Proportion

Proportion When two ratios (a:b) and (c:d) are equal, we say that the ratios are in proportion. It is denoted as a:b :: c:d Read as ‘a is to b’ as ‘c is to d’

Proportion law a : b :: c : d If two ratios are in proportion i.e., a : b :: c : d then the product of extremes is equal to product of means. Here a and d are called as extremes and b and c are the means a : b :: c : d Product of extremes = a x d Product of means = b x c Product of extremes = Product of means a x d = b x c Extremes Means

Example 1 : Check whether 3:5 and 6:10 are in proportionality Solution: To find if the two ratios are in proportion, Lets check if Product of extremes = Product of means 3 x 10 5 x 6 30 30 Hence they are in proportion 3 : 5 :: 6 : 10 Extremes Means =

Example 2: Check whether 4:7 and 8:21 are in proportionality Solution: To find if the two ratios are in proportion, Lets check if Product of extremes = Product of means 4 x 21 7 x 8 84 56 Hence they are not in proportion 4 : 7 :: 8 : 21 Extremes Means ≠

Given : The ratios 3:4 and 12:a are in proportionality Example 3: If 3:4 and 12:a are in proportionality, find the missing term Given : The ratios 3:4 and 12:a are in proportionality We know that If two ratios are in proportion then Product of extremes = Product of means 3 x a = 4 x 12 3 x a = 48 a = 48÷3 a = 16 Hence, a = 16 3 : 4 :: 12 : a Extremes Means

Try these Check whether the following ratios are in proportions. b. 4 : 2  10 : 15 2. If 3 : 6 and x : 12 are in proportion, Find the missing term