Fraction Operations - Mr. Mubashirwaqasmubashir.weebly.com/uploads/2/2/6/7/22677732/fraction_opera… · Model the fractions using a number line. The denominator is 5. So, you need

$Page 1: Fraction Operations - Mr. Mubashirwaqasmubashir.weebly.com/uploads/2/2/6/7/22677732/fraction_opera… · Model the fractions using a number line. The denominator is 5. So, you need$
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

284 MHR ● Chapter 6: Fraction Operations

Name: _____________________________________________________ Date: ______________

←←

2 numerator5 denominator

Multiples of 2: 2, 4, 6, 8, … Factors of 6: 2, 3, 6

a common multiple of each denominator

Add and Subtract Fractions

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

15

25

35

+ =

To subtract fractions with different denominators, use a common denominator. 1 1

– =2 6

36

1–

6

2=

6

Write the answer in lowest terms.

÷ 2

2 16 3

=

÷ 2

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

a) 1 16 6 6

+ =

+ =

16

16 6

?

÷ _____

6

=

÷ _____

b) 4 35 10

−

810

– 310

= 510

÷ _____

510

=

÷ _____

× 2

4 8=5 10

× 2

Get Ready ● MHR 285

Name: _____________________________________________________ Date: ______________

Add and Subtract Mixed Numbers

mixed number

• includes a whole number and a proper fraction 1 3e.g., 1 , 22 5

⎛ ⎞⎜ ⎟⎝ ⎠

improper fraction

• a fraction in which the numerator is greater than the denominator 10e.g., 8

⎛ ⎞⎜ ⎟⎝ ⎠

To subtract or add mixed numbers: Use Regrouping:

( )

1 14 22 42 14 2 Find a commmon denominator.4 4

2 14 2 Add.4 4

36 Write as a mixed number.4

+

= +

⎛ ⎞= + + +⎜ ⎟⎝ ⎠

=

Use Improper Fractions: 2 34 24 4

18 11 Write as improper fractions.4 47 Subtract the numerators.431 Write as a mixed number.4

−

= −

=

=

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

a) Use regrouping.

1 23 152 −

Find a common denominator.

= 3 110 10−

Subtract the whole numbers.

= ( )3 1

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎟⎜⎝ ⎠

− + −

Subtract the fractions.

= +

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎟⎜⎝ ⎠

−

=

b) Use improper fractions.

1 11 22 3+


= 1 26 6+

Write as improper fractions.

= 6 6+

Add the numerators.

= 6 6+

= 6

Write in lowest terms.

= 6


Name: _____________________________________________________ Date: ______________

An ecozone is an area that has similar plants

and animals.

Canada’s Ecozones Canada has many ecozones of different sizes. The boundaries between ecozones depend on geography, climate, animals, plants, and human activities.

a) The Pacific marine ecozone covers 110

of Canada’s coastline. The Northwest

Atlantic ecozone covers 15

of Canada’s

coastline. Use a common denominator to find the

sum of the 2 ecozones.

Common denominator for 110

and 15

:

1 110 51 1 2

10 5 2

110

+

×= +

×

= +

=

b) About 12

of the Prairies ecozone area is in

Saskatchewan, and about 13

of the area is

in Alberta. What fraction of the area is in Manitoba?

Add the areas in Alberta and Saskatchewan. Show your work.

Use your answer above to find the area that

covers Manitoba. Let 1 represent the whole part of the ecozone.

1

66

−

= −

=

Think 1 = 66

.

6.1 Warm Up ● MHR 287

Name: _____________________________________________________ Date: ______________


6.1 Warm Up 1. Write each fraction.

a)

b)

improper fraction:

mixed number:

2. Draw fraction strips to solve.

a) 1 13 3

+ b) 1 18 2

+

3. Solve. Write your answers in lowest terms.

a) 1 212 3

+ b) 3 15 2

−

4. Multiply.

a) 2 × 4 = b) 4 × 5 = c) 3 × 2 = d) 5 × 3 = e) 3 × 3 = f) 6 × 5 =


Name: _____________________________________________________ Date: ______________

You can model with pattern blocks instead of fraction strips.

=

=

6.1 Multiplying a Fraction and a Whole Number Working Example 1: Multiply Using a Model

proper fraction

• a fraction in which the denominator is greater than the numerator 5e.g., 8

⎛ ⎞⎜ ⎟⎝ ⎠

Find 3 × 56

using fraction strips. Write the product in lowest terms.

Solution

5 5 5 536 6 6 6

× = + +

Count the shaded parts of the strips:

5 5 56 6 6 6

+ + =

Write the answer in lowest terms. ÷ 3

15 =6 2

÷ 3

So, 3 × 5 56 2

= .

Draw fraction strips to find the product. Write the answer in lowest terms.

2 × 56

+ =

÷ ______

=

÷ ______

+

+

+

16_ 1

6_ 1

6_ 1

6_ 1

6_

16_ 1

6_ 1

6_ 1

6_ 1

6_

16_ 1

6_ 1

6_ 1

6_ 1

6_

16_

16_

16_

16_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_

16_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_ 1

6_

12_ 1

2_ 1

2_ 1

2_ 1

2_

6.1 Multiplying a Fraction and a Whole Number ● MHR 289

Name: _____________________________________________________ Date: ______________

Working Example 2: Multiply Using a Diagram

Find 3 × 25

. Write the product in lowest terms.

Solution

2 2 235 5 5

× = + +

Model the fractions using a number line. The denominator is 5. So, you need 5 equal parts between each whole number.

1 0 2

2 2 25 5 5 5

+ + =

So, 2 635 5

× = .

Draw a diagram to find each product.

a) 2 × 23

b) 3 × 34

1 0 2 + +

2 23 3

+ = 3 3 34 4 4

+ + =

You could draw rectangles instead of using a number line.

++

=


Name: _____________________________________________________ Date: ______________

34

of 8 means 34

× 8 or 8 × 34

.

Working Example 3: Apply Multiplication With Fractions

A spider has 8 legs.

An ant has 34

as many legs as a spider.

How many legs does an ant have? Solution

An ant has 34

of the number of legs of a spider.

Use repeated addition on the number line to show 8 × 34

.

0 4 61 2 3 5 The answer is .

So, 8 × 34

= .

An ant has legs.

Jenelle is making a recipe that needs 6 cups of flour.

She wants to make 23

of the recipe.

How many cups will she need to use?

Write a multiplication statement: 6 ×

Model the multiplication on the number line. Jenelle needs cups of flour.

You could draw rectangles.

10 2 3 4

+

=

+ + + + + +

6.1 Multiplying a Fraction and a Whole Number ● MHR 291

Name: _____________________________________________________ Date: ______________

1. The diagram models 3 × 65

.

a) The diagram represents + + =

b) Use the number line to model the same equation. c) Circle the model you like to use. FRACTION STRIPS or NUMBER LINE. Give 1 reason for your answer.

