R1Ratio & ProportionFoundation

Ratio

A ratio compares two or more amounts, like mixing 2 parts squash to 5 parts water. Ratios appear in recipes, maps and money problems — being confident with them earns marks across the whole paper.

35 min Video by Maths Genie AQA GCSE Maths

Sharing in a RatioWatch the walkthrough, then read the notes below.

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What you'll learn

Write and simplify ratios
Share an amount in a given ratio
Use ratios to find missing amounts
Link ratios to fractions

Simplifying ratios

Simplify a ratio by dividing all parts by their highest common factor, just like a fraction. $10 : 15$ simplifies to $2 : 3$ (divide both by 5).

Sharing in a ratio

To share an amount in a ratio, add the parts to find the total number of parts, work out the value of one part, then multiply.

1Total parts

= 3 + 5 = 8

2One part

= 40 \div 8 = £5

3Shares:

3 \times 5 = £15

and

5 \times 5 = £25

Answer£15 and £25

Tip — Check your shares add back up to the original total.

Remember these

one part = total \div number of parts

Sharing in a ratio.

a : b = \frac{a}{a + b} and \frac{b}{a + b}

Ratio as fractions of the whole.

Watch out for these

Dividing the total by one of the numbers in the ratio (e.g. ÷3).

Divide by the TOTAL number of parts (3 + 5 = 8).

Leaving a ratio unsimplified when asked for simplest form.

Divide all parts by their highest common factor.

Key takeaways

Simplify ratios by dividing all parts by the HCF.
Share: add parts, find one part, then multiply.
Always check the shares add to the total.

Test yourself

Ready to practise Ratio? Pick a mode and earn XP & Dobloons.