Fraction Operations

CHAPTER

6

Fraction Operations

GET READY

284

Math Link

286

6.1

Warm Up

287

6.1

Multiplying a Fraction and a Whole Number 288

6.2

Warm Up

294

6.2

Dividing a Fraction by a Whole Number

295

6.3

Warm Up

301

6.3

Multiplying Proper Fractions

302

6.4

Warm Up

309

6.4

Multiplying Improper Fractions and

Mixed Numbers

310

6.5

Warm Up

319

6.5

Dividing Fractions and Mixed Numbers

320

6.6

Warm Up

328

6.6

Applying Fraction Operations

329

Chapter Review

337

Practice Test

344

Wrap It Up!

347

Key Word Builder

348

Math Games

349

Challenge in Real Life

350

Answers

352

Name: _____________________________________________________

Date: ______________

Add and Subtract Fractions

To add fractions with the same denominators, add the numerators.

+

2 ¡û numerator

5 ¡û denominator

=

1

5

2

5

3

5

To subtract fractions with different denominators, use a common denominator.

a common multiple of

each denominator

1 1

¨C =

2 6

Write the answer in lowest terms.

3

6

¨C

¡Â2

1

6

2 1

=

6 3

2

=

6

Multiples of 2: 2, 4, 6, 8, ¡­

Factors of 6: 2, 3, 6

¡Â2

1. Add or subtract. Write your answers in lowest terms.

¡Á2

a)

1 1

+ =

6 6

b)

6

+

1

6

4 3

?

5 10

8

10

=

1

6

?

6

¡Â _____

¨C

3

10

=

5

10

¡Â _____

6

=

5

=

10

¡Â _____

¡Â _____

284

MHR ¡ñ Chapter 6: Fraction Operations

4 8

=

5 10

¡Á2

Name: _____________________________________________________

Date: ______________

Add and Subtract Mixed Numbers

mixed number

1 3?

?

? includes a whole number and a proper fraction ? e.g., 1 , 2 ?

2 5?

?

improper fraction

10 ?

?

? a fraction in which the numerator is greater than the denominator ? e.g.,

?

8?

?

To subtract or add mixed numbers:

Use Regrouping:

Use Improper Fractions:

2

3

1

1

4 ?2

4 +2

4

4

2

4

18 11

2

1

Write as improper fractions.

=4 +2

Find a commmon denominator. = ?

4 4

4

4

7

?2 1?

=

Subtract the numerators.

= ( 4 + 2 ) + ? + ? Add.

4

?4 4?

3

3

=1

Write as a mixed number.

=6

Write as a mixed number.

4

4

2. Add or subtract. Write your answers in lowest terms.

a) Use regrouping.

b) Use improper fractions.

3 1 ?1 2

5

2

11 + 2 1

2

3

Find a common denominator.

Find a common denominator.

?1

10

10

Subtract the whole numbers.

=1

+2

6

6

Write as improper fractions.

=3

?

??

??

= (3 ? 1) + ??

??

??

??

?

??

??

??

??

??

??

??

+

6

6

Add the numerators.

=

Subtract the fractions.

=

?

??

??

+ ??

??

??

??

?

??

??

??

??

??

??

??

=

6

+

6

=

6

Write in lowest terms.

=

=

6

Get Ready ¡ñ MHR 285

Name: _____________________________________________________

Canada¡¯s Ecozones

Date: ______________

An ecozone is an area

that has similar plants

and animals.

Canada has many ecozones of different sizes.

The boundaries between ecozones depend on geography, climate,

animals, plants, and human activities.

1

1

a) The Pacific marine ecozone covers

b) About of the Prairies ecozone area is in

2

10

of Canada¡¯s coastline. The Northwest

1

Saskatchewan, and about of the area is

1

3

Atlantic ecozone covers of Canada¡¯s

in Alberta. What fraction of the area is in

5

Manitoba?

coastline.

Use a common denominator to find the

Add the areas in Alberta and

sum of the 2 ecozones.

Saskatchewan. Show your work.

Common denominator for

1

1

and :

10

5

1 1

+

10 5

1 1¡Á 2

= +

10 5 ¡Á 2

=

1

+

10

Use your answer above to find the area that

covers Manitoba.

Let 1 represent the whole part of the

ecozone.

1?

=

=

=

286

MHR ¡ñ Chapter 6: Fraction Operations

6

?

6

Think 1 =

6

.

6

Name: _____________________________________________________

Date: ______________

6.1 Warm Up

1. Write each fraction.

a)

b)

improper fraction:

mixed number:

2. Draw fraction strips to solve.

1 1

a)

+

3 3

b)

1 1

+

8 2

b)

3 1

?

5 2

3. Solve. Write your answers in lowest terms.

a)

1 2

+

12 3

Find a common

denominator.

4. Multiply.

a) 2 ¡Á 4 =

b) 4 ¡Á 5 =

c) 3 ¡Á 2 =

d) 5 ¡Á 3 =

e) 3 ¡Á 3 =

f) 6 ¡Á 5 =

6.1 Warm Up ¡ñ MHR 287

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