_________________________________________________________________________

_________________________________________________________________________

2. Write the multiplication statement that each diagram shows.

a)

______________

+ + =

× =

b)

+

=

+

10 42 3

=

+

+

15_ 1

5_

15_ 1

5_

15_ 1

5_

15_ 1

5_ 1

5_ 1

5_ 1

5_ 1

5_

15_

15_

15_

15_

15_

15_

15_

15_

15_

15_

15_

15_ 1

5_

+

=

______________

+ =

× =


Name: _____________________________________________________ Date: ______________

1 whole

16

13

12

Of means to multiply.

3. Write the multiplication statement that each number line shows. a)

0 1 b)

10 2

4. Write the multiplication statement that each model shows.

a)

b)

5. Draw a diagram to find each product.

a) 4 × 12

b) 3 × 710

+ + +

6. The width of a Canadian flag is 12

of its length. The length of the flag is 4 m long.

What is the width of the flag?

4 × =

Sentence: ____________________________________________________________________

1 0 2

= �

�

6.1 Math Link ● MHR 293

Name: _____________________________________________________ Date: ______________

Use your answer from part a).

7. A minibus has room for 12 people. The bus is 34

full. How many people are on the minibus?

× 34

=

Sentence: ____________________________________________________________________

8. a) Write a word problem for 1 8.4

× b) Show how to solve your problem.

_________________________________ _________________________________ _________________________________ _________________________________ _________________________________

One quarter of Canada’s 20 ecozones are marine ecozones. They include parts of the oceans. The rest of Canada’s ecozones are terrestrial ecozones (land, rivers, lakes, and wetlands).

a) How many marine ecozones does Canada have?

One quarter = 4

Number of ecozones = 20

20 × =

Canada has marine ecozones. b) How many terrestrial ecozones does Canada have?

Number of ecozones = 20 Marine ecozones =

20 – marine ecozones = terrestrial ecozones

20 – =

Canada has terrestrial ecozones.

10 4 5 6 7 8 92 3

10 54 62 3


Name: _____________________________________________________ Date: ______________

6.2 Warm Up 1. Write the multiplication statement for each diagram.

a) 0 1

_______ × =

b)

=

+ + +

_______ × =

c) +

=

_______ × =

d) 0 1 2 3

_______ _______× =

2. Draw a diagram to solve.

a) 4 × 38

b)

7 × 12

3. Divide.

a) 15 ÷ 5 = b) 30 ÷ 6 = c) 40 ÷ 2 = d) 6 ÷ 3 = e) 12 ÷ 4 = f) 21 ÷ 7 =

6.2 Dividing a Fraction by a Whole Number ● MHR 295

Name: _____________________________________________________ Date: ______________

6.2 Dividing a Fraction by a Whole Number Working Example 1: Divide Using a Model

Find 14

÷ 3.

Solution

Use a fraction strip to show 14

:

The fraction strip shows that 14

is equal to 3 .12

Each of the 3 equal parts of 14

is 12

:

14

÷ 3 =

Use fraction strips to find the answer.

34

÷ 3

Shade the fraction strip to show 34

.

Divide each 14

into 3 equal parts.

34 12

=

Each of the 3 equal parts of 34

is 12

or 4

.

34

÷ 3 = 12

or 4

.

Divide each 14

into

3 equal parts.

14_ 1

4_ 1

4_ 1

4_

112— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12—

112— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12— 1

12—

14_ 1

4_ 1

4_ 1

4_


Name: _____________________________________________________ Date: ______________

Working Example 2: Divide Using Diagrams

Find 23

÷ 4. Write your answer in lowest terms.

Solution

Draw and label a number line that shows thirds. To model division by 4, divide each third into equal parts.

There are 12 parts in the whole, so each part is 12

.

Use brackets to divide 23

into 4 equal parts.

Each of the 4 parts is 12

or 16

.

So, 23

÷ 4 = 6

.

Use a number line to find each quotient. Write your answers in lowest terms. 12

÷ 5

Label the number line to show 12

.

Divide each half into 5 equal parts to show division by 5.

There are parts in the whole, so each part is .


into 5 equal parts. Each of the 5 parts is .

So, 12

÷ 5 = .

0 113_ 2

3_

0 113_ 2

3_

0 1

0 113_ 2

3_


Name: _____________________________________________________ Date: ______________

Working Example 3: Apply Division With Fractions

Mustafa used 34

of a jar of sauce on 6 servings of pasta.

He used the same amount of sauce on each serving. What fraction of the jar of sauce did he use on each serving? Solution

Find 34

÷ 6.

Label the number line to show quarters. To show division by 6, divide each quarter into 6 parts.

There are parts in the whole, so each part is 24

.


into 6 equal parts.

Each of the 6 parts is 24

.

So, 34

÷ 6 = 24

.


Mustafa used 8

of a jar of sauce on each serving.

÷ 3

324 8

=

÷ 3

14_ 1

2_ 3

4_0 1

14_ 1

2_ 3

4_0 1

0 1


Name: _____________________________________________________ Date: ______________

Four students equally shared 12

of a cake. What fraction of the cake did each student eat?

Find 12

÷ .

Label the number line to show halves.

Divide each half into equal parts to show the division.

There are parts in the whole. Each part is .


into equal parts.

So, 12

÷ =

1. a) Model 12

÷ 2 using fraction strips or a number line.

12

÷ 2 =

b) What did you use to solve the question? Circle FRACTION STRIPS or NUMBER LINE. Give 1 reason your choice. _________________________________________________________________________ _________________________________________________________________________

0 1


Name: _____________________________________________________ Date: ______________

2. Find the quotient using fraction strips.

a) 14

÷ 2

Divide the strip into quarters.

Shade 14

.

Divide each quarter into 2 equal parts. There are parts in the whole.

Each part is 8

. So, 14

÷ 2 = 8

b) 13

÷ 3

13

÷ 3 =

3. Find each quotient using a number line.

a) 35

÷ 2

0 1 Label the number line to show fifths. Divide each fifth into 2 equal parts. There are parts in

the whole, so each part is 1 .


into 2 equal parts.

Each part is .

So, 35

÷ 2 =

b) 12

÷ 4

0 1

So, 12

÷ 4 = .


Name: _____________________________________________________ Date: ______________

4. Two different fish curries, dhopa and molee curry, are made with coconut.

a) You need 12

of a coconut to make

2 servings of dhopa. What fraction of a coconut is in each

serving?

12

÷ 2 = ?

Draw a fraction strip to solve.

1 22

÷ =

b) You need 12

coconut to make 4 servings of

molee. What fraction of a coconut is in each

serving?

÷ = ?

Draw a number line to solve.

1 _____________2

÷ =

5. A container of orange juice is 23

full.

Four students share the juice equally. What fraction of the full container does each student get?

÷ =

Sentence: ____________________________________________________________________

The Montane Cordillera and Boreal Cordillera ecozones have almost equal areas.

Together, the 2 ecozones equal about 110

of the area of Canada.

What fraction of the area of Canada does each of these ecozones cover?

