wmath 11 name: unit learning guide review fractions

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Name:

UNIT 1 LEARNING GUIDE – REVIEW FRACTIONS

INSTRUCTIONS:

Using a pencil, complete the following questions as you work through the related lessons. Show ALL of your work as is explained in the lessons. Do your best and always ask questions if there is anything that you don’t understand.

1.1 WARM UP

1. Being able to do some question ‘in your head’ is important. Use the mental math strategy of

rounding (for example: +1/-1, +2/- 2, +10/-10,+20/-20, etc) to add the following numbers.

Write down how you would change the numbers in your head for each question.

Ex. 27 + 51 28 + 50 = 78 a. 47 + 16

b. 178 + 14

c. 580 + 355

d. 174 + 620

e. 388 + 218

2. Use the mental math strategy of expanding (splitting into place values) to add the following

numbers. Write down how you would change the numbers in your head for each question.

Ex. 53 + 28 𝟓𝟎 + 𝟑 𝟐𝟎 + 𝟖

𝟕𝟎 + 𝟏𝟏 = 𝟖𝟏

a. 14 + 43

b. 38 + 48

c. 147 + 312

d. 655 + 343

e. 238 + 517

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3. Use the mental math strategy of your choice to subtract the following numbers. Write down

how you would change the numbers in your head for each question.

a. 65 - 23

b. 89 - 72

c. 58 - 24

d. 72 - 36

e. 92 - 65

f. 45 - 26

4. Write an expression to represent the phrase

4 more than some number

4 times some number

4 times the sum of a number and 7

5 less than the product of 3 and a number

6 more than 5 times a number

8 minus some number

8 plus some number

a number decreased by 10

a number divided by 2

a number increased by 10

one-third of some number

the difference between a number and 12

the product of a number and 12

the quotient of 4 and some number

the quotient of a number and 12

the ratio of 8 and some number

the sum of a number and 12

twice a number

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4. Show all of the problem-solving steps that you use to solve the following words problems.

a. To excavate a foundation, a backhoe is rented for 2 days at $125 per day, and a bulldozer

is rented for 4 hours at $115 per hour. Find the total cost of renting the equipment.

b. If holes spaced 17 in. centre-to-centre are to be drilled in a stud, how far apart are the

two holes indicated on the diagram below?

c. Wei has prepared a playlist of 46 songs for the school dance. The dance starts at 7pm

and the principal said that it must be over at 9pm. Assuming that each song is 3 minutes

long, how many songs will Wei have to remove from his playlist?

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d. A cabinetmaker can cut 325 wooden plugs from an 8-ft board. How many plugs can he

cut from 71 boards of the same size?

e. A mason lays an average of 121 bricks per hour. How many hours will it take him to lay

4356 bricks?

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1.2 ORDER OF OPERATION

1. Calculate showing each step.

a. 43 + 2 − 1

b. 72 − 23 − 6 c. 2 ÷ 4 × 8

d. 5 × (23

− 8) × 5

e. 1 + 4 − 4 f. 2

4 ÷ (18 ÷ 9) − 5

g. 3 + 12 + 4

h. 3 ×(23 +5) + 2 i. 8 + 7 + 2 − 9

2. Calculate showing each step.

a. 36−8−1

9 ÷ 3

b. 8+(4)(5)

(14 ÷7)× 2

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c. 8.8 ÷ 4 + (1.5 − 0.4)

d. (2.5)(4) − (2.1)(2)

e. (4)(8+2)

22

f. (7)(9)−3

6×[7−5]

g. (4.3 + 0.2) ÷ [1.4 − 0.9]

h. [6.4 − 4] ÷ (0.1 × 4)

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1.3 INTRODUCTION TO FRACTIONS

1. Label these measuring tapes with the correct lengths at the marks indicated. Remember to

include the correct units: inches or centimetres.

