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Dividing up into a Ratio (Proportional Division)
In fractions you divide a whole into parts. Dividing a cake by 3 gives 3 equal
parts. If you take 2 of the parts you have two-thirds leaving just one-third of the
cake. The result is that you have separated the cake into two unequal ‘portions’.
The portion that you have (the two-thirds) is twice as big as the portion you left.
The ratio is two-thirds to one-third or 2 to 1.
What you have done is divided the cake in the ratio of 2 to 1. You can probably
think of other examples, such as a will, where the inheritance is divided between
the beneficiaries.
Adding quantities in a ratio is similar, such as a recipe for a cake or mixing sand
and cement in the correct proportions.
The method of doing proportional division is explained in the following
examples.
Example 1
Divide £500 in the ratio 2:3
1.
Add the numbers in the ratio to find the total number of parts:
2 + 3 = 5
2.
Divide the amount by the total number of parts to find the size of each part:
£500 ÷ 5 = £100
3.
Multiply the size of one part by the number of parts as given in the ratio, in
this case 2 and 3:
£100 × 2 = £200
£100 × 3 = £300
4.
Check (optional) that the resulting amounts add up to the given total:
£200 + £300 = £500
The two portions are £200 and £300.
The Method of One - In the above we used the method of one, also called the
unitary method. First, you divide the total amount by 5 to calculate the amount
for one part. Then, to calculate the amount for 2 of the 5 parts, you multiply the
unit amount by 2.
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