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75% is exactly the same as ³⁄₄

Percentages 2 (Difficult)

Welcome to the second of our difficult Eleven Plus maths quizzes on percentages. In the first, you were asked to express one number as a percentage (or proportion) of another – I hope you didn’t find it too hard! In this quiz, we’ll offer you more chance to practice.

There is a simple way to do it. Here’s an example:

What percentage of 20 is 4?
First, arrange the problem like this :
(4 ÷ 20) × 100%
Next, you can make it easier by turning it around, like this:
(4 × 100) ÷ 20
Work out the part in brackets:
400 ÷ 20
This gives you the answer = 20%

Just follow this formula and percentages should be simple. So, now you are ready, let’s begin. Good luck!

1 .

What percentage of 300 is 15?

(15 ÷ 300) × 100% = (15 × 100) ÷ 300 = 5%

2 .

If 7 pupils in a class of 28 fail their maths test, what percentage of the class does this represent?

15%

20%

25%

33.33%

(7 ÷ 28) x 100% = (7 × 100) ÷ 28 = 25%

3 .

What percentage of 56 is 12?
(Give your answer to two decimal places)

30%

27.33%

25%

21.43%

(12 ÷ 56) x 100% = (12 × 100) ÷ 56 = 21.43%

4 .

If 2 out of 12 people have green eyes, what percentage does this represent?
(Give your answer to two decimal places)

16.66%

21.33%

26.66%

33.33%

(2 ÷ 12) x 100% = (2 × 100) ÷ 12 = 16.66%

5 .

What percentage of 16 is 72?

22.22%

450%

44.44%

400%

(72 ÷ 16) x 100% = (72 × 100) ÷ 16 = 450%.
In ‘top-heavy’ fractions (e.g. ⁷²?₁₆), the percentage will be more than 100%

6 .

What percentage of 250 is 187.5?

85%

80%

75%

70%

(187.5 ÷ 250) x 100% = (187.5 × 100) ÷ 250 = 75%.
Decimal numbers are surprisingly easy to work with – multiplying them by 100 just means moving the digits two places to the left

7 .

What percentage of 270 is 54?

27.5%

25%

22.5%

20%

(54 ÷ 270) x 100% = (54 × 100) ÷ 270 = 20%

8 .

Of the 12,500 spectators at a football match, 1,000 came to support the away team and the rest came to support the home team. What percentage of the crowd followed the home team?

92%

64%

36%

(1,000 ÷ 12,500) x 100% = (1,000 × 100) ÷ 12,500 = 8%.
This tells you the proportion of away fans. To find the proportion of home fans, simply subtract 8 from 100:
100 – 8 = 92%

9 .

If, in a survey on holiday destinations, 24 out of 1,000 people said they went to Canada for their holiday this year, what percentage does this represent?

24%

2.4%

0.24%

0.024%

To convert parts of 1,000 to percentages, simply divide by 10

10 .

A company has a workforce of 748. Of these, 68 work in the offices and the rest work on the shop floor. What percentage of the workforce work in the offices?
(Give your answer to two decimal places)

15.15%

12.12%

9.09%

6.06%

(68 ÷ 748) x 100% = (68 × 100) ÷ 748 = 9.09%

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