In KS3 Maths, comparing numbers comes in many forms – bars in a graph, sectors in a pie chart, or figures in a table. One of the easiest and most common ways is using ratios.

Imagine Person A has £50 and Person B has £40. How much more does A have? Ratios help us compare. A has £10 more, but that doesn't really show the comparison well. Ratios, like 50:40, are handy. Since 50 and 40 share a factor of 10, it simplifies to 5:4, the simplest form.

Discover the Joy of Learning with Quizzes1.

Divide 240 litres in the ratio 3 : 5.

50 : 150

80 : 140

90 : 150

90 : 170

3 + 5 = 8 so first divide 240 litres by 8 then multiply by both 3 and 5

2.

The ratio of two bags of flour is 3 : 4. If the smaller bag holds 900 g of flour, how much does the larger bag hold?

1,000 g

1,100 g

1,200 g

1,300 g

A ratio such as 3:4 means 3/7 of one thing and 4/7 of another thing. The 7 comes from adding 3 and 4. The ratio 3:4 can also be written as a fraction 3/4 for calculations. In this case 900/x = 3/4 where x is the big bag of flour: so x = (4 x 900)/3. Use this method when dealing with ratios

3.

A drink is made from orange juice and lemonade in the ratio 3 : 7. How much lemonade is needed if 60 ml of orange juice is used?

110 ml

120 ml

130 ml

140 ml

60 ml / 3 = 20 ml and 7 x 20 ml = 140 ml

4.

Dean buys 75 shares for £262.50. How much would 325 shares cost Dean?

£1,037.10

£1,137.50

£1,317.50

£1,731.40

25 is a good figure to work with here - just divide £262.50 by 3 to find what 25 shares would cost, and go from there

5.

15 pints of milk cost £7.80. What is the cost of 22 pints of milk?

£10.80

£11.44

£14.44

£15.03

15 : 22 is roughly 2 : 3. £7.80 ÷ 2 = £3.90 so you know your answer will be approximately £3.90 x 3 = £11.70

6.

What is 12 kg : 4,800 g in its simplest form?

5 : 2

6 : 3

7 : 4

8 : 5

It may be easier to first convert 12kg into 12,000g

7.

What is 150 cm : 4 m in its simplest form?

2 : 7

3 : 8

4 : 9

5 : 9

The common factor is 50 cm. There are 3 x 50 cm in 150 cm and there are 8 x 50 cm in 4 m

8.

What is £8 : 420p in its simplest form?

13 : 25

17 : 28

19 : 33

40 : 21

The quantities in the ratio MUST be in the same units: in this case change the £8 to 800p

9.

A road map is drawn to a scale of 1 cm = 8 km. A distance of 6.5 cm on the map represents how many kilometres of the road?

52 km

56 km

65 km

81 km

The ratio for a 1cm = 8km scale is 1 : 800,000!

10.

Divide £85 in the ratio 1 : 4.

£17 : £68

£23 : £62

£40 : £45

£60 : £25

Remember the two numbers must total £85

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