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© Boardworks Ltd 20112 of 13 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?

© Boardworks Ltd 20113 of 13 Red to blue ratio

© Boardworks Ltd 20114 of 13 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 are two blue counters. For every twelve red counters there are eight blue counters. Is it possible to simplify this ratio? ÷ 4

© Boardworks Ltd 20115 of 13 Simplifying ratios Ratios can be simplified like fractions by dividing each part by the highest common factor. For example, 21 : 35 = 3 : 5 ÷ 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 64 : 16 = 4 : 1 ÷ 16 8 : 24 : 10 = 4 : 12 : 5 ÷ 2

© Boardworks Ltd 20116 of 13 Simplifying two and three part ratios

© Boardworks Ltd 20117 of 13 Equivalent ratio spider diagrams

© Boardworks Ltd 20118 of 13 = 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 Simplifying ratios with units = 3 ¢ : 10 ¢ When the ratio is simplified, add the units back in.

© Boardworks Ltd 20119 of 13 Simplifying ratios with units

© Boardworks Ltd 201110 of 13 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 ÷ 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

© Boardworks Ltd 201111 of 13 For example, calculate the ratio m : 4 m in whole number form. Simplifying ratios containing fractions 2 3 We can write this ratio in whole-number form by multiplying both parts by 3. 2 3 : 4 × 3 = 2 : 12 ÷ 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

© Boardworks Ltd 201112 of 13 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 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

© Boardworks Ltd 201113 of 13 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 = 1 : 1.25 The ratio of boys to girls in 9G is: 5 : 7 ÷ 5 = 1 : 1.4

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