110

÷ 2 =

Sentence: ________________________________________________________________________


Name: _____________________________________________________ Date: ______________

6.3 Warm Up 1. Draw diagrams to solve.

a) 1 36

÷ b) 3 24

÷

c) 255

× d) 163

×

2. Decide whether each fraction is closer to 0, 12

, or 1.

Use the number line to help you.

a) 35

0 13

5

b) 23

0 12

3

35

is closer to . 23

is closer to .

c) 78

0 1

d) 16

0 1

78

is closer to . 16

is closer to .

3. Multiply.

a) 4 × 2 = b) 5 × 3 =

c) 12 × 2 = d) 7 × 6 =

0 112


Name: _____________________________________________________ Date: ______________

6.3 Multiplying Proper Fractions Working Example 1: Multiply Using Paper Folding

Find 1 3 .2 5

×

Solution Fold a rectangular piece of paper into fifths along its length.

Open the paper and shade 35

of it.

Fold the paper in half across its width. Open the paper and draw slanted lines on half of it. Count the rectangles. There are equal rectangles. How many are shaded and have slanted lines?

1 32 5 10

× =

Find each product using paper folding.

a) 1 14 2

× b) 2 23 3

×

Fold paper into quarters along its length.

Shade 14

.

Fold paper in half across its width. Draw a line to show the fold. Draw slanted lines on half of it. There are equal rectangles. How many are shaded and have slanted lines?

1 14 2

× =

6.3 Multiplying Proper Fractions ● MHR 303

Name: _____________________________________________________ Date: ______________

26

of the rectangle is grey

and has slanted lines.

Working Example 2: Multiply Using Diagrams

Find 2 13 2

× . Write the product in lowest terms.

Solution Draw a rectangle. Draw lines to divide its length into thirds.

Draw a line to divide the width of the rectangle in half. 2 1 23 2 6

× =

÷ ____ 2 1=6 3

÷ ____

So, 2 1 13 2 3

× = .

Find each product using diagrams. Write your answers in lowest terms.

a) Find 1 1 .2 2

×

Divide the length in half.

Shade 12

.

Divide the width in half. Draw slanted lines on the top half.

1 12 2

×number of shaded parts with lines

total number of parts=

=

b) Find 1 3 .3 4

×


23_

23_

12_


Name: _____________________________________________________ Date: ______________

An estimate is reasonable if it is close to the actual answer.

Working Example 3: Multiply Using a Rule

Estimate and calculate 8 515 6

× .

Solution Estimate:

Is 815

closer to 0, 12

, or 1?

0 18

15 8 1

15 2≈

Is 56

closer to 0, 12

, or 1?

0 15

6 5 16

≈

8 515 6

×

1 12

≈ ×

12

≈

Calculate:

8 515 68 5 Multiply the numerators

15 6 Multiply the denominators

90

×

←×=

←×

=

Write in lowest terms. ÷ 10

9

=

÷ 10 Plot on a number line.

0 149

The answer is reasonable because it is close to

the estimate of 2

.


Name: _____________________________________________________ Date: ______________

Estimate and calculate. Write your answers in lowest terms. 3 25 9

×

Estimate:

Is 35

closer to 0, 12

, or 1?

35

≈

Is 29

closer to 0, 12

, or 1?

2 _____________9

≈

3 2 ___________5 9

_____________

× ≈ ×

≈

Calculate: 3 25 9

×

Multiply the numeratorsMultiply the denominators

× ←=

←×

=

÷ 3

Write in lowest terms.=

÷ 3

1. Brendan calculated 3 2 65 5 5

× = . Brendan made a mistake.

a) What mistake did he make?

_________________________________________________________________________

b) Find the correct answer.


Name: _____________________________________________________ Date: ______________

2. Find the products by drawing diagrams.

a) 5 16 2

×

Divide the length in sixths.

Shade 56

.

Divide the width in half. Draw slanted lines on the top half.

5 1 number of shaded parts with lines6 2 total number of parts

× =

=

b) 3 54 6

×

3. Estimate and calculate 3 28 3

× . Write your answers in lowest terms.

Estimate:

38

≈ 23

≈

3 2 _____________8 3

× ≈ ×

≈

Calculate:

3 28 3

×

×=

×

=

Write in lowest terms.=

Use paper folding to help you.


Name: _____________________________________________________ Date: ______________

4. Calculate. Write your answers in lowest terms.

a) 3 34 4

× b) 5 36 8

×

5. Tamar had 12

of an apple pie in her fridge. She ate 14

of it.

What fraction of the whole pie did she eat?

1 12

×

Sentence: ____________________________________________________________________

6. About 120

of the people in the world live in Canada or the United States.

Of the people who live in Canada or the United States, about 110

live in Canada.

What fraction of people in the world live in Canada? Show your work.

×

Sentence: ____________________________________________________________________


Name: _____________________________________________________ Date: ______________

7. Marius spends 13

of his time sleeping.

While he is asleep, he dreams for 14

of the time.

a) What fraction of the time is Marius

dreaming?

×

__________________________________ __________________________________

b) How many hours a day is Marius dreaming? Show your work.

Fraction from part a) × number of hours

__________________________________ __________________________________

British Columbia is about 110


The Pacific Maritime ecozone covers about 15

of British Columbia.

What fraction of the area of Canada does the Pacific Maritime ecozone cover? Show your work.

×

Sentence: _______________________________________________________________________


Name: _____________________________________________________ Date: ______________

6.4 Warm Up 1. Change the improper fraction to a mixed fraction.

a) 52

= 12

+ 12

+ 12

+ 12

+ 12

= 22

+ + 12

= 12

b) 43

c) 53

d) 64

2. Change the mixed number to an improper fraction.

a) 2 23

= 33

+ 33

+ 23

= 3

b) 1 12

c) 1 34

d) 3 14

1 2 3 4, , , ,1 2 3 4

… = 1


Name: _____________________________________________________ Date: ______________

6.4 Multiplying Improper Fractions and Mixed Numbers Working Example 1: Multiply Mixed Numbers Using a Model

Find 1 32 12 4

× .

Solution

Draw a rectangle.

12_2

34_1

Draw lines to separate each mixed fraction into a whole number and a proper fraction.

12_

2

34_

1

Show the area of each part in the diagram.

12_

2

34_

1

2 ¥ 34_

¥ 112_

¥12_ 3

4_

2 ¥ 1

Calculate the area of each part.

2 × 1 = 324

4

×

=

32112

=

=

1 12

×

=

1 32 4

8

×

=

Add the areas together: 2 + 112

+ 12

+ 38

= (2 + 1) + 1 1 32 2 8

⎛ ⎞+ +⎜ ⎟⎝ ⎠

Add the whole numbers.

= + 48

+ 48

+ 38


= 3 + 8

Add the numerators.

= 3 + 1 38

Change to a mixed fraction.

= 4 38

So, 1 3 32 1 42 4 8

× = .

A mixed number is made up of a whole number and a fraction.

