Grade 8 Unit 4

Grade 8 Unit 4 Fractions (with answers)

Name: _________________________ Date: __________________________ Homeroom: ___________

Student: ❏ correctly identify the operation required to solve a given problem with positive

fractions. ❏ correctly multiply fractions by whole numbers, fractions and mixed numbers. ❏ correctly divide fractions by whole numbers, fractions and mixed numbers. ❏ correctly solve a given problem involving fractions, using the proper order of

operations.

Unit 4 - Fractions 1


Fraction Review

+ 612

712

- 85

41

- 1211

32

+ 85

41

+ 53

21

- 43

53

2 + 53 3

10

4 + 95

32

6 - 2 72


Review Notes


Fraction Review 1) Write each pair of fractions as equivalent fractions with a common denominator.

2) Compare each pair of fractions using the symbols <, >, =.

and 53

42

and 85

43

and 210

115

and 32

81

and 73

32

<

and 52

21

<

and 68

84

>


3) Simplify each fraction.

4) Place 2 , , , and on the number line.52

415

1034

96

85

= 84 = 6

15

= 1510 = 6

10


5) Calculate.

6) Yesterday Cody read of the novel War and Peace. Today, he read of the31

61

novel. Use a fraction to describe how much of the novel Cody has read so far.

He has read .

7) Rosa wrote of her book report on Tuesday and another on Wednesday.21

51

What fraction of her book reports does she still have to write?

+ 51

43

+ 41 9

10

+ 53

51

+ 31 7

12


She has left to write. 8) Calculate.

- 65

62

- 1211

51

- 712 5

1

- 710 4

1


Lesson 1 - Multiplying a Whole Number by a Fraction

Notes


Lesson 1 - Multiplying a Whole Number by a Fraction

The equation 5 x means you are making 5 groups of .43

43

If you add 5 times you will get .43

415

This can also be solved by multiplying 5 x 3 and keeping the denominator the same.

1) Maura pours of a cup of water into a pot and repeats this 7 times.32

How many cups of water, in total, does she pour into the pot? Write your answer as a mixed number.

2) Write 5 x as a repeated addition equation then calculate the answer.43

Write the answer as an improper fraction and a mixed number.


3)Multiply.

4) Art class is of an hour each school day.65

How many hours of art does a student have in five days?

2 x 31

5 x 53

3

6 x 83

4 x 52

3 x 67

8 x 24

16


5) Devin needs of a cup of flour to make one batch of bannock. How many cups43

of flour will he need if he decides to make six batches, one for each of his aunts?

6) Doug multiplied a whole number by a fraction. The numerator of the fraction product was 30. List three possible whole number and fraction combinations he could have been using.

7) Write a word problem for a situation where you would have to multiply 4 x 32

to find the answer.

Need cup per batch and you want to make 4 batches. 9) At a party, Megan notices that 15 pitchers of lemonade are filled to the same level, but not to the top. He combines all the lemonade to fill six whole pitchers. What fraction of each of the 15 pitchers was full?


Lesson 2 - Multiplying Fractions

Notes


Lesson 2 - Multiplying Fractions

1) About of Canadians who are 12 and older downhill ski. About of these110 5

2

skiers are between the ages of 12 and 24. What fraction of the Canadian population between the ages of 12 and 24 are downhill skiers?

2) If of the students in Windham Ridge School are in Grades 7 and 8, and32

if of these students are girls, what fraction of the students in the school85

are girls in Grades 7 and 8?


3) Calculate.

4) Ben’s bed takes up of the width of his bedroom and of the length.31

53

What fraction of the floor area does the bed use up?

x 21

83

x 54

31

x 61

52

x 43

62

( ) (- )41

54

(- ) (- )53

32


5) Jessica is awake for of the day. She spends of that time at home.32

85

What fraction of the day is Jessica awake at home? How many hours is Jessica awake at home?

