GCSE-ready- Home
- Lessons
- KS3 Mathematics
- Ratio: simplifying and sharing
Ratio: simplifying and sharing
🎬 The doodle video for this lesson is coming soon. Subscribe on YouTube to see it first.
A ratio compares quantities. It tells you how many of one thing there are for every so many of another.
Simplifying ratios
Divide every part by the same number, just like simplifying fractions.
12 : 18 = 2 : 3 (÷ 6)
Use the same units first: 50p : £2 = 50 : 200 = 1 : 4.
12 : 18 = 2 : 3 (÷ 6)
Use the same units first: 50p : £2 = 50 : 200 = 1 : 4.
Sharing in a ratio
Share £45 in the ratio 2 : 3.
Total parts: 2 + 3 = 5. One part: 45 ÷ 5 = £9.
Shares: 2 × 9 = £18 and 3 × 9 = £27.
Total parts: 2 + 3 = 5. One part: 45 ÷ 5 = £9.
Shares: 2 × 9 = £18 and 3 × 9 = £27.
Ratios and fractions
If boys : girls = 3 : 5, there are 8 parts altogether.
The fraction who are girls is 58.
If you know one part, scale up: in 2 : 7, if the smaller share is 14, one part is 7, so the larger is 49.
The fraction who are girls is 58.
If you know one part, scale up: in 2 : 7, if the smaller share is 14, one part is 7, so the larger is 49.
Share 40 sweets between Amir and Ben in the ratio 3 : 5.
- Total parts: 3 + 5 = 8
- One part: 40 ÷ 8 = 5
- Amir: 3 × 5 = 15, Ben: 5 × 5 = 25
Answer: 15 and 25
Simplify a ratio by dividing all parts by a common factor. To share, add the parts, find one part, then multiply.
Check you have got it
Answer 6 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.