Lesson 6.8 Name Compare and Order Fractions Number and ...

Name

Compare and Order Fractions

Essential Question How can you order fractions?

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Jody has equal-size bins for the recycling center.

She

filled

3 _

5

of

a

bin

with

plastics,

_1_

12

of

a

bin

with

paper,

and

_9_

10

of

a

bin

with

glass.

Which

bin

is

the

most full?

Lesson 6.8

Number and Operations-- Fractions--4.NF.A.2 MATHEMATICAL PRACTICES MP2, MP4, MP6

? Underline what you need to find. ? Circle the fractions you will compare.

Example 1 Locate

and

label

3_5,

_1_

12

,

and

_9_

10

on

the

number line.

0

1

1

2

Sometimes it is not reasonable to find the exact location of a point on a number line. Benchmarks can help you find approximate locations.

STEP 1 Compare each fraction to 1_2.

_3_

1__ _1__

1__ _9__

1__

5 2 12 2 10 2

_ and _ are both greater than 1_2.

_ is less than 1_2.

Label

_1_

12

on

the

number

line

above.

STEP 2

Compare

3 _

5

and

_19_0.

Think: Use 10 as a common denominator.

3__ 5

=

______?_______ ?

=

_____

Since

_6_

10

_19_0,

you

know

that

3 _

5

_19_0.

Label

3 _

5

and

_9_

10

on

the

number

line

above.

The fraction the greatest distance from 0 has the greatest value.

The fraction with the greatest value is _.

So, the bin with __ is the most full.

?

Compare

the

distance

between

3 _

5

and

0

and

the

distance

between

_9_

10

and

0.

What

can

you

conclude

about

the

relationship

between

3 _

5

and

_9_

10

?

Explain.

MTaatlkh

MATHEMATICAL PRACTICES 4

Use Models How do you nknuomwbeyroluinleoccaotrerdec3_5t_loy?n the

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Chapter 6 371

Example 2 Write

_17_0,

1_3,

_17_2,

and

_8_

10

in

order

from

least

to

greatest.

0

1

1

2

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.

STEP 2

Compare

_7_

10

to

_7_

12

and

_18_0.

Think:

_7_ 10

and

_7_ 12

have

a

common

numerator.

_7__

_7__

10 12

Think:

_7_ 10

and

_8_ 10

have

a

common

denominator.

_7__

_8__

10 10

Locate

and

label

_17_0,

_7_

12

,

and

_8_

10

on

the

number

line

above.

The fractions in order from least to greatest are ___ .

So, _ < _ < _ < _ .

Try

This!

Write

3_4,

3_6,

1 _

3

,

and

_2_

12

in

order

from

least

to

greatest.

_ < _ < _ < _

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372

Name

SShhaarree aanndd SShhooww

MATH

BOARD

1. Locate and label points on the number line to help you write

_130_,

1_112_,

and

5 _

8

in

order

from

least

to

greatest.

0

1

1

2

Write the fraction with the greatest value.

2.

_7__, _1_, _9__ 10 5 10

3.

5__, _7__, _7__ 6 12 10

4.

2__, _1_, _2_, _2_ 8 8 4 6

Write the fractions in order from least to greatest.

5.

1__, _3_, 1__ 4 6 8

6.

3__, _2_, _3__, _4_ 5 3 10 5

7.

3__, _7__, _5__ 4 12 12

OOnn YYoouurr OOwwnn

Write the fractions in order from least to greatest.

8.

2__, _1_, _5_ 5 3 6

9.

4__, _5__, _1_ 8 12 6

MTaatlkh

MATHEMATICAL PRACTICES 2

Use Reasoning How can

benchmarks help you

order fractions?

10.

__7__, _9__, _4_ 100 10 5

? Houghton Mifflin Harcourt Publishing Company

MATHEMATICAL PRACTICE

2

Reason Quantitatively Algebra Write a numerator that makes

the statement true.

11.

1__ 2

<

____

10

<

4__ 5

12.

1__ 4

<

_5__ 12

<

____

6

13.

____

8

<

3__ 4

<

_7_ 8

Chapter 6 ? Lesson 8 373

MATHEMATICAL PRACTICES .0%&-t3&"40/tM",&4&/4&

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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?

b. What information do you need to solve the problem?

c. What information is not necessary? d. How will you solve the problem?

5-Kilometer Race Results

Name

Time

Nancy Lionel Mavis

2 _ 3

hour

_7_ 12

hour

3 _ 4

hour

e. Show the steps to solve the problem.

WRITE Math t Show Your Work f. Complete the sentences.

The runner who finished first is _. The runner who finished second is _. The runner who finished third is _.

15. DEEPER Alma used 3 beads to make

a necklace. The lengths of the beads are

5 _

6

inch,

_5_

12

inch,

and

1 _

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 _ 4

cup

pecans

1 _ 2

cup

almonds

_2_ 12

cup

peanuts

7 _ 8

cup

walnuts

Order the ingredients used in the recipe from least to greatest.

374

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Name

Compare and Order Fractions

Practice and Homework

Lesson 6.8

Write the fractions in order from least to greatest.

1.

5 _ 8

,_122_

,_180_

2.

1 _ 5

,2_3

,5_8

COMMON CORE STANDARD--4.NF.A.2 Extend understanding of fraction equivalence and ordering.

Use benchmarks and a number line.

Think

:

5 _ 8

is

close

to

1 _ 2

._122_

is

close

to

0.

_8_ 10

is

close

to

1.

_____

0

2

12

15

8

1

28

10

__ _122_ _ < 5_8 ................
................

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