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Auralith Learning

Year 8 · Maths · Ratio and scale · Lesson 1

Simplifying ratios

Learn what a ratio is and how to simplify any ratio, including three-part ratios, ratios with units, decimals and fractions, and the form 1 : n.

Whiteboard video lesson: Simplifying ratios

36-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Understand what a ratio is and why the order matters
  • Simplify ratios by dividing every part by a common factor
  • Make units the same before simplifying
  • Simplify ratios with decimals and fractions
  • Write a ratio in the form 1 : n

The method

  1. Find a number that divides into every part.
  2. Divide every part by that number.
  3. Keep going until nothing else divides.
  4. If there are units, make them the same first.

Key words: ratio, simplify, common factor, highest common factor, equivalent ratio.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Simplify the ratio 4 : 6.

  1. Step 1: 4 : 6 = 2 : 3 (÷ 2)
  2. Step 2: Nothing else divides into 2 and 3

Answer: 2 : 3

Question 2

Simplify the ratio 10 : 25.

  1. Step 1: 10 : 25 = 2 : 5 (÷ 5)
  2. Step 2: Nothing else divides into 2 and 5

Answer: 2 : 5

Question 3

Simplify the ratio 12 : 8.

  1. Step 1: 12 : 8 = 3 : 2 (÷ 4)
  2. Step 2: Nothing else divides into 3 and 2

Answer: 3 : 2