Checking and securing understanding of simplifying and unitising ratios | Maths

Starter quiz

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

$\frac{2}{3}$

$\frac{1}{3}$ ✓

$\frac{3}{9}$ ✓

$\frac{1}{2}$
Select the correct ratio of shaded to unshaded squares shown on this diagram.

8 : 16 ✓

1 : 3

$\frac{1}{3}$

$\frac{8}{16}$

0.8
Select which of these show $\frac{6}{18}$ written in its simplest form.

$\frac{2}{3}$

$\frac{1}{3}$ ✓

$\frac{3}{9}$

$\frac{1}{2}$
Which of these shows the ratio of circles to triangles?

6 : 4 ✓

4 : 6

6 : 10

4 : 10
Write the ratio of circles to triangles.

'2 : 3' ✓
Write the ratio of triangles to circles.

'3 : 2' ✓

Exit quiz

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

2 : 3 ✓

4 : 6

3 : 2

6 : 4

1 : 1.5
Select the ratio of shaded to unshaded squares written in its simplest form

1 : 2 ✓

1 : 3

2 : 4

8 : 16

2 : 1
Write the ratio 30 : 36 in its simplest form

'5 : 6' ✓
Which of these are unitary ratios?

4 : 1 ✓

2 : 3

11 : 111

1 : 2.3 ✓

9 : 1 : 18 ✓
Write the ratio of triangles to circles in the form $1 : n$ where $n$ is a decimal.

'1 : 1.5' ✓
A travel company offer for every £10 you get $16. Write the ratio of £ to $ in the form 1 : $n$

'1 : 1.6' ✓

Worksheet

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Lesson Details

Key learning points

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