6.4 Multiplying Improper Fractions and Mixed Numbers ● MHR 311

Name: _____________________________________________________ Date: ______________

Find each product using a model.

a) 1 11 12 3

×

Label the outer edges of the diagram. Label the inside of the diagram. Calculate the area of each part. 1 × 1 =

1 × 12

=

1 × =

1 12 3

× =

Add all the areas together.

+ + +

b) 1 12 14 4

×

Label the outer edges of the diagram. Label the inside of the diagram. Calculate the area of each part.



Name: _____________________________________________________ Date: ______________

Working Example 2: Multiply Mixed Numbers Using a Rule

Estimate and calculate 1 14 22 3

× . Write the product in lowest terms.

Solution Estimate: Round each mixed number to the closest whole number.

14 52

≈

123

≈

5 × 2 =

So, 1 14 22 3

× ≈ .

Calculate: Write the mixed numbers as improper fractions.

1 2 2 2 2 142 2 2 2 2 2

2

= + + + +

=

1 123 3 3 3

3

= + +

=

Multiply the improper fractions.

1 1 9 74 22 3 2 3

Multiply the numerators2 3 Multiply the denominators

6

× = ×

× ←=

←×

=

Write in lowest terms. ÷ 3

636 2

=

÷ 3 1102

=

20 = 102

.

So, 21 1= 10 +2 2

.

1 2 3, ,1 2 3

... = 1


Name: _____________________________________________________ Date: ______________

Estimate and calculate.

1 11 310 2

×

Estimate:

11 _____________10

≈

13 _____________2

≈

× =

So, 1 11 3 _____________10 2

× ≈ .

Calculate: Change to improper fractions.

1110

= +

=

132

= + + +

=

Multiply the improper fractions.

1 11 310 2

Multiply the numerators= Multiply the denominators

=

×

= ×

× ←←

×


Name: _____________________________________________________ Date: ______________

1. Henri multiplied 1 12 32 4

× like this:

2 × 3 = 6 and 1 12 4

× = 18

, so 1 1 12 3 62 4 8

× = .

a) What mistake did Henri make?

_________________________________________________________________________ _________________________________________________________________________ b) What is the correct answer?

2. Write each improper fraction as a mixed number.

a) 113

33

3

= + + +

=

b) 176

56

5_____________6

= + +

=


Name: _____________________________________________________ Date: ______________

3. Write each mixed number as an improper fraction.

a) 344

4 4 34 4 4

4

= + + + +

=

b) 728

78

= + +

=

4. Use a model to find each product.

a) 1 11 15 2

×

Draw rectangle to solve.

Label the diagram parts. Multiply each area.


b) 1 11 22 3

×

Draw rectangle to solve.

Label the diagram parts. Multiply each area.



Name: _____________________________________________________ Date: ______________

5. Estimate and calculate. Write your answers in lowest terms.

a) 4 105 7

×

b) 1 22 15 3

×

Estimate:

4 _____________5

≈

10 _____________7

≈

× =

So, 4 10 ________ .5 7

× ≈

Calculate:

4 105 7

Multiply the numeratorsMultiply the denominators

×

× ←=

←×

=


÷ _____

= _________=

÷ _____

Estimate: Calculate:

10 3= 17 7

Is your calculation close to your estimate?


Name: _____________________________________________________ Date: ______________

6. Two and a half laps of a running track equal 1 km. How many laps equal 3 km?

3 ×

Write the mixed number as an improper fraction. Multiply the improper fractions.


Sentence: __________________________________________________________________

7. On a day in Winnipeg with 10 12

hours of daylight, it was sunny for 13

of the time.

How many hours was it sunny?

Sentence: __________________________________________________________________


Name: _____________________________________________________ Date: ______________

8. Andreas has $18.

a) Bonnie has 1 23

times as much as Andreas.

How much money does Bonnie have?

b) Cheryl has 1 35

times as much as Bonnie.

How much money does Cheryl have?

c) How much money do they have altogether? Sentence: ________________________________________________________________________

The Hudson Plains ecozone covers 126


The Northern Arctic ecozone is about 3 910

times as big as the Hudson Plains ecozone.

What fraction of the area of Canada does the Northern Arctic ecozone cover? 126

× 3 910

Write the mixed number as an improper fraction. Multiply the fractions. Sentence: _______________________________________________________________________


Name: _____________________________________________________ Date: ______________

6.5 Warm Up 1. Write each fraction as a mixed number.

a) 185

b) 233

2. Write each mixed number as an improper fraction.

a) 337

b) 3111

3. Write each set of fractions with a common denominator.

a) 12 1, , 15 3

= b) 5 7, , 2 8

=

Multiples of 15: 15, 30, 45, 60, … Multiples of 3: 3, 6, 9, 12, 15, 18, … The lowest common multiple is .

c) 3 1, , 4 6

= d) 12 9, , 9 6

=

4. Divide.

a) 12 ÷ 2 =

b) 40 ÷ 8 =

c) 13 ÷ 1 = d) 24 ÷ 3 =


Name: _____________________________________________________ Date: ______________

6.5 Dividing Fractions and Mixed Numbers Working Example 1: Divide Using Diagrams

Find 2 13 4

÷ .

Solution

Draw diagrams to see how many 14

s are in 23

.

Divide 1 rectangle into 3 parts. Shade 2 of the parts. Divide another rectangle into 4 parts.

The diagrams show that the number of 14

s in 23

is between 2 and 3.

A common denominator of 14

and 23

is .

So, divide a rectangle into twelfths. Shade the parts up to the dotted line.

2 13 4

÷ = 223

or 3

Find 3 14 3

÷ using diagrams.

Shade 3 parts of the first rectangle. Draw a dotted line from the end of the shaded part through the other 2 rectangles.

A common denominator of 13

and 34

is .

Divide the third rectangle into twelfths. Shade the parts up to the dotted line.

Count the number of shaded parts: 12

. In 912

, there are whole groups

of 412

, plus 4

of another group. There are whole groups of 312

.

So, 3 1 _____________ or .4 3 4

÷ =

In 8 ,12

there are 2 whole groups of

3 ,12

plus 23

of another group.

6.5 Dividing Fractions and Mixed Numbers ● MHR 321

Name: _____________________________________________________ Date: ______________

Working Example 2: Divide Using a Rule


a) 7 18 4

÷

Solution Estimate:

Draw a diagram showing 78

.

Draw a diagram divided into quarters.

Draw a dotted line from 78

to the next diagram.

The number of quarters in 78

is between 3 and . So, 7 18 4

1÷ ≈ 3

2.

reciprocal • flip the fraction to switch the numerator and denominator

• example: the reciprocal of 23

is 32

Calculate: Method 1: Divide Using a Common

Denominator 7 18 4

÷


78 8

= ÷

Divide the numerators.

72

=


132

=

Method 2: Divide Using Multiplication

To divide by a fraction, multiply by its reciprocal.

7 18 47 48 1

8

÷

= ×

=

÷ 4

28 78 2

=

÷ 4

132

=

flip the numerator and denominator


Name: _____________________________________________________ Date: ______________

b) 1 32 32 4

÷

Solution Estimate:

12 32

≈ and 33 44

≈ .

