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Number (Intermediate) - Ratio
 
Simplifying Ratios | Dividing in a Given Ratio | Finding the Missing Value
 

Simplifying Ratios

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

Example 1: Writing down and simplifying a ratio.

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

Jane
  
Sally
  
80
:
120
  

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.

80
:
120
  
÷
40
  
2
:
3
  

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

If the units are different, for example 90cm : 1.5m, then they must be changed to the same as below.

90
:
150
  
 
÷
30
3

:
5
  

 

Dividing in a Given Ratio

Example 1: Share £80 between Tim and Jack in the ratio 3 : 5.

This means that Tim gets 3 parts and Jack gets 5 parts.

3 + 5 = 8 parts altogether

So £80 ÷ 8 = £10
   (the value of one part)
     
Tim = 3 parts so 3 x 10 = £30
 and
 Jack = 5 parts so 5 x 10 = £50

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.

 

Finding the Missing Value

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

The longer section = 3 parts

3 parts = 15cm

1 part = 15 ÷ 3 = 5cm

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