who finished second is _.
The runner who finished third is _.
DEEPER
Alma used 3 beads to make
a necklace. The lengths of the beads are
5_ inch, __
5
1_
6
12 inch, and 3 inch. What are the
lengths in order from shortest to longest?
16.
SMARTER
Victor has his
grandmother’s recipe for making
mixed nuts.
3 cup pecans
_
4
1_ cup almonds
2
2 cup peanuts
__
12
7_ cup walnuts
8
Order the ingredients used in the recipe
from least to greatest.
374
© Houghton Mifflin Harcourt Publishing Company
15.
Practice and Homework
Name
Lesson 6.8
Compare and Order Fractions
COMMON CORE STANDARD—4.NF.A.2
Extend understanding of fraction equivalence
and ordering.
Write the fractions in order from least to greatest.
8
2 ,__
1. _5 ,__
8 12 10
2. _1 ,2_ ,5_
5 3 8
Use benchmarks and a number line.
2 is close to 0.
Think: 5_ is close to 1_ .__
12
8
_____
2
8 is close to 1.
__
10
0
2
12
1
2
5
8
1
8
10
8
2 <5
__
_ < __
12
8
10
_____
6
3. _1, 2_, __
2 5 10
7 , __
5
4. _4, __
6 12 10
____
5. _1, 5_, 1_
4 8 2
____
____
Problem
Problem Solving
Solving
6. Amy’s math notebook weighs 1_2 pound,
7_
8
© Houghton Mifflin Harcourt Publishing Company
her science notebook weighs pound,
and her history notebook weighs 3_4 pound.
What are the weights in order from lightest
to heaviest?
8.
7. Carl has three picture frames. The
thicknesses of the frames are 4_5 inch,
3
5_
__
12 inch, and 6 inch. What are the thicknesses
in order from least to greatest?
_______
_______
_______
_______
Math How is ordering fractions on a number line
similar to and different from ordering whole numbers on a
number line?
WRITE
Chapter 6
375
Lesson Check (4.NF.A.2)
1. Juan’s three math quizzes this week took
_1
3
_4
6
_1
5
him hour, hour, and hour to complete.
List the lengths of time in order from least
to greatest.
2. On three days last week, Maria ran
_3
4
mile, 7_8 mile, and 3_5 mile. List the distances
in order from least to greatest.
Spiral Review (4.OA.B.4, 4.NBT.B.5, 4.NBT.B.6, 4.NF.A.1)
3. Santiago collects 435 cents in nickels.
How many nickels does he collect?
5. Alicia wrote these numbers: 2, 9, 15, 21.
50 minutes. What is the total number of
minutes of the three classes?
6. Mrs. Carmel serves 6_8 of a loaf of bread with
dinner. Write a fraction with a denominator
of 4 that is equivalent to 6_8 .
© Houghton Mifflin Harcourt Publishing Company
Which of Alicia’s numbers is NOT
a composite number?
4. Lisa has three classes that each last
FOR MORE PRACTICE
GO TO THE
376
Personal Math Trainer