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Simplifying Ratios


We like to express ratios as whole numbers, using the simplest numbers possible. We simplify ratios in a similar way to how we simplify fractions. To do this, we often divide by the highest common factor (HCF). For example, let's look at how to simplify the ratio $3:15$3:15.

The HCF between $3$3 and $15$15 is $3$3, so we're going to divide both numbers by $3$3.

So $3:15=1:5$3:15=1:5 and $1:5$1:5 is the simplified ratio.



When we're simplifying ratios, we have to keep them equivalent (i.e. multiply or divide both sides by the same number).


Or, if our ratio contains fractions, we need to multiply by the denominator to get a whole number. 

For example, let;s simplify the ratio $4:\frac{1}{2}$4:12:

$4:\frac{2}{3}$4:23 $=$= $12:2$12:2 (Both sides of the ratio have been multiplied by 3 to remove the denominator)
  $=$= $6:1$6:1 (Both sides were divided by 2 to simplify the ratio)



Before you simplify a ratio, you need to make sure you have both quantities in the same unit of measurement. For example, if one side of your ratio is in kilograms and the other is in grams, you need to convert one side so that they are both in kilograms or both in grams.


Worked Examples

Question 1

Simplify the ratio $10:24$10:24

Question 2

Simplify the ratio $12:45:18$12:45:18

Question 3

Express $5$5 years to $33$33 months as a simplified ratio.


Question 4

Simplify the ratio $11x:18x$11x:18x.



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