A. ______________ B. ______________ C. ______________ D. ______________

E. ______________ F. ______________ G. ______________ H. ______________

2. Label these measuring tapes at the following points, with an arrow and the letter of the

question.

a) 4" b) 11

2" c) 5

1

4" d) 10 cm e) 6.5 cm f) 13.3 cm

g) 63

8" h) 4

5

16" i) 7

17

32" j) 120 mm k) 188 mm l) 214 mm

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3. Circle the fractions below which can be reduced:

30/32 4/16 5/8 3/8 1⁄4 11/16 48/64 2/3 3/5 4/4

4. Reduce each fraction to its lowest terms.

a. 14

35

b. 18

45

c. 55

77

d. 22

38

e. 9

32 f.

16

64

g. 6

16

h. 21

35 i.

75

225

5. Connect each improper fraction and mixed number on the left with its equivalent on the right.

a. 𝟏𝟑

𝟒 𝟐

𝟑

𝟒

b. 𝟑𝟏

𝟐

𝟕𝟐

𝟒𝟖

c. 𝟏𝟏

𝟒

𝟏𝟒

𝟖

d. 𝟑𝟔

𝟏𝟔 𝟏𝟓

𝟏

𝟐

e. 𝟏𝟏

𝟐 𝟐

𝟏

𝟒

f. 𝟐𝟏

𝟑

𝟐𝟏

𝟗

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6. Which one is bigger? Add a less than (<) or more than (>) symbol between the sets of

numbers to show which number is bigger. Hint: You will need to have the numbers in the

same format in order to accurately compare them.

Ex. 25

9 <

24

9 𝟐

𝟓

𝟗=

𝟐𝟑

𝟗

𝟐𝟑

𝟗 <

𝟐𝟒

𝟗

a. 31

4

11

4

b. 43

10 4

2

10

c. 51

6

17

3

d. 45

8 6

e. 64

9 7

5

9

7. Plot the following fractions on the given number lines.

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1.4 MULTIPLYING FRACTIONS

1. Multiply the following fractions. Convert to a mixed number when possible and reduce

all fractions to lowest terms.

Ex. 5

3×

2

3

𝟓×𝟐

𝟑×𝟑=

𝟏𝟎

𝟗= 𝟏

𝟏

𝟗

a. 1

5×

5

6

b. 7

10×

5

6

c. 3

8×

2

7

d. 5 ×7

10

e. 15

64×

1

12

f. 3

16×

1

12

g. 8 ×1

24

2. Simplify the following fractions, then multiply. Always state the answer in its simplest

terms.

Ex. 2

6×

1

3

a. 5

18×

3

10

b. 18

25×

15

24

c. 21

35×

15

28

d. 15

66×

2

3

e. 63 ×2

3

f. 16 ×3

40

g. 32

39×

26

42

1 2

36

´1

3=1

9

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3. Multiply the following. . Always state the answer in its simplest terms.

a. 12

1 ×

6

5 = b. 1

3

10 ×

12

5 =

c. 2

1 × 1

3

1 = d. 3

16

1 ×

5

1 =

e. 18 × 12

1 = f. 16 × 2

8

1 =

g. 68

3 × 1

5

3 = h. 2

3

2 × 4

8

3 =

i. 49

4 × 4

4

2 = j. 3

8

1 × 2

5

2=

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4. Solve the following word problems and express your answer as a fraction. Reminder: Show

all of your work. Diagrams can be helpful.

a. A recipe for French toast that serves 6 calls for ½ cup granulated sugar, ¾ cup of evaporated milk, ⅓ teaspoon of vanilla, and 12 thick slices of French bread. How much of each ingredient is needed to serve twelve?

b. What is the total mass of 7 cast-iron pulleys if each has a mass of 3

10 kg?

c. One-quarter of an order of lumber is used to build steps. Of the remaining ¾ of the

order, 2

3 of it is used to build a small deck. What fraction of the original order was used

to build the deck?

d. The price of computers has fallen by 52 . If the price of a computer was originally

$10 275, by how much has the price fallen?

