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Ratio

A ratio compares the sizes of parts or quantities to each other.

What is the ratio of red counters to blue counters?

red : blue

= 9 : 3

= 3 : 1

For every three red counters there is one blue counter. This means that the ratio is 3 : 1.

Is this ratio the same as the ratio of blue counters to red counters?

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Red to blue ratio

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In this example, what is the ratio of red counters to blue counters?

Ratio

red : blue

= 12 : 8

= 3 : 2

By finding the highest common factor of these numbers, we can see that for every three red counters there aretwo blue counters.

For every twelve red counters there are eight blue counters.

Is it possible to simplify this ratio?

÷ 4 ÷ 4

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Simplifying ratios

Ratios can be simplified like fractions by dividing each part by the highest common factor.

For example, 21 : 35

= 3 : 5÷ 7 ÷ 7

For a three-part ratio, all three parts must be divided by the same number.

For example, 6 : 12 : 9

= 2 : 4 : 3

÷ 3 ÷ 3

64 : 16

= 4 : 1÷ 16 ÷ 16

8 : 24 : 10

= 4 : 12 : 5

÷ 2 ÷ 2

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Simplifying two and three part ratios

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Equivalent ratio spider diagrams

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= 3 : 10

When a ratio is expressed in different units, we must write the ratio in the same units before simplifying.

For example, simplify the ratio 90¢ : $3.

The first step to take is to write the ratio using the same units.

90 ¢ : 300 ¢

Once the units are the same we don’t need to write them in the ratio.

90 : 300÷ 30 ÷ 30

Simplifying ratios with units

= 3 ¢ : 10 ¢When the ratio is simplified, add the units back in.

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Simplifying ratios with units

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When a ratio is expressed using decimals we can simplify it by writing it in whole-number form.

We can write this ratio in whole-number form by multiplying both parts by 10.

0.8 : 2

= 8 : 20

× 10 × 10

÷ 4 ÷ 4

= 2 : 5

Simplifying ratios containing decimals

Once the ratio is in whole number form, apply simplification if this is possible.

For example, simplify the ratio 0.8 cm : 2 cm.

= 2 cm : 5 cm

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For example, calculate the ratio m : 4 min whole number form.

Simplifying ratios containing fractions

23

We can write this ratio in whole-number form by multiplying both parts by 3.

23 : 4

× 3 × 3

= 2 : 12

÷ 2 ÷ 2

= 1 : 6

We can apply a similar principle when dealing with ratios involving fractions.

Use simplification methods wherever possible to reduce the ratio to its simplest form.

= 1 m : 6 m

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Comparing ratios

We can compare ratios by writing them in the form 1 : m or m : 1, where m is any number.

The ratio 5 : 8 can be written in the form 1 : m by dividing both parts of the ratio by 5.

5 : 8

= 1 : 1.6

÷ 5 ÷ 5

The ratio 5 : 8 can be written in the form m : 1 by dividing both parts of the ratio by 8.

5 : 8

= 0.625 : 1

÷ 8 ÷ 8

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Comparing ratios

The ratio of boys to girls in class 9P is 4 : 5. The ratio of boys to girls in class 9G is 5 : 7. Which class has the higher proportion of girls?

The ratio of boys to girls in 9P is:

4 : 5÷ 4 ÷ 4

= 1 : 1.25

The ratio of boys to girls in 9G is:

5 : 7÷ 5 ÷ 5

= 1 : 1.4