There are three ways to represent fractions of numbers - fractions, decimals and percentages. Percentages are a part of everyday life and you'll need to be able to calculate increase and decreases in percentages if you ever want to understand interest rates or pay rises!

To calculate a percentage increase, first divide the percentage by 100 and then multiply by the original figure. So, to find a 5% increase on £800, first divide 5 by 100 (0.05) and then multiply by 800 to get 40. Add this to the original figure to get £840.

To calculate a percentage decrease, follow the same steps but this time subtract 40 from 800 to give an answer of £760.

Put your numbers hat on and practise with the following quiz increases and decreases in percentages. If you can get the full 100% in this quiz, you've cracked it!

1.

What percentage is 8.5 of 68?

12

12.5

13

13.5

8.5 ÷ 0.68 = 12.5

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.

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

3%

4%

5%

6%

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

4.

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

97,000 ÷ 100 = 970

88,000 ÷ 970 = 90.722

5.

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

0.0387 x 100 = 3.87

6.

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

0.3804 x 100 = 38.84

0.3804 x 100 = 38.84

7.

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

8.

What percentage of 68 is 10.2?

15

17

17.5

20

68 ÷ 100 = 0.68

10.2 ÷ 0.68 = 14.70588235294118....

10.2 ÷ 0.68 = 14.70588235294118....

9.

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

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

10.

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....

(13,500 ÷ 2,300) x 100 = 17.037....

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