We can use cross product rule of proportion to check whether two ratios are proportional.
Let us consider the proportion
a : b = c : d
To know the cross product rule, first we have to know about extremes and means.
It has been explained in the picture given below.
Cross product rule :
Product of extremes = Product of means
ad = bc
Example 1 :
Check whether the following two ratios are proportional.
4 : 2 and 20 : 6
Solution :
Product of extremes = 4 x 6 = 24
Product of means = 2 x 20 = 40
Product of extremes ≠ Product of means
The given two ratios do not satisfy the cross product rule of proportion.
So, the two ratios 4 : 2 and 20 : 6 are not proportional.
Example 2 :
Check whether the following two ratios are proportional.
6/9 and 2/3
Solution :
Product of extremes = 6 x 3 = 18
Product of means = 9 x 2 = 18
Product of extremes = Product of means
The given two ratios satisfy the cross product rule of proportion.
So, the two ratios 6/9 and 2/3 are proportional.
Example 3 :
Check whether the following two ratios are proportional.
4/3 and 16/12
Solution :
Product of extremes = 4 x 12 = 48
Product of means = 3 x 16 = 48
Product of extremes = Product of means
The given two ratios satisfy the cross product rule of proportion.
So, the two ratios 4/3 and 16/12 are proportional.
Example 4 :
Check whether the following two ratios are proportional.
12 : 24 and 3 : 4
Solution :
Product of extremes = 12 x 4 = 48
Product of means = 24 x 3 = 72
Product of extremes ≠ Product of means
The given two ratios do not satisfy the cross product rule of proportion.
So, the two ratios 12 : 24 and 3 : 4 are not proportional.
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