HOW TO FIND IF TWO RATIOS ARE PROPORTIONAL

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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