# 1 ratios 9C5 - 9C6 tell how one number is related to another. may be written as A:B, or A/B, or A to B. compare quantities of the same units of measurement.

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1 ratios 9C5 - 9C6 tell how one number is related to another. may be written as A:B, or A/B, or A to B. compare quantities of the same units of measurement do not have a name or unit of measurement. The order of the numbers in a ratio is important

2 To tell if two ratios are equal … …if this results in the same answer for both ratios, then they are equal. a x d = b x c Cross multiply

3 Sometimes we need to think about the units … 7 mm to 1 cm  7 : 1

4 Ratios compare quantities of the same kind. So to rewrite statements as ratios eg. 7 mm to 1 cm EXPRESS BOTH QUANTITIES IN THE SAME UNITS. = 7 mm to 10mm = 7:10

5 To express ratios in their simplest form … 1.Are both quantities in the same units? Eg. 45 cm to 1.5m 45 cm to 150 cm 2.Cancel the units and write the 2 numbers as a ratio = 45 : 150 3.Divide both numbers by the highest common factor = 3 : 10

6 To determine whether ratios are in direct proportion – 1/ Write the ratios in fraction form 2/ Cross-multiply This statement is a DIRECT PROPORTION 1 : 3  2 : 6 (1 x 6) = (2 x 3 ) YES, these ratios are in direct proportion.

7 Using proportions to solve … Find the value of a in the following direct proportion. cross multiply … 30 x a = 2 x 45 30a = 90 30 30 a = 90 30 a = 3

8 To simplify ratios that contain common fractions, eg. write each fraction with a common denominator, then cancel each denominator… = 10:9 or... just cross multiply.

9 To simplify ratios that have decimal fractions change both numbers into whole numbers by multiplying them by 10 or 100 etc… (this eliminates the decimal point) then divide by highest common factor, which in this case would be 7. = 3: 5 Eg. 2.1 : 3.5 21:35

10 To find the greater ratio Which is the greater ratio in the pair 3 : 5; 2 : 3

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12 SIMILAR TRIANGLES have exactly the same shape, but different size. The ratios of the corresponding sides are equal.

13 Increasing & decreasing numbers using ratios

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15 Dividing a number using a ratio

16 SPEED A ratio is a comparison of two quantities with the same units. A rate is a comparison of two quantities with different units. Speed is classed as a rate rather than a ratio.

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