Add and Subtract Fractions with Unlike Denominators

Add and Subtract Fractions with Unlike Denominators

Check your understanding of important skills.

Name Part of a Whole Write a fraction to name the shaded part.

1.

number of

shaded parts _

2.

number of

shaded parts _

number of total parts _

number of total parts _

fraction _

fraction _

Add and Subtract Fractions Write the sum or difference in simplest form.

3. 3__ 1 1__ 5 6 6 _

4. _4__ 1 _1__ 5 10 10 _

5. 7__ 2 3__ 5 8 8_

6.

_9__ 2 _2__ 5 12 12 _

Multiples Write the first six nonzero multiples.

7. 5 ___

8. 3 ___

9. 7 ___

WITH

TM

There are 30 senators and 60 members of the House of Representatives in the Arizona Legislature. Suppose 20 senators and 25 representatives came to a committee meeting. Be a math detective to write a fraction that compares the number of legislators that attended to the total number of legislators.

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Online

Chapter 6 241

Vocabulary Builder

Visualize It Use the 3 words to complete the H-diagram.

Add and Subtract Fractions with Like

Add and Subtract Fractions with Unlike

Review Words

benchmark 3common multiple 3denominators 3difference 3equivalent fractions

mixed number 3numerators 3simplest form 3sum

Preview Words

3common denominator

Understand Vocabulary

Draw a line to match the word with its definition.

1. common multiple 2. benchmark 3. simplest form 4. mixed number 5. common

denominator 6. equivalent fractions

? a number that is made up of a whole number and a fraction

? a number that is a multiple of two or more numbers

? a common multiple of two or more denominators

? the form of a fraction in which the numerator and denominator have only 1 as their common factor

? a familiar number used as a point of reference

? fractions that name the same amount or part

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242

GO ? eStudent Edition ? Multimedia eGlossary

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Name

Addition with Unlike Denominators

Essential Question How can you use models to add fractions that have different denominators?

Investigate

Hilary fabric

is making a tote bag for

and

1 _

4

yard

of

red

fabric.

her

friend.

She

uses

1 _

2

yard

of

How much fabric does Hilary

blue use?

Materials n fraction strips n MathBoard

A.

Find

1 _

2

1

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

1_4.

Record the addends, using like denominators.

Lesson 6.1

sum

1

C.

Record

the

sum

in

simplest

form.

1__ 2

1

1__ 4

5

_

So, Hilary uses _ yard of fabric.

MATHEMATICAL PRACTICES

How can you tell if the sum of the fractions is less than 1?

Draw Conclusions N

1. Describe how you would determine what fraction strips, all with the

same

denominator,

would

fit

exactly

under

1 _

2

1

1 _

3

.

What

are

they?

2.

Explain the difference between finding fraction strips with

the

same

denominator

for

1 _

2

1

1 _

3

and

1 _

2

1

1 _

4

.

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Chapter 6 243

Make Connections N

Sometimes, the sum of two fractions is greater than 1. When adding fractions with unlike denominators, you can use the 1-whole strip to help determine if a sum is greater than 1 or less than 1.

Use

fraction

strips

to

solve.

3 _ 5

1

1 _ 2

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 _ 5

and

1 _ 2

.

Place

the

fraction

strips

under

the sum. At the right, draw a picture

of the model and write the equivalent

fractions.

3__ 5

=

_

1__ 2

=

_

STEP 3

Add the fractions with like 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

=

_

+

_

= _ , or _

MATHEMATICAL PRACTICES

In what step did you find out that the answer is greater than 1? Explain.

Share and Show

Use fraction strips to find the sum. Write your answer in simplest form.

1.

2.

1__ 2

1

3__ 8

5

_

1

_

5

_

1__ 2

1

2__ 5

5

_

1

_

5

_

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244

Name

Use fraction strips to find the sum. Write your answer in simplest form.

3.

4.

