Sharing in a Ratio

Split amounts fairly according to a given ratio.

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

This lesson focuses on Sharing in a Ratio: split amounts fairly according to a given ratio.

Definition: Sharing in a Ratio

Split amounts fairly according to a given ratio.

Key ideas

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.

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.

Key term — Ratio: A comparison of two or more quantities, written with a colon, such as 3:2.

Worked example: Sharing in a Ratio

Share £40 in the ratio 3:2.

£24 and £16 — 5 shares of £8 each.

Answer: £24 and £16 — 5 shares of £8 each.

Common mistakes
  • Simplifying only one part of a ratio Every part must be divided by the same number, or the comparison changes.
  • Mixing up the order when sharing £30 shared 2:3 gives £12 then £18 — match each share to the right person in order.

Practice

Are the ratios 4:6 and 10:15 equivalent?
Simplify both ratios.

Yes — both simplify to 2:3.

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

Sharing in a Ratio — quick check

Which of these best defines "Ratio"?

A comparison of two or more quantities, written with a colon, such as 3:2.

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
  • Sharing in a Ratio: split amounts fairly according to a given ratio.
  • Sharing in a ratio: Add the parts to find the total number of shares, then divide the amount by that total.
  • Proportion: A statement that two ratios are equal, such as 1:2 = 2:4.
  • Watch out for: simplifying only one part of a ratio