1 32 3 3 42 4

4

÷ ≈ ÷

≈

Calculate: Method 1: Divide Using a Common

Denominator

1 32 32 4

÷ Write as improper fractions.

1 2 2 122 2 2 2

2

= + +

=

3 4 4 4 334 4 4 4 4

4

= + + +

=

5 15 Find a common denominator.2 410 15 Divide the numerators.4 4

Write in lowest terms.15

3

÷

= ÷

=

=

Method 2: Divide Using Multiplication

1 32 3 Write as improper fractions.2 4

15 .2 4

5 4 Write as a reciprocal.2 15

Write in lowest terms.30

÷

= ÷

= ×

=

÷ 10

30=

÷ 10


Name: _____________________________________________________ Date: ______________


a) 45

÷ 310


b) 3 16

÷ 1 23



Name: _____________________________________________________ Date: ______________

You could also divide using common denominators.

5 20 520 ÷ = ÷8 1 8

160 5= ÷8 8

Working Example 3: Apply Division With Fractions

Baby teeth are replaced by adult teeth as people get older.

Children have 58

as many teeth as adults do. Children have 20 teeth.

How many teeth do adults have? Solution

Divide 20 by 58

to find the number of adult teeth.

5208

÷ Multiply by the reciprocal.

20 81

160

32

= ×

=

=

Adults have teeth.

Check: Use multiplication to check the division. 5 328

5 Multiply the numerators8 Multiply the denominators

820

×

←32= ×

←1

=

=

One serving of lasagna is 16

of the tray.

How many servings are in 3 trays of lasagna?

3 ÷ 6

Multiply by the reciprocal.

There are servings of lasagna in 3 trays of lasagna.

Check your answer. 16

16 1

_____________

×

= ×

=

=


Name: _____________________________________________________ Date: ______________

In 58

, there are _____ whole groups

of 28

, plus 12

of another group.

1. Mike solved 3 24 3

÷ .

Is Mike’s method correct? Circle YES or NO. Give 1 reason for your answer.

Mike’s Work:

3 2÷4 34 2= ×3 38=9

__________________________________________________________________________

2. Find 5 18 4

÷ using diagrams.

Divide 1 rectangle into 8 parts. Shade 5 parts.

Draw a dotted line from the end of the shaded part through the other 2 rectangles.

Divide the second rectangle into 4 parts.

A common denominator of 8 and 4 is . Divide the third rectangle into eighths. Shade the parts up to the dotted line.

5 18 4

÷

= 12

= Write as an improper fraction.


Name: _____________________________________________________ Date: ______________

3. Divide using a common denominator.

a) 3 95 10

÷

= ÷ Find a commondenominator.

= Divide thenumerators.

= Write in lowestterms.

b) 1 512 6

÷

112 2 2

2

= +

=

Write as animproper fraction.

÷ Find a commondenominator for2 and 6.

= ÷ Divide thenumerators.

=

4. Divide using multiplication.

a) 3 44 5

÷

34

=

= × Write as a reciprocal.

b) 2 51 23 6

÷

Write as

improper fractions.

6.5 Math Link ● MHR 327

Name: _____________________________________________________ Date: ______________

5. In a comedy show, each performer has 1

4 of an hour to perform.

How many performers are there in a 2-h show?

24

÷

There are performers in 2 h.

6. It takes 122

cups of flour to make 1 cake. How many cakes can you make with 15 cups of flour?

Sentence: ____________________________________________________________________

The wettest part of the Prairies ecozone is the Manitoba Plain. The average yearly amount of precipitation is about 70 cm.

This amount of precipitation is 425

of the amount in the dry grasslands.

What is the average annual precipitation in the grasslands?

470 25

÷

Sentence: _________________________________________________________________

Precipitation is water that falls as rain, snow,

sleet, or hail.

2 = 21


Name: _____________________________________________________ Date: ______________

6.6 Warm Up 1. Use the order of operations to calculate.

a) 4 × 7 – 10 = – 10 Multiply. = Subtract.

b) 7 – 2 × 3 = 7 – Multiply. = Subtract.

c) 8 × (3 – 1) = 8 × Brackets. = Multiply.

d) 10 – (2 + 6) ÷ 2 = 10 – ÷ 2 Brackets. = 10 – Divide. =

2. a) Divide 1 25

÷ using a common

denominator.

b) Divide 459

÷ by multiplying by the

reciprocal.

3. Change mixed numbers to improper fractions.

a) 133

b) 225

= + + +

=

Brackets, multiply or divide, then add or subtract.

6.6 Applying Fraction Operations ● MHR 329

Name: _____________________________________________________ Date: ______________


6.6 Applying Fraction Operations Working Example 1: Use the Order of Operations

Calculate using the order of operations.

a) 1 124 2

÷ ×

Solution

1 124 2

÷ ×

2 4 11 1 2

= × × Divide by multiplying the reciprocal.

12

= × Multiply.

82

=

= Write in lowest terms.

b) 13

× (9 – 2)

Solution

13

× (9 – 2) Brackets.

= 13

× Multiply.

= 3

= 123

Write as a mixed fraction.

77 =1


Name: _____________________________________________________ Date: ______________

1 + 1 + 34

+ 14

= 2 + 44

= 2 + 1 = 3

c) 1 3 12 1 14 4 4

⎛ ⎞÷ +⎜ ⎟⎝ ⎠

Solution

1 3 12 1 14 4 4

⎛ ⎞÷ +⎜ ⎟⎝ ⎠

Add the whole numbers.Add the fractions.

124 1

= ÷

4 1= ÷ Write the mixed number as an improper fraction.

14 3

= × Multiply by the reciprocal.

12= Write in lowest terms.

34

=

a) 4 – 2 ÷ 35

241

= − × Multiply bythe reciprocal.

41

= −

= − Find a commondenominator.

=

b) 124

× 12

– 58

4 4 1 9+ + =4 4 4 4


Name: _____________________________________________________ Date: ______________

time-and-a-half = 112

Working Example 2: Apply Fraction Operations

Bev earns $25/h as a machine operator. When she works more than 40 h in a week, she earns time-and-a-half. How much does Bev earn for working 46 h in a week?

To earn time-and-a-half means to be paid for 1 12

h when you work for 1 h.

Solution Method 1: Calculate in Stages Bev works 40 h at her regular pay of $25/h. Amount earned at regular rate: 40 × 25 = How many hours does she work at time-and-a-half? 46 – 40 = 6 h at time-and-a-half = ? h at regular rate

6 × 1 12

= 6 ×

= 61

× 32

= 2

= 9 6 h at time-and-a-half = 9 h at regular rate Amount earned at time-and-a-half: 9 × 25 = Total earnings = amount earned at regular rate + amount earned at time-and-a-half = + 225 = Bev earns $ for working 46 h in a week.