3__ 8

1

1__ 4

5

_

1

_

5

_

3__ 4

1

1__ 3

5

_

1

_

5

_

Use fraction strips to find the sum. Write your answer in simplest form.

5.

2__ 5

1

_3__ 10

5

_

6.

1__ 4

1

_1__ 12

5

_

7.

1__ 2

1

_3__ 10

5

_

8.

2__ 3

1

1__ 6

5

_

9.

5__ 8

1

1__ 4

5

_

10.

_1_ 2

1

1__ 5

5

_

11.

3__ 4

1

1__ 6

5

_

12.

1__ 2

1

2__ 3

5

_

13.

7__ 8

1

1__ 4

5

_

14.

Explain how using fraction strips with like denominators

makes it possible to add fractions with unlike denominators.

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Chapter 6 ? Lesson 1 245

Problem SolvingN

MATHEMATICAL PRACTICES

Model ? Reason ? Make Sense

Pose a Problem

15.

Maya

and

1 _

4

makes cup of

trail mix by combining dried fruit. What is the

1 _

3

cup

of

mixed

total amount of

nuts

ingredients in her trail mix?

1__ 3

1

1__ 4

5

_7__ 12

Maya

uses

_7_

12

cup

of

ingredients.

Write a new problem using different amounts for each ingredient. Each amount should be a fraction with a denominator of 2, 3, or 4. Then use fraction strips to solve your problem.

Pose a problem.

Solve your problem. Draw a picture of the fraction strips you use to solve the problem.

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? Explain why you chose the amounts you did for your problem.

246

FOR MORE PRACTICE: Standards Practice Book, pp. P121?P122

Name

Subtraction with Unlike Denominators

Essential Question How can you use models to subtract fractions that have different denominators?

Investigate

Mario fills Friday. On

a hummingbird Monday, Mario

feeder with

sees

that

1 _

8

_ 3

4

cup

cup of

of sugar water sugar water is

on left.

How much sugar water did the hummingbirds drink?

Materials n fraction strips n MathBoard

A.

Find your

3_4M2ath1_8B.oPalardc.eTthherenep1_4lascteripas1_8usntdrieprutnhdee1r-twhheo1_4lesstrtirpips.on

B. Find fraction strips all with the same denominator that fit

exactly

under

the

difference

3 _

4

2

1 _

8

.

Lesson 6.2

difference

C.

Record the difference.

3__ 4

2

1__ 8

5

_

So, the hummingbirds drank _ cup of sugar water.

MATHEMATICAL PRACTICES

How can you tell if the difference of the fractions is less than 1? Explain.

Draw Conclusions

1. Describe how you determined what fraction strips, all with the same denominator, would fit exactly under the difference. What are they?

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2.

Explain whether you could have used fraction strips

with any other denominator to find the difference. If so, what

is the denominator?

Chapter 6 247

Make ConnectionsN

Sometimes you can use different sets of same-denominator fraction strips to find the difference. All of the answers will be correct.

Solve.

2 _

3

2

1 _

6

A Find fraction strips, all

with the same

denominator, that

fit exactly under the

difference

2 _ 3

2

1_6.

B Find another set of fraction

strips, all with the same

denominator, that fit

exactly under the

difference

2 _ 3

2

1_6.

Draw

the

fraction strips you used.

C Find other fraction

strips, all with the same

denominator, that

fit exactly under the

difference

2 _ 3

2

1 _ 6

.

Draw

the

fraction strips you used.

?

?

?

2 _ 3

2

1 _ 6

5

3 _ 6

2 _ 3

2

1 _ 6

5

_

While each answer appears different, all of the answers

can be simplified to _ .

Share and Show

Use fraction strips to find the difference. Write your answer in simplest form.

1.

2.

2 _ 3

2

1 _ 6

5

_

MATHEMATICAL PRACTICES

Which other fraction strips

with the same denominator could fit

exactly

in

the

difference

of

2 _ 3

2

1_6?

?

_7__ 10

2

2__ 5

5

_

?

2__ 3

2

1__ 4

5

_

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248

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