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11.1 Writing Ratios

GCSE Maths Foundation · Edexcel · Chapter 11: Ratio and Proportion

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: writing a ratio from a situation, simplifying ratios and a first look at sharing. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Write a ratio from words, pictures or a list of numbers, in the right order
  • Simplify a ratio by dividing every part by a common factor
  • Simplify ratios with three parts
  • Share an amount in a given ratio

Key words

  • Ratio: A way to compare two or more amounts. 3 : 5 is read “3 to 5”.
  • Part: Each number in a ratio. 3 : 5 has two parts and 8 parts in total.
  • Simplest form: A ratio is in its simplest form when the parts are whole numbers with no common factor except 1.
  • Equivalent ratios: Ratios that compare amounts in the same way, such as 2 : 3, 4 : 6 and 20 : 30.
  • HCF: The highest common factor: the biggest number that divides into all the parts.

Writing a ratio

A ratio compares one amount with another. Write the amounts in the same order as the words, with a colon between them. There are no units in a ratio.

Worked example: order matters

A football team won 11 games and lost 4. Write the ratio of losses to wins.
The question says losses first, so write the losses first.

Answer: losses : wins = 4 : 11

Key fact: 3 : 5 and 5 : 3 are different ratios. Always check the order in the question.

Simplifying a ratio

Divide every part by the same number. Keep going until the only common factor is 1. Dividing by the HCF does it in one step.

  • 10 : 25; Divide each part by 5; Simplest form 2 : 5
  • 36 : 24; Divide each part by 12; Simplest form 3 : 2
  • 21 : 49; Divide each part by 7; Simplest form 3 : 7
  • 60 : 45; Divide each part by 15; Simplest form 4 : 3

Worked example: step by step

A class has 16 girls and 12 boys. Write the ratio girls : boys in its simplest form.
16 : 12 → divide both by 2 → 8 : 6 → divide both by 2 → 4 : 3
Check: 4 and 3 have no common factor except 1, so you have finished.

Answer: 4 : 3

Ratios with three parts

A ratio can compare three amounts. Divide all three parts by the same number.

Worked example: a three-part ratio

A garden centre sells 20 roses, 35 tulips and 15 lilies. Write roses : tulips : lilies in its simplest form.
20 : 35 : 15. The HCF of 20, 35 and 15 is 5.
20 ÷ 5 = 4, 35 ÷ 5 = 7, 15 ÷ 5 = 3

Answer: 4 : 7 : 3

Key fact: A ratio is simplest when no number (other than 1) divides into every part. 6 : 9 : 4 is already simplest, even though 6 and 9 share a factor of 3.

Sharing in a ratio

To share an amount in a ratio: add the parts, find the value of one part, then multiply. A bar model shows it clearly.

Worked example: sharing money

Ali and Bea share £45 in the ratio 2 : 3. How much does each get?
Total parts: 2 + 3 = 5. One part: £45 ÷ 5 = £9.
Ali: 2 × £9 = £18. Bea: 3 × £9 = £27. Check: £18 + £27 = £45 ✓

Answer: Ali £18, Bea £27

Common mistakes

  • Writing the numbers in the wrong order. “Boys to girls” means boys first.
  • Stopping too soon. 12 : 18 → 6 : 9 is not finished: divide by 3 again to get 2 : 3.
  • Dividing only one part. Every part must be divided by the same number.
  • When sharing, dividing by one of the parts instead of the total number of parts.

Revision questions

Try these, then check your answers below each one.

Question 1. Write 30 : 45 in its simplest form. (Choose from: 6 : 9, 2 : 3, 3 : 2, 10 : 15.)

Answer: 2 : 3

Working: The HCF is 15. 30 ÷ 15 = 2 and 45 ÷ 15 = 3, so 2 : 3.

Question 2. A netball team won 9 matches and lost 6. Write the ratio wins : losses in its simplest form.

Answer: 3:2

Working: 9 : 6. Divide both by 3: 3 : 2.

Question 3. Sam says, “The ratio 4 : 5 is the same as the ratio 5 : 4.” Is Sam correct?

Answer: No

Working: No. The order matters. 4 : 5 means 4 of the first thing for every 5 of the second. 5 : 4 is the other way round.

Related lessons

Continue in the full course

This lesson is section 11.1 (EGCMF1101) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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