Ratio calculator: share an amount or simplify a ratio

1. Add the parts to get the total number of parts.
2. Divide the amount by the total parts to find one part.
3. Multiply by each part.

Example: share £60 in the ratio 2:3. Total parts $= 5$; one part $= 60 \div 5 = 12$; shares $= 2 \times 12 = £24$ and $3 \times 12 = £36$. Check: $24 + 36 = 60$.

With three parts, share £120 in the ratio 1:2:3: six parts, one part is £20, so £20, £40 and £60.

Divide every part by the highest common factor.

• $12 : 18$: the HCF is 6, so $2 : 3$.
• $15 : 25 : 35$: the HCF is 5, so $3 : 5 : 7$.
• $0.5 : 2$: multiply by 10 to get $5 : 20$, then divide by 5: $1 : 4$.

Our HCF calculator finds the highest common factor for larger numbers.

Before simplifying, write both quantities in the same unit. 50 cm to 2 m is $50 : 200$, which simplifies to $1 : 4$, not $50 : 2$. Once the units match, the ratio has no units.

If Amy and Ben share sweets in the ratio 3:5 and Amy gets 18, one part is $18 \div 3 = 6$, so Ben gets $5 \times 6 = 30$ and the total is 48. If you know the difference instead (Ben gets 12 more than Amy), the difference is $5 - 3 = 2$ parts, so one part is 6.

• Dividing the amount by one part of the ratio instead of the total parts.
• Getting the order wrong: the ratio of boys to girls is not the ratio of girls to boys.
• Simplifying without making the units match first.

Practise with our ratio questions and our guide to ratio and proportion.

• A bar model (one box per part) makes every ratio question easier to see.
• Always check the shares add up to the total.
• Ratios link to fractions: in 2:3, the first share is $\tfrac{2}{5}$ of the total.