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Auralith Learning

Year 8 · Maths · Ratio and scale · Lesson 2

Sharing in a ratio

Learn to share an amount in a given ratio using bar models, including three-part ratios, money with pence, questions where you know one share, and difference problems.

Whiteboard video lesson: Sharing in a ratio

43-minute video lesson

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

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What your child will learn

  • Share an amount in a ratio with two or three parts
  • Use a bar model to find one part
  • Solve problems where one share is given
  • Solve problems using the difference between shares

The method

  1. Add the parts of the ratio.
  2. Divide the total by the number of parts to find one part.
  3. Multiply one part by each number in the ratio.
  4. Check: the shares add up to the total.

Key words: share, ratio, bar model, one part, total.

Worked examples

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

Question 1

Share £20 in the ratio 2 : 3.

  1. Step 1: Total parts: 2 + 3 = 5
  2. Step 2: Draw a bar model: First 2 boxes, Second 3 boxes
  3. Step 3: One part: £20 ÷ 5 = £4
  4. Step 4: First: 2 × £4 = £8
  5. Step 5: Second: 3 × £4 = £12
  6. Step 6: Check: £8 + £12 = £20

Answer: £8 and £12

Question 2

Share 30 sweets in the ratio 1 : 2.

  1. Step 1: Total parts: 1 + 2 = 3
  2. Step 2: Draw a bar model: First 1 box, Second 2 boxes
  3. Step 3: One part: 30 ÷ 3 = 10
  4. Step 4: First: 1 × 10 = 10
  5. Step 5: Second: 2 × 10 = 20
  6. Step 6: Check: 10 + 20 = 30

Answer: 10 and 20

Question 3

Share £45 in the ratio 4 : 5.

  1. Step 1: Total parts: 4 + 5 = 9
  2. Step 2: Draw a bar model: First 4 boxes, Second 5 boxes
  3. Step 3: One part: £45 ÷ 9 = £5
  4. Step 4: First: 4 × £5 = £20
  5. Step 5: Second: 5 × £5 = £25
  6. Step 6: Check: £20 + £25 = £45

Answer: £20 and £25