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11.5 Comparing Using Ratios

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

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: comparing ratios using the form 1 : n, fractions and percentages. 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

  • Compare two ratios by writing both in the form 1 : n (or n : 1)
  • Compare proportions by changing ratios to fractions, decimals or percentages
  • Decide whether two ratios are equivalent
  • Compare a ratio with a fraction in a real-life problem

Key words

  • Unit ratio: A ratio with one part equal to 1, such as 1 : 4.5.
  • Proportion: A part compared with the whole, often written as a fraction, decimal or percentage.
  • Stronger / weaker: A stronger drink has more squash for each part of water.
  • Equivalent: Two ratios are equivalent if they simplify to the same ratio.

Comparing using 1 : n

Ratios like 2 : 9 and 3 : 14 are hard to compare as they are. Make the same part equal to 1 in both, then compare the other part.

Worked example: which drink is stronger?

Jug A mixes squash and water in the ratio 2 : 9. Jug B uses 3 : 14. Which drink is stronger?
A: 2 : 9 = 1 : 4.5 (divide by 2). B: 3 : 14 = 1 : 4.666… (divide by 3).
In A each part of squash has less water, so A is stronger.

Answer: Jug A is stronger

Comparing using fractions and percentages

To compare proportions of a whole, change each ratio into a fraction of the whole, then into a decimal or percentage.

Worked example: two classes

In class P the ratio boys : girls is 7 : 8. In class Q it is 9 : 11. Which class has the greater proportion of girls?
P: girls = 8/15 = 0.533… = 53.3%. Q: girls = 11/20 = 0.55 = 55%.

Answer: Class Q

Key fact: A bigger number in the ratio does not always mean a bigger proportion. Always compare with the whole.

Are two ratios the same?

Simplify both ratios (or write both as 1 : n). If you get the same answer, they are equivalent. Shapes that are enlargements of each other have sides in the same ratio.

  • Small; Width : height 12 cm : 9 cm; Simplest form 4 : 3
  • Large; Width : height 20 cm : 15 cm; Simplest form 4 : 3
  • Poster; Width : height 30 cm : 24 cm; Simplest form 5 : 4

Worked example: same shape?

Is the poster the same shape as the small photo?
12 : 9 = 4 : 3 = 1.333… : 1. 30 : 24 = 5 : 4 = 1.25 : 1. These are different.

Answer: No, the poster is a different shape

Ratio against fraction

When one fact is a ratio and the other is a fraction, change both to the same form before comparing.

Worked example: two sports clubs

In Club A, 3/8 of the members are under 16. In Club B, the ratio under 16 : 16 and over is 2 : 3. Which club has the greater proportion under 16?
A: 3/8 = 0.375 = 37.5%. B: 2 parts out of 5 = 2/5 = 0.4 = 40%.

Answer: Club B

Common mistakes

  • Comparing the numbers in the ratios directly: 3 : 14 is not “stronger” just because 3 > 2.
  • Using the wrong denominator: for boys : girls = 7 : 8 the girls are 8/15, not 8/7.
  • Making a different part equal to 1 in each ratio, so the comparison is not fair.
  • Rounding too early. Keep at least 3 decimal places until the end.

Revision questions

Try these, then check your answers below each one.

Question 1. Write 5 : 18 in the form 1 : n. What is n?

Answer: 3.6

Working: 18 ÷ 5 = 3.6, so 1 : 3.6.

Question 2. Three drinks mix squash and water in these ratios. Which drink is the strongest (most squash for each part of water)? (Choose from: A: 1 : 4, B: 2 : 9, C: 3 : 11.)

Answer: C: 3 : 11

Working: A 1 : 4, B 1 : 4.5, C 1 : 3.67. C has the least water per part of squash.

Question 3. In a choir the ratio of boys to girls is 7 : 13. What percentage of the choir are girls?

Answer: 65 %

Working: 13/20 = 0.65 = 65%.

Related lessons

Continue in the full course

This lesson is section 11.5 (EGCMF1105) 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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