Concept of Proportion

In concept of proportion we will learn how a proportion is an expression which states that the two ratios are in equal.

When four quantities are so related that the ratio between the first and the second quantities is equal to the ratio between the third and the fourth quantities; the quantities are said to be in proportion.

Thus, proportion is equality of two ratios.


In order to represent a proportion; either put the sign of equality (=) between the two ratios or put a double colon (::).

Thus, 3, 4, 9 and 12 are in proportion and is expressed as:

3 : 4 = 9 : 12 or 3 : 4 :: 9 : 12

Consider the following examples to understand the concept of proportion:

(i) What is the ratio of the number of boys to the number of girls in a group of 8 boys and 12 girls?

The required ratio = number of boys/number of girls

     = 8/12

     = (2 × 4)/(3 × 4)

      = 2/3

(ii) What is the ratio of the number of boys to the number of girls in another group of 18 boys and 27 girls?

The required ratio = number of boys/number of girls

                                  = 18/27

                                  = (2 × 9)/(3 × 9)

                                  = 2/3

It is observed, in the above explanations (i) and (ii), that the ratios 8/12 and 18/27 are equal.

i.e., 8/12 = 18/27

or, 8 : 12 = 18 : 27

Such an equality of two ratios is called a proportion and is read as “8 is to 12 as 18 is to 27”.

The numbers 8, 12, 18 and 27 that are used in the proportion, are called its terms, i.e., 8 is the first terms, 12 is the second term, 18 is the third term and 27 is the fourth term of the proportion 8 : 12 = 18 : 27.


Similarly, suppose 5, 12, 25, and 60 are in proportion which is written as 5 : 12 : : 25 : 60 and is read as 5 is to 12 as 25 is to 60.

Also, 5 : 12 = 25 : 60

⇒ 5/12 = 25/60

⇒ 5/12 = 5/12


Are 3, 5, 18 and 30 in proportion?

The numbers, 3, 5, 18, 30 are in proportion because,

3/5 = 18/30

⇒ 3/5 = 3/5










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