Ratio
A ratio compares two or more quantities, showing how much of one there is compared to another, written with a colon (e.g. 3:5). Ratios are simplified in the same way as fractions, by dividing every part by their highest common factor.
Method
- To simplify a ratio, divide every part of the ratio by the highest common factor of all the parts.
- To share an amount in a given ratio, add the parts of the ratio together to find the total number of shares, divide the amount by this total to find the value of one share, then multiply by each part.
- To find one quantity given another and the ratio, work out the value of one share first, then multiply by the relevant part.
- Ratios can be written as fractions of the whole: a ratio of a:b means the first quantity is a/(a+b) of the total.
- To combine two ratios, such as a:b and b:c, scale them so the shared quantity (b) matches in both before combining into a:b:c.
Worked example
Share 72 sweets between Amir and Bea in the ratio 4:5.
- Add the parts of the ratio: 4 + 5 = 9.
- Divide the total amount by the number of shares: 72 divided by 9 = 8.
- This means one share is worth 8 sweets.
- Amir gets 4 shares: 4 x 8 = 32 sweets.
- Bea gets 5 shares: 5 x 8 = 40 sweets.
- Check: 32 + 40 = 72, which matches the total.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE exam paper, with a full mark scheme.
The angles in a triangle are in the ratio 2:3:4. Work out the size of each angle.
A fruit drink is made from apple juice and orange juice in the ratio 3:5. A jug contains 800 ml of the drink in total. How much more orange juice than apple juice is in the jug?
Next topics
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.