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A beehive increases by 7% a day.

Level 7-8 Numbers - Percentages - Increases and Decreases

Percentages help compare changes. Learn to increase or decrease amounts, find multipliers, and reverse percent changes in realistic KS3 money and measure problems.

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Fascinating Fact:

Inflation uses percentage increases to show how prices change over time. A 3 percent annual rise adds £3 to every £100 spent.

In KS3 Maths, you’ll calculate percentage increases and decreases using multipliers, compare discounts, and solve reverse-percentage problems. Expect money, measures, and data contexts where clear working and sensible rounding matter.

Key Terms

Percentage change: How much a value increases or decreases compared with the original, expressed per 100.
Multiplier: A single number to apply a percentage change, e.g., increase by 12% → multiply by 1.12; decrease by 12% → multiply by 0.88.
Reverse percentage: Finding the original amount by dividing the final amount by the multiplier used.

Frequently Asked Questions (Click to see answers)

How do I increase a number by a percentage?

Use a multiplier of 1 + (percentage/100). Example: increase £240 by 15% → £240 × 1.15 = £276.

How do I decrease a number by a percentage?

Use a multiplier of 1 − (percentage/100). Example: decrease £80 by 25% → £80 × 0.75 = £60.

How do I find the original price before a percentage change?

Divide by the multiplier. Example: £45 after 10% off means original = £45 ÷ 0.90 = £50.

Try These Related Quizzes

1 .

A beehive increases by 7% a day. Initially there are 1,250 bees. How many will there be after a week?

1,620

1,800

2,000

2,007

A calculator is helpful for this kind of calculation! This problem is an example of compound increase. Problems like this can be solved using the compound interest formula:

M = P( 1 + i )n

Here, M = the final number of bees; P = the initial number of bees; i = the percentage increase (if it is a decrease, it will be negative; n = the number of days (but it could be weeks/months/years or any time period, depending on the problem) and it is the POWER to which (1 + i) has to be raised. Plug in the numbers and do the calculation

2 .

Barbara bought a box of 35 pens for £40.25. She sold all the pens for £1.70 each. What was her percentage profit?

39.4%

40.7%

45.8%

47.8%

Not a bad little earner!

3 .

Due to severe weather, a polar bear colony goes from 328 bears to 246. What percentage decrease is this?

20%

22%

25%

26%

Remember, the change is always compared with the original value

4 .

Michelle bought a caravan for £13,500 and sold it two years later for £11,200. What is the percentage loss?

13%

14%

15%

17%

13,500 - 11,200 = 2,300
(13,500 ÷ 2,300) x 100 = 17.037....

5 .

What percentage of 68 is 10.2?

17.5

68 ÷ 100 = 0.68
10.2 ÷ 0.68 = 14.70588235294118....

6 .

A burger now costs £3.75 after a 3% reduction in price. What was the original price of the burger?

£2.88

£3.17

£3.87

£4.44

3.75 ÷ 97 = 0.0387
0.0387 x 100 = 3.87

7 .

Pete's hourly wage goes up from £7.20 to £7.56. What percentage increase is this?

The increase is 36p. To work out the percentage 0.36 / 7.2 = 0.05 = 5%

8 .

The price of a concert ticket is £33 after a 7% increase. What is the original price of the ticket?

£30.84

£31.11

£33.65

£34.86

33 ÷ 107 = 0.3084
0.3084 x 100 = 30.84

9 .

The Green family bought a house five years ago for £97,000. They sell it for £185,000. What is their percentage profit (to the nearest 1%)?

81%

85%

89%

91%

185,000 - 97,000 = 88,000
97,000 ÷ 100 = 970
88,000 ÷ 970 = 90.722

10 .

What percentage is 8.5 of 68?

12.5

13.5

8.5 ÷ 0.68 = 12.5

You can find more about this topic by visiting BBC Bitesize - Percentages

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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