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e. Boll’s Electrical has a washing machine on sale for ⅓ off the regular price of $429. What is the sale price of the washing machine

f. For a family party, Tanisha made 52 of the desserts. If a total of 40 desserts were

brought to the party, how many did Tanisha supply?

g. While riding her bike, Susan burns 450 calories every ½ hour. Based on this rate, how

many calories will Susan burn if she rides the bike for 1¾?

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1.5 DIVIDING FRACTIONS

1. Find the reciprocal of each number.

a. 10

17 b. 6 c.

3

7 d. 23

2. Solve. Reminder: After changing the division into a multiplication, simplify the fractions

before solving.

Ex. 16 ÷2

3

8 16

1´3

21

=24

1= 24

a. 24 ÷3

8 b.

6

7÷ 3

c. 3

4÷

1

8 d.

4

5÷

24

35

e. 1

9÷

13

6 f.

7

2÷

14

3

g. 8

3÷ 6 h. 18 ÷

3

10

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3. Calculate the following. Give all answers in simplest form

a. 22

5× 1

5

6 b. 8 ÷ 2

4

7

c. 13

5× 3

3

4 d. 4

6

9÷ 1

6

21

e. 71

3÷ 3

1

2 f. 7

1

2× 2

2

3

g. 4

5÷ 4

3

5 h. 6

3

4÷ 3

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4. Solve the following word problems.

a. Five boards each 75

8 in. long are needed. If they are to be cut from one board,

how long must the board be? Allow 1 in. for waste.

b. How many shelves for a bookcase can be cut from a board 153

4 ft long if each shelf

is to be 31

4 ft?

c. Jackson bought cheese that weighs ¾ pound. If she divides it into portions that

are each 1

8 pound, how many portions can he make?

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1.6 ADDING AND SUBTRACTING FRACTIONS

1. Add or subtract the following fractions. Give al answers in simplest form.

a. 9

11+

7

11= b.

7

12+

7

12=

c. 4

5−

1

5= d.

6

8−

1

8=

e. 2

5+

4

5= f,

7

8+

5

8=

g. 6

7−

2

7=

h. 18

21−

11

21=

2. Label the mark for the first number in each question on the measuring tapes. Then, add

the two numbers by moving to the right by the second number. Lastly, mark the total on the same measuring tape.

Example: 15

8+ 1

7

8= 3

1

2

a. 2

1

4+ 1

1

4=

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b. 11

8+ 2

3

4=

c. 33

16+

1

2=

d. 31

2+ 2

5

16=

3. Add or subtract the following fractions. Give al answers in simplest form.

a. 4

7−

2

5= b.

3

8+

1

3=

c. 7

10+

1

3= d.

3

4−

1

5=

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e. 8

12−

3

14= f.

3

21+

5

63=

g. 10

18−

8

21= h.

13

21−

7

28=

4. Add or subtract the following fractions. Give all answers in simplest form.

a. 21

3− 1

1

2= b. 3

2

3+ 1

1

2=

c. 5 − 35

8= d. 3

13

18− 2

6

21=

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e. 42

9+ 2

13

18= f. 12

5

16− 9

7

12=

5. Answer the following questions. Express your answers using a fraction.

a. A business is owned by three people. The first person owns 5

12 of the business,

and the second person owns 1

3 of the business. What portion of the business

does the third person own?

b. Lorena poured 22

3 cups of milk in her measuring cup. But she only needed 1

1

4

cups of milk. She wants to pour the amount of milk she does not need back in the milk carton. How much should she pour back?

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c. A bolt extends through ¾” thick plywood, a washer that is ⅛” thick, and a nut that is 16

3 ” thick. The bolt should be ⅝” longer than the sum of the thickness of

the plywood, washer and nut. What is the minimum length of the bolt?

d. Seth earns $560 per week. He has 51 of his income withheld for federal taxes,

151 of his income withheld for provincial taxes, and 25

1 of his income withheld

for medical coverage. How much income is left each week after those deductions?