6) The Grade 8 class raised of the money to support the school’s archery program.52

The Grade 8 boys raised of the Grade 8 money.32

What fraction of the whole money raised did the Grade 8 boys raise?

7) Cheyenne gets home after 4 p.m. on school days about of the time.21

She gets home after 5 p.m. on about of those days.52

On what fraction of the school days does she get home after 5 p.m.?


Lesson 3 - Multiplying Fractions Greater than 1

Notes


Lesson 3 - Multiplying Fractions Greater than 1

Mixed numbers must be turned into improper fractions in order to multiply.

1) A large bag of popcorn holds 2 times as much as a small bag.21

Aaron has 1 large bags.21

He is pouring the popcorn into smaller bags to give to his friends.

`

2) Maura is making 3 dozen cookies. If of the cookies have icing, how many21

72

dozen cookies have icing?

1


3) Calculate. Simplify the answer.

x 232

41

x 185

21

x 251

32

3 x 231

41

1 x 221

21

1 x 254

32

3 x 251

41

3 x 261

32

1 x 161

41


4) A smoothie recipe requires 1 cups of blueberries. How many cups of blueberries41

do you need for 2 batches?

How much for 2 batches?21

How much for 3 batches?31

5) The product of three improper fractions is .314

What could the fractions be?


Mid-Chapter Review 1) Calculate. Write each answer as an improper fraction and a mixed number.

2) The product of a fraction and a whole number is .524

What could the fraction and the whole number be?

3) Use repeated addition to show 3 x .94

6 x 51

8 x 53

4 x 512

5 x 94


4) Use a picture to show of .3

283

5) What is the missing fraction?

6) About of the traditional dancers of a First Nations school are girls. About of43

41

these students are in Grade 8. What fraction of the students who dance are Grade 8 girls?

of is ___41

72

is ___ of 53

54

___ of is43 3

12

of is ___73

54


7) Calculate and simplify the answer.

x 43

65

x 61

87

x 93

98

1 x 131

32

x 373

21

x 152

53

2 x 343

43

3 x 651

83


Cumulative Review

(-12) - (-20) = 8

(+236) + (-236) =

0

(-10) + (-3) =

-13

x = (4)(-20)

x = -80

(-4) x (3) x (-6) = 72

(-81) ÷ (-9) = x

9

9 x (-3) + (-15) ÷ 3 = 22

= −6−24

4

(-5) (-10) = x

x = 50

(-5) = - 3x3

x = -6

5x + 3 = 30 + 8

x = 7

= (-7)5w

w = -35


Cumulative Review

3x + 5 = 11

x = 2

3x - 4 = 8

x = 4

(-20) = 4(x -1)

x = -4

-3d + 5 = (-4)

d = 3

Combine like terms.

4x + 5 - 2 + 5x - 3x

6x + 3

2c - 7 = (-2)

62

36

112

121

√81

9

b = 8

√27

5.2

√15

3.8 or 3.9


Lesson 4 - Dividing Fractions by Whole Numbers

Notes


Lesson 4 - Dividing Fractions by Whole Numbers 1) Maeve had art class 9 out of 20 school days last month. She worked with a partner

about of the time. For what fraction of the school days last month did she work21

with a partner in art?

2) Two-thirds of a room still has to be tiled. Three workers are going to share the job. What fraction of the room will each worker tile if they all work at the same rate?

3) How can you solve ÷ 4 using multiplication of fractions?21


4) Calculate.

5) Ken used of a can of paint to cover four walls.65

How much of the can did he use for each wall?

6) Brett used of his blue seed beads to make a Native regalia breastplate.61

He wanted to use the same color of beads to make two pairs of moccasins. What fraction of the beads that he originally had could he use for one moccasin?

÷ 498

÷ 492

÷ 496

÷ 653

÷ 532

÷ 387


Lesson 5 - Dividing Fractions

Notes


Lesson 5 - Dividing Fractions

1) To win a contest at school, the students knew that at least of the students98

in the school had to participate. At one point, only of the students had signed up.41

How many more groups of that size had to sign up to have a chance to win?

