Maths Library

Simplifying Ratios: Year 7 maths

This topic covers expressing relationships as ratios and simplifying them to their simplest form. Students practise finding highest common factors across two or three terms and converting mixed units.

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What this covers

Simplifying Ratios is taught in Year 7 (age 11 to 12, KS3) as a main teaching focus. It sits in the Ratio strand.

Worked example

Simplify the ratio 18 : 24

  1. Identify highest common factor of 18 and 24, which is 6
  2. Divide first part: 186 = 3
  3. Divide second part: 246 = 4
  4. Write simplified ratio: 3 : 4

Answer: 3:4

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Two-part ratios with common factors 2, 5, or 10
  2. Two-part ratios requiring larger single HCF divisions, up to 12
  3. Three-part ratios, e.g. 12 : 18 : 24
  4. Ratios involving decimals or fractions needing scaling to integers first
  5. Ratios with mixed units requiring unit conversion, e.g. 40 cm to 1.2 m

Common mistakes

  • Reversing the order of terms in the ratio
  • Simplifying numbers with different units without converting units first

Curriculum links

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

  • Simplify ratios and divide a given quantity into two or more parts in a given ratio.

Sample sheet and answers

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

Simplifying Ratios

Year 7 maths

Qs
6
Marks
6
NameDateScore / 6
1.
Simplify the ratio 14 : 16.
[1]
2.
Simplify the ratio 20 : 24.
[1]
3.
Simplify the ratio 6 : 9.
[1]
4.
Simplify the ratio 28 : 32.
[1]
5.
Simplify the ratio 5 : 10.
[1]
6.
Simplify the ratio 32 : 36.
[1]

Answer key

  1. 7 : 8Divide both parts by 2; 7 : 8
  2. 5 : 6Divide both parts by 4; 5 : 6
  3. 2 : 3Divide both parts by 3; 2 : 3
  4. 7 : 8Divide both parts by 4; 7 : 8
  5. 1 : 2Divide both parts by 5; 1 : 2
  6. 8 : 9Divide both parts by 4; 8 : 9