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1.7 ORDER OF OPERATIONS WITH FRACTIONS

1. Solve. Show all steps.

a.

b.

c.

d.

e.

f.

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g.

h.

i.

j.

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k.

l.

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UNIT 1 – ANSWER KEY

SECTION 1.1

1.a. 63 b. 192 c. 935 d. 794 e. 606 2.a. 57 b. 86 c. 459 d. 998 e. 755 3. Strategies may vary a. 42 b. 17 c. 34 d. 36 e. 27 f. 19 4. x + 4 4x 4(y + 7) 3w – 5 5x + 6 8 – t t + 8 y – 10 x / 2 y + 10 1/3 x w – 12 12w 4 / x z / 12 8 / x w + 12 2y 4a. $710 b. 119” c. 6 songs d. 23 075 plugs e. 36 hours.

SECTION 1.2

1. a.65 b. 35 c.4 d. 0 e.1 f.3 g.8 h.41 i. 8 2. a. 9 b. 7c. 3.3 d. 5.8 e. 10 f. 5 g.9 h. 6

SECTION 1.3

1. A. 3 /4” B. 2 1/8” C. 3 7/8” D. 5 “ E. 2 cm 20mm F. 5.5 cm 55 mm G. 9.2 cm 92 mm

H. 11.6 cm 116 mm 3. 30/32 4/16 48/64 4/4 4. a. 2

5 b.

2

5 c.

5

7 d.

11

19 e.

9

32 f.

1

4 g.

3

8

h. 3

5 i. 1

3 5. a.

14

8 b. 15

1

2 c. 2

3

4 d. 2

1

4 e.

72

48 f.

21

9 6. a. > b. > c. < d. < e. <

SECTION 1.4

1. a. 1

6 b.

7

12 c.

3

28 d. 3

1

2 e.

5

256 f.

1

64 g.

1

3 2. a.

1

12 b.

9

20 c.

9

28 d.

5

33 e. 42 f. 1

1

5 g.

32

63

3. a. 1 ¼ b. 13/24 c. 2/3 d. 49/80 e. 27 f. 34 g. 10 1/5 h. 11 2/3 i .20 j. 7 ½

4. a. sugar 1 cup milk 1 ½ cups vanilla 2/3 t bread 24 slices b.21

10kg c.

1

2 d.$4110

e. $286 f. 16 g. 1575 cal.

SECTION 1.5

1. a. 17/10 b. 1/6 c.7/3 d. 1/23 2. a. 64 b. 2

7 c. 6 d. 1

1

6 e.

2

39 f.

3

4 g.

4

9 h. 60

3. a. 4 2/5 b. 3 1/9 c. 6 d. 3 17/27 e. 2 2/21 f. 20 g. 4/23 h. 2 1/4 4. a.39 1/8” b. 4 c. 6

SECTION 1.6

1. a. 1 5/11 b.1 1/6 c. 3/5 d. 5/8 e. 1 1/5 f. 1 ½ g. 4/7 h. 1/3 2. a.3 ½ b.3 7/8 c. 3 11/16 d. 5 13/16 3. a. 6/35 b.17/24 c. 1 1/30 d.11/20 e. 19/42 f.2/9 g.11/63 h.

31/84 4. a. 5

6 b. 5

1

6 c. 1

3

8 d. 1

55

126 e. 6

17

18 f. 2

35

48 5.a.

1

4 of the business b. 1

5

12 c. c. 1

11

16 “ d. $388.27

SECTION 1.7

1. a. 35

9 b. 1

7

20 c.

16

65 d.

89

100 e.

3

8 f.

27

32 g. 1

1

6 h.1

19

35 i.

49

81 j.

13

30 k.

3

4 l .

52

75

wmath 11 name: unit learning guide review fractions

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