2) Calculate.

÷ 1211 3

12

÷ 1211

61

÷ 1211

71

÷ 43 1

10

÷ 65 1

10

÷ 1110

32


3) Kate needs of a cupful of berries to make a Saskatoon berry soup. She can find43

only a cup measure. About how many times will she have to fill the cup to have31

the right amount of berries?

4) Tom used 25 tiles to tile of the floor.51

About how many tiles does he need to finish the job?

125

5) There were 2 containers of orange juice in Ben’s fridge. How many glasses of21

juice can he pour if each glass uses about of a container?51


6) Kane needs to measure 2 cups. How many times must he fill a cup measure?21

21

5 7) Calculate.

8) Steph has written of a page for her report in 1 hour. About how much time will32

she need to complete the entire report at this rate?

5 ÷ 31

15

1 ÷ 43

65

2 ÷ 21

83

÷ 53

65


9) Kylar is cooking a turkey. It takes 4 hours to cook. She checks it every 20 minutes,21

or of an hour.31

How many times will she check the turkey before it is cooked?

Why can you keep subtracting from 4 to answer the question?31

21

See how many s are in

10) TIm has only a cup measuring cup.31

How much flour could Craig measure by filling the cup 5 times?

How many times would Craig have to fill his measuring cup to measure 2 cups83

of flour?


Lesson 6 - More Dividing Fractions - and with Mixed Numbers

1) Jane wants to pour 1 large cans of paint into small cans. Each small can87

holds as much paint as a large can. How many small cans will Jane fill?53

2) Calculate.

÷ 93

92

÷ 21

31

÷ 84

87

÷ 54

32

÷ 51

52

÷ 920 5

3


3) Rebecca has of a container of trail mix. He is filling snack packs that each use32

about of a container. How many snack packs can Rebecca make?51

4) Calculate.

÷ 89

83

3

÷ 37

65

÷ 411

23

1 ÷ 32

73

5 ÷ 231

43

6 ÷ 253

31


5) Annette filled 2 pitchers with of punch she made. How many pitchers would21

32

she fill if she used all the punch she made?

6) Devin takes 4 minutes to run once around the track. How many laps can he do in21

each time period?

30 minutes?

20 minutes?

15 minutes? 7) Printers print at different rates. How many pages does each printer print each minute?

20 pages in 1 minutes? 21

20 pages in minutes? 6031


Lesson 6 - Order of Operations

1) Do all steps in brackets 2) Multiplication and division - work from left to right 3) Addition and subtraction - work from left to right

Cross out numbers once you have used them so you do not use them a second time.

Work down and be organized with your work.

Label your steps before solving.

A)

B)

= 9


C)

D)

=

E)

=


F)

=

G)

=

H)


I)

=

J)

K)


L)

M) What is the missing digit in the following equation?

x = 144

N)


Chapter Review

1) of is = 32

41

2) of is = 21

96

3) 1 of is = 51

74

4) Calculate.

x 53

85

1 x 152

43

x85

73

x 592

31


5) Calculate.

6) =

7) =

÷ = 254

52

÷ = 85

51

÷ = 51

85 3 ÷ 1 = 2

141


8) Calculate.

9) About of the students in Cody’s school come by bus. About of these students32

31

are on the bus for more than an hour and a half each day. What fraction of the students are on the bus for more than an hour and a half each day?

10) Phil used of his sugar to make of a batch of cookies. How much sugar32

43

would she have needed to make a whole batch?

8 x 54

6 x 53

9 x 72

12 x 32

8


11) Calculate.

12) =

13) =

÷ 3910

÷ 2910

÷ 654

÷ 85

41

÷ 83

92

3 ÷ 21

43

Documents

Grade 8 Unit 4