KS3 Maths · Year 7 · Chapter 4: Percentages · Lesson 3

Calculating a percentage change

Year 7About 60 minutesCalculator allowed48 marks

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Quick questions to start.

A1
Needed today
Write $1.4$ as a percentage.
[1 mark]
Answer
A2
Needed today
Write $35$ out of $140$ as a percentage.
[1 mark]
Answer
A3
Last lesson
What is the multiplier for a decrease of $12%$ ?
[1 mark]
Answer
A4
From chapter 1
Find the highest common factor of $24$ and $36$ .
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

The price of a phone goes up from $£160$ to $£208$ . Work out the percentage increase.

Hint old value

\times

multiplier

=

new value, so the multiplier is new

\div

old.

B1
A puppy's mass goes up from $4.5$ kg to $6.3$ kg. Work out the percentage increase.
[2 marks]
Answer

Example 2

In a sale a washing machine is reduced from $£450$ to $£378$ . Work out the percentage reduction.

Hint The multiplier is less than

1

for a decrease. The decrease is

100%

take away the multiplier as a percentage.

B2
The number of members of a club falls from $125$ to $95$ . Work out the percentage decrease.
[2 marks]
Answer

Example 3

A charity raised $£850$ in one year and $£2125$ the next year. Work out the percentage increase.

Hint The multiplier is more than

2

, so the increase is more than

100%

B3
The number of people living in a village rises from $3600$ to $8820$ . Work out the percentage increase.
[2 marks]
Answer

Example 4

Chloe's time for a race goes down from $1$ hour $20$ minutes to $1$ hour $8$ minutes. Work out the percentage decrease.

Hint Change both times into minutes first.

B4
A journey takes $2$ hours $15$ minutes. After a new road opens, it takes $1$ hour $48$ minutes. Work out the percentage decrease in the time.
[3 marks]
Answer

Practice

Year 7

C1
A number changes from $64$ to $56$ . Is this an increase or a decrease? By what percentage?
[2 marks]
Answer
C2
A bus fare goes up by $30$ p, from $£2.40$ to $£2.70$ . Work out the percentage increase.
[2 marks]
Answer

C3
Tom's pay goes up from $£2430$ to $£2575$ a month. Work out the percentage increase, to $1$ decimal place.
[2 marks]
Answer
C4
A shop sold $840$ games in May and $966$ games in June. Work out the percentage change.
[2 marks]
Answer
C5
A house price goes up from $£150 000$ to $£180 000$ . A car price goes up from $£8000$ to $£10 000$ . Which has the greater percentage increase? Show your working.
[3 marks]
Answer

Exam-style questions

GCSE Foundation

D1
The number of birds visiting a garden falls from $80$ to $60$ . Leo says, "That is a $33%$ decrease, because $20$ out of $60$ is about $33%$ ."
Is Leo correct? Give a reason for your answer.
[3 marks]

D2
The table shows the number of votes for three parties in two elections.
(a)
Work out the percentage change in the votes for the Red party. Say whether it is an increase or a decrease.
[2 marks]
Answer
(b)
Work out the percentage change in the votes for the Green party. Say whether it is an increase or a decrease.
[2 marks]
Answer
(c)
Which party had the greatest percentage change in its votes?
[1 mark]
Answer
Total for D2: 5 marks
D3
The price of a sofa goes up from $£560$ to $£644$ .
(a)
Show that the multiplier for this change is $1.15$ .
[1 mark]
(b)
Write down the percentage increase.
[1 mark]
Answer
(c)
In a sale the price of the sofa is reduced from $£644$ to $£483$ . Work out the percentage reduction.
[2 marks]
Answer
Total for D3: 4 marks
D4
In a sale every price is reduced by $£30$ .
(a)
A coat was $£150$ . Work out the percentage reduction for the coat.
[2 marks]
Answer
(b)
Ella says, "Every item has the same percentage reduction, because they all have $£30$ off." Use an item that was $£600$ to show that Ella is wrong.
[2 marks]
Total for D4: 4 marks
D5
A car was worth $£12 000$ when it was new. After $3$ years it was worth $£7680$ .
(a)
Work out the percentage decrease in its value.
[2 marks]
Answer
(b)
In the next year its value fell by a further $25%$ . Work out the total percentage decrease from when the car was new.
[2 marks]
Answer
Total for D5: 4 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
The prices in a shop go up by $20%$ one year and by $25%$ the next year. Work out the total percentage increase over the two years.
[4 marks]
Hint 1 · What to try
Choose a price to try, for example $£100$ , and follow it through both years.
Hint 2 · The first line
After the first year $£100$ becomes $£120$ . In the second year the $25%$ is taken of $£120$ .
Hint 3 · The full method
$120 \times 1.25 = 150$ , so $£100$ became $£150$ : a $50%$ increase, not $45%$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out a percentage increase from an old and a new value.
I can work out a percentage decrease from an old and a new value.
I can work out increases of more than 100%.
I can explain why a change is compared with the original value.

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