Maths Library

Simplifying Ratios: Year 8 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 8 (age 13 to 14) 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 Australian Curriculum v9. Check wording and codes against the official document.

  • AC9M8N04 Solve practical problems involving ratios, rates, and percentage change.

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 8 maths

Qs
6
Marks
18
NameDateScore / 18
1.
Isla has 14 red pens and 16 blue pens. Write the ratio of red to blue in its simplest form.
[3]
2.
Simplify the ratio 35 : 42.
[3]
3.
Ben has 10 red pens and 15 blue pens. Write the ratio of red to blue in its simplest form.
[3]
4.
Simplify the ratio 63 : 72.
[3]
5.
Simplify the ratio 10 : 20.
[3]
6.
Grace has 72 red pens and 81 blue pens. Write the ratio of red to blue in its simplest form.
[3]

Answer key

  1. 7 : 8Divide both by 2; 14 : 16 = 7 : 8
  2. 5 : 6Divide both parts by 7; 5 : 6
  3. 2 : 3Divide both by 5; 10 : 15 = 2 : 3
  4. 7 : 8Divide both parts by 9; 7 : 8
  5. 1 : 2Divide both parts by 10; 1 : 2
  6. 8 : 9Divide both by 9; 72 : 81 = 8 : 9