# Ratios

Ratios look like this…. …and there’s a few things you might be asked to do with them.

Simplify A Ratio

E.g. Reduce 7.2 : 6 to its simplest form.

• Start by multiplying by 10,100,1000 or whatever to get rid of any decimals. Here you would then get 72 : 60
• Now just like a fraction, find the highest common factor to simplify it down (here the HCF is 12)

So the answer is 6 : 5

Remember to make sure you have the same units on both sides of the ratio (examiners might be tricky and put mm one side and cm on the other so be careful).

Reduce The Ratio To 1 : n

E.g. Reduce 4 : 14 to the form 1 : n

• Here you just divide both sides by the first number

So the answer is 1 : 3.5

Figure Out The Amounts Each Person Gets In A Set Ratio

E.g. Tom, Mark and Jess share 200 in the ratio 1:3:4. How much does Mark get?

• Start by adding up all the numbers in the ratio to get the total number of parts

1 + 3 + 4 = 8

• Divide the total number by the number of parts to get one part

200/8 = 25

• Multiply to find the correct amounts

So Mark has 3 x £25 = £75