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# Simplifying ratios

A ratio is written in reduced form if the numbers in the ratio have no common factor.

$\Tblue{4:3}$ is in reduced form

$\Tgreen{20:25}$ is not reduced because $\Tred{5}$ is a common factor.

To reduce a ratio, find the highest common factor (HCF) of the numbers and divide the numbers by it.

The reduced form of $\Tgreen{20:35}$ is $\Tblue{4:7}$ because $\HCF(\Tgreen{20},\Tgreen{35}) = \Tred{5},\quad \Tgreen{20} = \Tblue{4}\times \Tred{5},\quad \Tgreen{35} = \Tblue{7}\times \Tred{5}.$

A TV screen has a width of $\Tblue{48}$ cm and a height of $\Tgreen{27}$ cm. Its width to height ratio is $\Tblue{48}:\Tgreen{27}= \Tblue{16}\times\Tred{3}:\Tgreen{9}\times\Tred{3} = \Tblue{16}:\Tgreen{9}.$

This television has an aspect ratio of 16:9. This refers to the lengths of its sides. The ratio 16:9 is in its simplest form.