Ratio and Proportion

Ratio A ratio compares the sizes of parts or quantities to each other. What is the ratio of red counters to blue counters? red : blue = 9 : 3 = 3 : 1 For every three red counters there is one blue counter.

What is the ratio of red counters to yellow counters to blue counters? Ratio red : yellow : blue = 12 : 4 : 8 = 3 : 1 : 2 For every three red counters there is one yellow counter and two blue counters.

Simplifying ratios Ratios can be simplified like fractions by dividing each part by the highest common factor. 21 : 35 = 3 : 5 ÷ 7 For a three-part ratio all three parts must be divided by the same number. 6 : 12 : 9 = 2 : 4 : 3 ÷ 3

Dividing in a given ratio A ratio is made up of parts. We can write the ratio 2 : 3 as: 2 parts : 3 parts The total number of parts is: 2 parts + 3 parts = 5 parts Divide £40 in the ratio 2 : 3. £40 ÷ 5 = £8 We need to divide £40 by the total number of parts.

Proportion There are many ways to express a proportion. We can express this proportion as: 12 out of 163 in every or75% Proportion compares the size of a part to the size of a whole. What proportion of these counters are red?

Direct proportion problems 3 packets of crisps weigh 90 g. How much do 6 packets weigh? 3 packets weigh 90 g. × 2 6 packets weigh × g. If we double the number of packets then we double the weight. The number of packets and the weights are in direct proportion.

Now try these: Divide:

Answers: 1.6:42. 16:43. 10:44. 18: : : :68. 50: : : : : : : : :8:417. 6:4: :20: :10: :9: :21: :24: :36: :28: :24: £80, £ :9: :8: :150: :10:12.5