We can simplify ratios in a similar way to fractions. If we divide all parts by the same amount we are keeping the ratio equivalent.
Examples:
1) 10:20 divide both sides by 10 we get 1:2 this is simplified.
2) 27:36 divide both sides by 9 we get 3:4
3) 24:64:16 divide all parts by 8 we get 3:8:2
We can also divide in a ratio
Examples:
1) Share £200 between Anna and Bob in the ratio 1:3
There are 4 parts all together (1 + 3 = 4) so divide the original amount by the number of parts £200 divide 4 = £50 so Anna gets 1 part = £50 and Bob gets 3 x £50 = £150 their amounts add up to the starting amount.
2) Share £1000 between Carl, Dave and Emma in the ratio 2:3:5
2 + 3 + 5 = 10
£1000 divide 10 = £100
Carl gets 2 x £100 = £200
Dave gets 3 x £100 = £300
Emma gets 5 x £100 = £500.
Direct Proportion
Lots of questions involving direct proportion are either about ingredients or the cost of items.
Examples:
1) This is a list of ingredients needed to make 24 scones
600g flour
100g dried fruit
250g butter
Water to mix
a) How much dried fruit is needed for 6 scones?
1st see how the number of scones the ingredients are for relates to the amount in the question.
6 scones is a quarter of the original 24 so we divide the amount of dried fruit in the original list of ingredients.
100g divide 4 = 25g of dried fruit to make 6 scones
b) How much flour would you need for 36 scones?
36 scones is 1.5 times as many as the list of ingredients so multiply the amount of flour by 1.5 (or add half as much on again)
600g x 1.5 = 900g of flour needed to make 36 scones