Write as an improper fraction: 2 1 3+ =2 2 2


Name: _____________________________________________________ Date: ______________

Method 2: Evaluate One Expression

Bev’s regular rate of pay is $25/h. For 6 h at time-and-a-half, Bev is paid 1 12

× h.

An expression of her total earnings is: 125 40 1 62

⎛ ⎞× + ×⎜ ⎟⎝ ⎠

125 40 1 62

⎛ ⎞× + ×⎜ ⎟⎝ ⎠

Brackets first.

= 25 40 6

⎛ ⎞⎜ ⎟⎜ ⎟× + ×⎜ ⎟⎜ ⎟⎝ ⎠

Write the mixed number as an improper fraction.

= 3 625 402 1

⎛ ⎞× + ×⎜ ⎟⎝ ⎠

Multiply the numbers in the bracket.

= 25 402

⎛ ⎞⎜ ⎟⎜ ⎟× +⎜ ⎟⎜ ⎟⎝ ⎠

Add.

= 25 × 49 Multiply. = 1225 Bev earns $ for working 46 h in a week.

Ron earns $15/h as a security guard. When he works more than 35 h in 1 week, he earns time-and-a-half. How much does Ron earn for working 43 h in a week? Ron worked 35 h at regular pay. Amount earned at regular pay: 35 × 15 = Hours worked at time-and-a-half: 43 – 35 =

8 × 1 12

Amount earned at time-and-a-half: × 15 = Total earnings = + =

18 = 18 ÷ 2 = 92

40 + 9 = 49

2 1 3+ =2 2 2


Name: _____________________________________________________ Date: ______________

1. Mia missed the lesson on how to find the answer for 1 1 22 4 3

⎛ ⎞+ ×⎜ ⎟⎝ ⎠

.

a) List the steps to solve this question. ____________________________ ____________________________ ____________________________

b) Find the answer.

2. Calculate.

a) 34

– 12

× 23

Multiply.

= 34

– Find a commondenominator.

= –

=

b) 3 12

÷ 1 314 4

⎛ ⎞−⎜ ⎟⎝ ⎠


= 3 12

÷

⎛ ⎞⎜ ⎟⎜ ⎟−⎜ ⎟⎜ ⎟⎝ ⎠

Brackets first.

=

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟÷⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠


= × Multiply bythe reciprocal.

=

=


Name: _____________________________________________________ Date: ______________

3. Calculate.

a) 5 1 36 3 4

− ×

Multiply. Find a common denominator. Subtract.

b) 1 3 532 4 6

÷ − Change to improper fraction.

Divide. Subtract.

c) 7 2 18 3 4

+ −

d) 1 1 212 3 3

× ÷


Name: _____________________________________________________ Date: ______________

4. Leo earns $16/h as a gardener. When he works more than 35 h in 1 week, he earns time-and-a-half. How much does he earn for working 36 h in a week?

Hours worked at regular pay = Amount earned at regular pay: 35 × = Hours worked at time-and-a-half: 36 – 35 =

Time worked over 35 hours: × 1 12

=

Amount earned at time-and-a-half: 1 12

× 16

Total earnings = +

=

Sentence: ___________________________________________________________________

16 = 161


Name: _____________________________________________________ Date: ______________

Let all the land on the farm equal 1.

5. Two thirds of the land on a farm is used for beef cattle. The rest of the land is used to grow crops.

a) How much land is used to grow crops?

Draw a diagram to help you.

213

23

−

= −

=

Sentence: ________________________

_________________________________

b) Half of the land for crops is used to grow corn. What fraction of the land is used to grow corn?

× 12

Sentence: ________________________

_________________________________

About 14

of the species of mammals that live in Canada can

be found in the Taiga Shield ecozone. About 50 species of mammals can be found in this ecozone. a) How many species of mammals live in

Canada?

1504

÷

Sentence: ___________________________

___________________________________

b) How many species of mammals in Canada live outside the Taiga Shield ecozone?

Sentence: ___________________________

___________________________________

Chapter Review ● MHR 337

Name: _____________________________________________________ Date: ______________

6 Chapter Review Key Words For #1 to #3, write the number that matches the description.

1. 3 14

improper fraction

2. 89

mixed number

3. 113

proper fraction 4. a) Unscramble the letters to make a key word.

CIRCLOPERA: R L

b) What does this word mean?

_______________________________________________________________________ 6.1 Multiplying a Fraction and a Whole Number, pages 288–293

5. Find the product using a diagram.

5 × 14

Divide each rectangle into 4 parts.

Shade 1 part in each rectangle.

Add the shaded parts.

5 × 14

14

= + + + +

=

=

+

=

+ + +


Name: _____________________________________________________ Date: ______________

6. Use a number line to multiply.

4 × 23

= + + +

=

=

7. The average mass of a porcupine is about 12 kg.

The average mass of a raccoon is about 34

of a porcupine’s mass.

What is the average mass of a raccoon?

×

Sentence: __________________________________________________________________

8. The length of a rectangle is 6 cm. The width is 23

of the length.

What is the width?

Sentence: __________________________________________________________________

Use diagrams or a number line to help you.

0 31 2


Name: _____________________________________________________ Date: ______________

6.2 Dividing a Fraction by a Whole Number, pages 295–300 9. Use a diagram to divide.

a) 34

÷ 2

Divide and shade the fraction strip to

show 34

.

Divide each quarter into 2 equal parts. There are parts in the whole,

so each part is .

So, 34

÷ 2 = .

b) 23

÷ 4

Label the number line to show thirds. 0 1

Divide each third into 4 equal parts. There are parts in a whole, so

each part is .


into 4 equal

parts.

Each part is .

So, 23

÷ 4 = .

10. A recipe for making 6 servings of potato salad includes 12

an onion.

What fraction of an onion is in each serving?

÷

Sentence: __________________________________________________________________

0 1


Name: _____________________________________________________ Date: ______________

6.3 Multiplying Proper Fractions, pages 302–308 11. Use a diagram to solve.

a) 1 32 4

×

Divide the length in half.

Shade 12

.

Divide the width into quarters.

Draw slanted lines on 34

of it.

# of shaded parts with linestotal # of parts

=

So, 1 32 4

× = .

b) 2 13 4

×

Divide the length in thirds.

Shade 23

.

Divide the width into quarters.

Draw slanted lines on 14

of it.

# of shaded parts with linestotal # of parts

=

So, 2 13 4

× = .

12. Estimate and calculate 3 35 5

× .

Estimate:

Is 35

closer to 0, 12

or 1?

35

≈

3 35 5

× ≈ ×

≈

Calculate: 3 35 5

×

=


Name: _____________________________________________________ Date: ______________

6.4 Multiplying Improper Fractions and Mixed Numbers, pages 310–318

13. Estimate and calculate 83

× 65

. Write your answers in lowest terms.

Estimate: Change to mixed numbers:

83

= + + 23

= 23

65

= 55

+

=

8 _____________3

≈ and 6 _____________5

≈

× =

So, 8 6 ______________3 5

× ≈ .

