There are infinitely many equivalent ratios.
A ratio is in its simplest form if the HCF of all the parts is one and all parts are integers.
A ratio is in unitary form if one of the parts is equal to one.
A ratio in unitary form may not be a simplified ratio.

Common misconception

Not simplifying the ratio completely or over-simplifying a three part ratio when two of the parts share a further common factor

Link two part ratios back to simplifying fractions and remind pupils to consider if either number is a multiple of 3 as this is often missed. Remind pupils that to simplify a ratio, every part must share the common factor you are dividing by.

Keywords

Unitary ratio - A unitary ratio is any ratio where one part of the ratio is 1

Pupils may not be used to writing ratios containing fractions or decimals when writing unitary ratios. It is important that pupils know that these are not simplified ratios but they are a useful form to write a ratio in, particularly for scale drawings or maps.

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.

Which of these are equivalent to $$\frac{6}{18}$$?

$$\frac{2}{3}$$

Correct answer: $$\frac{1}{3}$$

Correct answer: $$\frac{3}{9}$$

$$\frac{1}{2}$$

Q2.

Select the correct ratio of shaded to unshaded squares shown on this diagram.

Correct answer: 8 : 16

1 : 3

$$\frac{1}{3}$$

$$\frac{8}{16}$$

0.8

Q3.

Select which of these show $$\frac{6}{18}$$ written in its simplest form.

$$\frac{2}{3}$$

Correct answer: $$\frac{1}{3}$$

$$\frac{3}{9}$$

$$\frac{1}{2}$$

Q4.

Which of these shows the ratio of circles to triangles?

Correct answer: 6 : 4

4 : 6

6 : 10

4 : 10

Q5.

Write the ratio of circles to triangles.

Correct Answer: 2 : 3, 2:3

Q6.

Write the ratio of triangles to circles.

Correct Answer: 3 : 2, 3:2

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6 Questions

Q1.

What is the ratio of triangles to circles in its simplest form?

Correct answer: 2 : 3

4 : 6

3 : 2

6 : 4

1 : 1.5

Q2.

Select the ratio of shaded to unshaded squares written in its simplest form

Correct answer: 1 : 2

1 : 3

2 : 4

8 : 16

2 : 1

Q3.

Write the ratio 30 : 36 in its simplest form

Correct Answer: 5 : 6, 5:6

Q4.

Which of these are unitary ratios?

Correct answer: 4 : 1

2 : 3

11 : 111

Correct answer: 1 : 2.3

Correct answer: 9 : 1 : 18

Q5.

Write the ratio of triangles to circles in the form $$1 : n$$ where $$n$$ is a decimal.

Correct Answer: 1 : 1.5, 1:1.5

Q6.

A travel company offer for every £10 you get $16. Write the ratio of £ to $ in the form 1 : $$n$$

Correct Answer: 1 : 1.6, 1:1.6