# Equivalent ratios and simplest form

If you are making orange squash and you mix one part orange to four parts water, then the ratio of orange to water will be $$1:4$$ ($${1}$$ to $${4}$$).

• If you use $${1}$$ litre of orange, you will use $${4}$$ litres of water $$(1:4)$$.
• If you use $${2}$$ litres of orange, you will use $${8}$$ litres of water $$(2:8)$$.
• If you use $${10}$$ litres of orange, you will use $${40}$$ litres of water $$(10:40)$$.

These ratios are all equivalent:

$1:4~=~2:8~=~10:40$

Both sides of the ratio can be multiplied or divided by the same number to give an equivalent ratio.

Question

Write the ratio $$40:28$$ in its simplest form.

To work this out, look for a number that will divide into $${40}$$ and $${28}$$.

$${2}$$ divides into both numbers, so $$40:28$$ can be written as $$20:14$$.

You can divide these by $${2}$$, so the simplified ratio is $$10:7$$.

No number divides into $${10}$$ and $${7}$$ exactly, so $$10:7$$ is the simplest form of the ratio.