Maths Library

Sharing in a Ratio: Year 10 maths

This topic covers dividing a quantity into parts according to a given ratio. Students practise calculating total parts, finding the value of one part, and scaling up each share.

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What this covers

Sharing in a Ratio is taught in Year 10 (age 14 to 15, KS4) as a main teaching focus. It sits in the Ratio strand.

Worked example

Share £60 in the ratio 2 : 3

  1. Calculate total parts: 2 + 3 = 5 parts
  2. Find value of one part: 605 = £12
  3. Multiply each part: 2 x 12 = £24 and 3 x 12 = £36

Answer: £24 : £36

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Two-part ratio sharing small whole numbers, sum of parts <= 10
  2. Two-part ratio with larger whole numbers and money quantities
  3. Three-part ratio sharing integer amounts
  4. Given the difference between parts or one part's value rather than the total
  5. Multi-step word problems involving ratios changing or combining parts

Common mistakes

  • Dividing the total amount by each ratio digit directly rather than the sum of parts
  • Misidentifying which person receives which share when names are assigned

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Work with ratio relationships and direct and inverse proportional reasoning in real-world contexts.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Sharing in a Ratio

Year 10 maths

Qs
6
Marks
18
NameDateScore / 18
1.
Chloe shares 96 sweets in the ratio 3 : 5. How many sweets are in each share?
[3]
2.
Isla shares 21 sweets in the ratio 5 : 2. How many sweets are in each share?
[3]
3.
Ella shares 24 sweets in the ratio 5 : 1. How many sweets are in each share?
[3]
4.
Priya shares 77 sweets in the ratio 5 : 2. How many sweets are in each share?
[3]
5.
Noah shares 72 sweets in the ratio 2 : 6. How many sweets are in each share?
[3]
6.
Farid shares 110 sweets in the ratio 5 : 5. How many sweets are in each share?
[3]

Answer key

  1. 36 and 60Total parts: 3 + 5 = 8; One part is 96 ÷ 8 = 12; Shares: 3 × 12 = 36 and 5 × 12 = 60
  2. 15 and 6Total parts: 5 + 2 = 7; One part is 21 ÷ 7 = 3; Shares: 5 × 3 = 15 and 2 × 3 = 6
  3. 20 and 4Total parts: 5 + 1 = 6; One part is 24 ÷ 6 = 4; Shares: 5 × 4 = 20 and 1 × 4 = 4
  4. 55 and 22Total parts: 5 + 2 = 7; One part is 77 ÷ 7 = 11; Shares: 5 × 11 = 55 and 2 × 11 = 22
  5. 18 and 54Total parts: 2 + 6 = 8; One part is 72 ÷ 8 = 9; Shares: 2 × 9 = 18 and 6 × 9 = 54
  6. 55 and 55Total parts: 5 + 5 = 10; One part is 110 ÷ 10 = 11; Shares: 5 × 11 = 55 and 5 × 11 = 55