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Middle Years

4.05 Percentage increase and decrease

Worksheet
Addition and subtraction in percentage change
1

Here is a grid of 100 blue squares. Each small square represents 1\% of the total:

a

Choose the image that represents 3\% more than the original grid:

A
B
C
D
b

Describe what was done to the original grid to increase it by 3\%.

c

Write an expression to represent the 3\% increase in squares.

d

Choose the image that represents 6\% less than the original grid:

A
B
C
D
e

Describe what was done to the original grid to decrease it by 6\%.

f

Write an expression to represent the 6\% decrease in squares.

2

Bob wants to decrease 110 by 60\%.

a

Calculate 60\% of 110.

b

Should Bob add or subtract the amount from part (a) from 110? Explain your answer.

c

Hence, decrease 110 by 60\%.

3

Lucy wants to increase 70 by 60\%.

a

Calculate 60\% of 70.

b

Should Lucy add or subtract the amount from part (a) from 70? Explain your answer.

c

Hence, increase 70 by 60\%.

Percentage increase
4

Increase:

a

80 by 5\%.

b

120 by 10\%.

c

72 by 40\%.

d

320 by 25\%.

e

\$140 by 9\%.

f

\$30\,000 by 20\%.

g

80\text{ km} by 15\%.

h

400\text{ mL} by 35\%.

5

Abed wants to increase 1500 by 30\%.

a

Calculate 30\% of 1500 and add the answer to 1500.

b

Calculate 130\% of 1500.

c

Are your answers to (a) and (b) the same? Explain why this is.

6

Tracy wants to increase 80 by 30\%.

a

What single percentage should she multiply 80 by?

b

Explain how you got your percentage in part (a).

7

What single percentage should a quantity be multiplied by in order to increase the quantity by:

a
17\%
b
5\%
c
40\%
d
9.4\%
e
33\%
f
127\%
g
38\%
h
212\%
8

Evaluate the following using a single percentage:

a

Increase 80 by 60\%

b

Increase 400 by 45\%

c

Increase 900 by 8\%

d

Increase 80 by 40\%

e

Increase 1200 by 45\%

f

Increase 1200 by 8\%

9

A bag of rice weighs 120 \text{ kg}. The company who makes these bags decides to increase their weight by 45\%. Find the new weight of the bag.

Percentage decrease
10

Decrease:

a

70 by 8\%.

b

260 by 10\%.

c

96 by 60\%.

d

250 by 20\%.

e

\$480 by 18\%.

f

\$55\,000 by 45\%.

g

200\text{ km} by 22\%.

h

650\text{ mL} by 30\%.

11

Derek wants to decrease 120 by 70\%.

a

What single percentage should he multiply 120 by?

b

Explain how you got your percentage in part (a).

12

What single percentage should a quantity be multiplied by in order to decrease the quantity by:

a
17\%
b
5\%
c
40\%
d
9\%
e
32\%
f
52\%
g
38\%
h
65\%
13

Evaluate the following using a single percentage:

a

Decrease 80 by 60\%

b

Decrease 400 by 45\%

c

Decrease 900 by 8\%

d

Decrease 80 by 40\%

e

Decrease 1200 by 45\%

f

Decrease 1200 by 8\%

14

A discus thrower has a personal best of 60 \text{ m}. In their most recent competition they fall short of their personal best by 30\%. Find the distance of their throw in this competition.

Percentage change
15

A percentage increase was applied to the number 60 in order to get 108.

a

Find how much was added to 60 to get 108.

b

Express the increase as a percentage of 60.

16

A percentage increase was applied to the number 180 in order to get 207.

a

Find how much was added to 180 to get 207.

b

Express the increase as a percentage of 180.

17

A percentage decrease was applied to the number 90 in order to get 27.

a

Find how much was subtracted from 90 to get 27.

b

Express the decrease as a percentage of 90.

18

A percentage decrease was applied to the number 180 in order to get 117.

a

Find how much was subtracted from 180 to get 117.

b

Express the decrease as a percentage of 180.

19

In training for her next marathon, Sally increased her practise route from 7000 \text{ m} to 7910 \text{ m}. What percentage has Sally increased the distance of her practice route by?

20

Luke's record for juggling a football was 70 keep ups. After buying some new football boots, this increased to 112. Express this increase as a percentage of the original record.

21

Sharon's daily pay was \$150. When she began working shorter hours in order to study, her pay decreased to \$90 per day. Express this decrease as a percentage of her original pay.

22

Jimmy had a bowling high score of 60 points. After practising for a week, this increased to 93. Express this increase as a percentage of his original high score.

23

Sophia is able to write 220 words in a minute. After sustaining a thumb injury, this decreased to 143 words a minute. Express this decrease as a percentage of her original rate.

24

During the editing phase when making a movie, the director ordered that the movie be cut down from 200 minutes to 124 minutes. What percentage did the movie's duration decrease by from its original length?

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