Simplifying Ratios

Reduce ratios to their simplest form like fractions.

  • Define and explain Simplifying Ratios in your own words
  • Use key terms such as Proportion accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

Ratios compare quantities and proportion keeps them in step — from mixing paint to reading maps, they describe how things scale together.

This lesson focuses on Simplifying Ratios: reduce ratios to their simplest form like fractions.

Definition: Simplifying Ratios

Reduce ratios to their simplest form like fractions.

Key ideas

Simplifying ratios

Divide every part by the same number, just like cancelling fractions: 10:15 simplifies to 2:3. A ratio in simplest form is easiest to read.

Sharing in a ratio

Add the parts to find the total number of shares, then divide the amount by that total. For £30 in the ratio 2:3, there are 5 shares of £6.

Key term — Proportion: A statement that two ratios are equal, such as 1:2 = 2:4.

Worked example: Simplifying Ratios

Are the ratios 4:6 and 10:15 equivalent?

Yes — both simplify to 2:3.

Answer: Yes — both simplify to 2:3.

Common mistakes
  • Simplifying only one part of a ratio Every part must be divided by the same number, or the comparison changes.
  • Adding instead of multiplying when scaling Doubling a recipe means multiply by 2, not add 2 — scaling is always multiplication.

Practice

Share £40 in the ratio 3:2.
How many shares in total?

£24 and £16 — 5 shares of £8 each.

A drink mixes juice and water in the ratio 1:4. How much juice is in 500 ml of drink?
Total parts = 5.

100 ml — 500 ÷ 5 = 100.

Simplify 12:18.
Divide by the highest common factor.

2:3 — both divide by 6.

5 notebooks cost £7.50. What do 8 cost?
Find the cost of one first.

£12 — one notebook costs £1.50, and 8 × £1.50 = £12.

Quick check

Simplifying Ratios — quick check

Which of these best defines "Proportion"?

A statement that two ratios are equal, such as 1:2 = 2:4.

A map scale is 1:50,000. A road measures 6 cm on the map. What is its real length in km?

3 km — 6 × 50,000 = 300,000 cm = 3 km.
Key takeaways
  • Simplifying Ratios: reduce ratios to their simplest form like fractions.
  • Simplifying ratios: Divide every part by the same number, just like cancelling fractions: 10:15 simplifies to 2:3.
  • Scale factor: The number you multiply by to enlarge or reduce a shape, recipe or map.
  • Watch out for: simplifying only one part of a ratio