Calculate:

83

× 65

=

÷ 3

=

÷ 3

=

14. The distance from Winnipeg to Regina is 570 km.

The distance from Winnipeg to Calgary is 2 13

times the distance from Winnipeg to Regina.

What is the distance from Winnipeg to Calgary?

× 2 13

Sentence: ____________________________________________________________________


Name: _____________________________________________________ Date: ______________

6.5 Dividing Fractions and Mixed Numbers, pages 320–327 15. Divide.

a) 23

÷ 56

2 Multiply by the reciprocal.3


= ×

=

=

b) 3 12

÷ 2 14

Write the mixed numbers as improper

fractions. Multiply by the reciprocal. Write as a mixed number.

16. A horse eats 12

of a bale of hay per day.

How long will 15 bales of hay last?

15 ÷

Sentence: __________________________________________________________________


Name: _____________________________________________________ Date: ______________

6.6 Applying Fraction Operations, pages 329–336 17. Calculate.

a) 13

+ 32

× 13

= 13

+


b) 1 12

÷ 7 58 8

⎛ ⎞−⎜ ⎟⎝ ⎠

= 1 12

÷

18. Tracy earns $12/h as a cashier. When she works more than 32 h in 1 week, she earns time-and-a-half. How much does Tracy earn for working 40 h in 1 week?

Amount earned at regular pay: × = Hours worked at time-and-a-half: – =

Time worked over 32 h: × 1 12

Amount earned at time-and-a-half:

× =

Total earnings = + =

Sentence: ____________________________________________________________________

Brackets first.


Name: _____________________________________________________ Date: ______________

6 Practice Test For #1 to #5, choose the correct answer.

1. Which expression does not equal 4 × 13

?

A 1 13

B 43

C 13

× 4 D 13

× 13

× 13

× 13

2. Which expression equals 4 25 3

÷ ?

A 45

× 23

B 54

× 32

C 45

× 32

D 54

× 23

3. What is the reciprocal of 23

?

A 43

B 32

C 31

D 46

4. What is the value of the expression 12

+ 16

× 34

?

A 1224

B 58

C 2324

D 54

5. What is 34

÷ 512

in lowest terms?

A 95

B 516

C 3620

D 1548


Practice Test ● MHR 345

Name: _____________________________________________________ Date: ______________

Change the mixed number into an

improper fraction.

Short Answer 6. Calculate.

a) 38

× 56

b) 65

÷ 710

c) 3 35

× 38

d) 1 314 4

⎛ ⎞+⎜ ⎟⎝ ⎠

÷ 1 12

7. Leisha worked 6 12

h for $14/h.

How much did she earn?

Sentence: __________________________________________________________________

Brackets, multiply or divide, then add

or subtract.


Name: _____________________________________________________ Date: ______________

8. In computer terminology, a bit is 18

of a byte.

How many bits are needed to make 16 bytes?

Sentence: __________________________________________________________________ 9. Printer paper is sold in packages of 500 sheets.

If a printing job uses 1 34

packages of paper, how many sheets were used?

Sentence: ___________________________________________________________________

Practice Test ● MHR 347

Name: _____________________________________________________ Date: ______________

Most of the Boreal Plains ecozone is covered by woods and forests.

Province/ Territory

Fraction of Boreal Plains in the Province/Territory

Alberta 1325

British Columbia

120

Manitoba 17100

Northwest Territories

150

The total area of the Boreal Plains ecozone is about 750 000 km2. The table shows the approximate fraction of this ecozone found in different locations. Using the information in the table, write a word problem that can be answered using division of fractions or multiplication of fractions.

Saskatchewan625

Examples: Multiplication question: How many square kilometres does the Boreal Plains ecozone cover in Saskatchewan?

Answer: 750 000 × 625

= 4 500 00025

= 180 000 km2

Division question: For this ecozone, how many times larger is the area in British Columbia than the area in the Northwest Territories?

Answer: 120

÷ 150

= 120

× 501

= 5020

= 2 12

a) Your question: _________________________________________________________________________

b) Your answer:


Name: _____________________________________________________ Date: ______________

Unscramble the letters of each term. Use the clues to help you.

A B

1. 34

ONODTRIEMAN

2. For 56

, this would be 65

.

AOPCELRCIR

3. 1112

EANTRMROU

4. 23

ORERPP ATCFINRO

5. answer to a division question

OETNQITU

6. answer to a multiplication question

DURTOPC

7. This would include the following list: • brackets • multiply and divide in order • add and subtract in order

RDEOR FO EAOPINOSR

8. 425

IDXME BREUNM

9. 156

OMIRREPP ATINFORC

Math Games ● MHR 349

Name: _____________________________________________________ Date: ______________

Math Games

Fabulous Fractions

23 4

5

1 6789

1. Play Fabulous Fractions with a partner.

Rules: • Each player spins the spinner once to decide who will play first.

If there is a tie, spin again. The player with the highest number goes first.

• For each turn, spin the spinner 4 times. Write down the 4 numbers.

• Use the 4 numbers to create 2 fractions with the greatest product. Write the fractions on your multiplication sheet. • Write the answer in lowest terms. • The player with the greater answer scores a point. • If the answers are equal, each player scores a point. • The first player with 10 points wins.

Use the tally chart to keep track.

Player 1 Player 2

2. Repeat #1, but use the 4 results to create 2 fractions with the

greatest quotient. Record the fractions on your division sheet.

Player 1 Player 2

• spinner with 9 sections

numbered 1 to 9 per pair of students

• paper clip per pair of students • Fabulous Fractions

Multiplication BLM per student

• Fabulous Fractions Division BLM per student

I spun 6, 7, 1, and 4.

My fractions are ×6 17 4

.

I spun 6, 7, 1, and 4.

My fractions are ÷6 17 4

.


Name: _____________________________________________________ Date: ______________

Challenge in Real Life

Create a Class Flag Mr. Jansen’s grade 8 class is made up of 10 boys and 14 girls. You are a student in Mr. Jansen’s class. Create a class flag that will show the students’ interests.

• Organize Mr. Jansen’s Class

Flag BLM • Organize Your Class Flag BLM • 2 different coloured pencils

1. The flag is divided into 24 equal parts to show the number of students in the class. a) Colour 10 parts in the flag with

1 colour to show the number of boys. b) Colour 14 parts in the flag with a

different colour to show the number of girls.

c) One fifth of the boys are in the band.

How many boys are in the band?

1 1051 105 1

5

______________

×

= ×

=

=

There are boys in the band. • Draw an instrument in

of the boys’ boxes.

d) One half of the boys play hockey. None of the hockey players are in the band. How many boys play hockey?

1 102

×

• Draw a hockey puck in of the boys’ boxes.

e) One half of the girls play volleyball. How many girls play volleyball?

Draw a volleyball in of the girls’ boxes.

Challenge in Real Life ● MHR 351

Name: _____________________________________________________ Date: ______________

2. Now, create your own class flag.

a) Collect information about your own class. You could ask: • Are you in the band? • Is math your favourite subject? • Do you like rock music? • Do you love pizza?

