Simplifying Ratios

This is one of the three types of questions that learners can get on ratio.

Example 1: Writing down and simplifying a ratio.

Jane and her sister Sally are 80 cm and 120 cm tall respectively. Write down the ratio of their heights.

Write down the numbers given with  :  in between. They must be in the same units.

Then simplify by dividing both sides by the same number.

The ratio of Jane's height to Sally's is 2 : 3.

If the units are different, for example 90 cm : 1,5 m, then they must be changed to the same as below.

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Dividing in a Given Ratio

Example 1: Share R80 between Tsepo and Pravesh in the ratio 3 : 5.

This means that Tsepo gets 3 parts and Pravesh gets 5 parts.

3 + 5 = 8 parts altogether.

The rules for this operation are as follows:

a) Add the numbers in the ratio.
b) Divide the amount by this total.
c) Multiply the numbers in the ratio by this value.

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Finding the Missing Value

Example 1: A line is divided in the ratio 2 : 3. If the longer section is 15 cm long, how long is the shorter section?

The longer section = 3 parts.

3 parts = 15 cm

1 part = 15 ÷ 3 = 5 cm

The shorter section = 2 x 5 cm = 10 cm.

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