In KS3 Maths you'll come across many ways of comparing numbers - bars in a graph, sectors in a pie chart, figures in a table. Perhaps the easiest, and most common, ways to compare numbers is by using ratios.

If one person (Person A) has £50 and another (Person B) has £40 then how much more does the first person have? How do the two amounts compare to one another? Well, we can say that Person A has £10 more than Person B but that doesn't relate the two amounts very well. £10 is only a tiny figure out of £1,000 yet a large amount of £15. Ratios are a nifty way of comparing quantities. In our example the ratio is 50 : 40. Because the numbers 50 and 40 have a common factor of 10, this can be cancelled down to 5 : 4, known as the simplest form.

Ratios allow us to quickly compare different quantities. Try this quiz and see how well you can cope with ratios. Take your time and read each question carefully before choosing your answers. Good luck!

1.

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.

Divide £85 in the ratio 1 : 4.

£17 : £68

£23 : £62

£40 : £45

£60 : £25

Remember the two numbers must total £85

3.

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

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.

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

6.

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

7.

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

8.

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

9.

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

10.

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!

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