Record your information in the chart.

Question # of Boys # of Girls

Example: Are you in the band? Yes = 2 Yes = 3

b) Design a flag that shows the class information. Show your calculations.


Answers Get Ready, pages 284–285

1. a) 13

b) 12

2. a) 1210

b) 536

Math Link, page 286

a) 310

b) 16

6.1 Warm Up, page 287

1. a) 25

b) 223

2. a) b)

3. a) 34

b) 110

4. a) 8 b) 20 c) 6 d) 15 e) 9 f) 30 6.1 Multiplying a Fraction and a Whole Number, pages 288–293

Working Example 1: Show You Know

53


a) 43

b) 94


4 Communicate the Ideas

1. a) 6 6 6 185 5 5 5

+ + =

b) c) Answers may vary. Example: I prefer fraction strips because I find it

easier to see the answer. Practise

2. a) 2 635 5

× = b) 5 1024 4

× =

3. a) 1 336 6

× = b) 2 635 5

× =

4. a) 1 332 2

× = b) 1 446 6

× =

5. a) 2

b) 210

Apply

6. 2 m 7. 9 people 8. a) Answers will vary. Example: There are 8 seats at a restaurant counter.

The seats are 14

full. How many people are at the counter?

b) 8 × 14

= 2

Math Link a) 5 b) 15 6.2 Warm Up, page 294

1. a) 1 667 7

× = b) 2 843 3

× = c) 8 1625 5

× = d) 34 34

× =

2. a) 128

b) 72

3. a) 3 b) 5 c) 20 d) 2 e) 3 f) 3 6.2 Dividing a Fraction by a Whole Number, pages 295–300

Working Example 1: Show You Know 14


110

Working Example 3: Show You Know 1 142 8

÷ =

Communicate the Ideas

1. a) 14

b) Answers may vary. Example: I prefer fraction strips because they make it easier to visualize the fractions.

Practise

2. a) 18

b) 19

3. a) 310

b) 18

Apply

4. a) 14

of a coconut b) 18

of a coconut

5. 16

of a full container

Math Link 120


1. a) 118

b) 38

c) 2

d) 2

+ + + =

+ =

+ =

+

1 0 2

10 42 3

+ + =+

+ + + + + + =

0 1510

610

710

810

910

410

310

210

110

+ +

=

+ + =

0 1410

510

610

710

810

910

110

210

310

0 114

12

23

+ + ++ =

+ ++ + + =

Answers ● MHR 353

2. Estimates may vary. a) 1 b) 12

c) 1 d) 0

3. a) 8 b) 15 c) 24 d) 42 6.3 Multiplying Proper Fractions, pages 302–308


a) 18

b) 49


a) 14

b) 14


Estimate: 0; Calculate: 215


1. a) Brendan should multiply the denominators. b) 625

Practise

2. a) 512

b) 58

3. Estimate: 14

; Calculate: 14

Apply

4. a) 916

b) 516

5. 18

of the pie

6. 1200

of the world’s people

7. a) 112

of his time b) 2 hours

Math Link

150

of the area of Canada


1. a) 122

b) 113

c) 213

d) 112

2. a) 83

b) 32

c) 74

d) 134

6.4 Multiplying Improper Fractions and Mixed Numbers, pages 310–318


a) 2 b) 13216


Estimate: 4; Calculate: 17320


1. a) Henri forgot to multiply 2 × 14

and 3 × 12

. b) 188

Practise

2. a) 233

b) 526

3. a) 194

b) 238

c) 114

d) 137

4. a) 415

b) 132

5. a) Estimate: 1; Calculate: 117

b) Estimate: 4; Calculate: 233

Apply

6. 7 12

laps

7. 132

hours

8. a) $30 b) $48 c) $96 Math Link

320

of the area of Canada


1. a) 335

b) 273

2. a) 247

b) 1411

3. a) 12 5,15 15

b) 20 7,8 8

c) 9 2,12 12

d) 24 27,18 18

4. a) 6 b) 5 c) 13 d) 8 6.5 Dividing Fractions and Mixed Numbers, pages 320–327


124


a) Estimate: 3; Calculate: 223

b) Estimate: 2; Calculate: 9110


18 Communicate the Ideas

1. NO. Mike needs to multiply by the reciprocal of 23

.

Practise

2. 122

3. a) 23

b) 95

4. a) 1516

b) 1017

12_

1

15_

1 1 ¥ 1 ¥ 112_

1 ¥ 15_ ¥ 1

5_1

2_

12_

1

13_

2 1 ¥ 1 ¥ 112_

1 ¥ 13_ ¥ 1

3_1

2_

12_

1

13_

1 1 × 1 × 112_

1 × 13_ × 1

3_1

2_

14_

2

14_

1 2 × 1 × 114_

2 × 14_ × 1

4_1

4_

5–8

1–4

1–2

2÷ =


Apply

5. 8 performers 6. 6 cakes Math Link

25 cm 6.6 Warm Up, page 328

1. a) 18 b) 1 c) 16 d) 6

2. a) 110

b) 1114

3. a) 103

b) 125

6.6 Applying Fraction Operations, pages 329–336


a) 23

b) 12


$705 Communicate the Ideas

1. a) Step 1: Find the common denominator for 12

and 14

. Step 2: Add the

fractions in the brackets. Step 3: Multiply by 23

. b) 12

Practise

2. a) 512

b) 7

3. a) 712

b) 536

c) 7124

d) 34

Apply

4. $584

5. a) 13

of the land b) 16

of the land

Math Link

a) 200 species b) 150 species Chapter Review, pages 337–343

1. mixed number 2. proper fraction 3. improper fraction 4. a) reciprocal b) the inverse of a fraction

5. 114

6. 223

7. 9 kg 8. 4 cm

9. a) 38

b) 16

10. 112

of an onion

11. a) 38

b) 16

12. Estimate: 14

; Calculate: 925

13. Estimate: 3; Calculate: 135

14. 1330 km

15. a) 45

b) 519

16. 30 days

17. a) 56

b) 6

18. $528 Practice Test, pages 344–346

1. D 2. C 3. B 4. B 5. A

6. a) 516

b) 1 57

c) 1 720

d) 1 13

7. $91 8. 128 bits 9. 875 sheets Wrap It Up!, page 347

Answers will vary. Example: a) How many square km does the Boreal Plains ecozone cover in Manitoba? b) 127 500 km2 Key Word Builder, page 348

1. denominator 2. reciprocal 3. numerator 4. proper fraction 5. quotient 6. product 7. order of operations 8. mixed number 9. improper fraction Challenge in Real Life, pages 350–351

1. a) and b) Answers will vary. c) 2 d) 5 e) 7 2. Answers will vary.

0 31 2

0 123

+ ++ + =

Documents

Fraction Operations - Mr. Mubashirwaqasmubashir.weebly.com/uploads/2/2/6/7/22677732/fraction_opera… · Model the fractions using a number line. The denominator is 5. So, you need