Ratios And Proportion

The concept of ratio and proportion is one of the most essential concepts in maths. This introduction to these concepts covers all the related concepts with solved examples. In simple terms, the ratio is just a way to compare two quantities while the proportion is an equation which shows that two ratios are equivalent.


In certain circumstances, the comparison by the process of division makes good sense when compared to performing their difference. Hence, the comparison of two quantities by the process of division method is called as ‘Ratio’ between two numbers.


The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘:‘.

A ratio can be written as a fraction, say 2/5. Or can write it by using “to,” as “2 to 5.”We happen to see various comparisons or say ratios in our daily life.

Take the example of a comparison between the number of girls to the number of boys in a classroom. Out of the total students in a class, if the number of boys is 5 and the number of girls being 3, then the ratio between girls and boys can be written as 3:5( Girls: Boys). The ratio can also be written in the form of factor like 3/5.


Ratio and proportions are said to be faces of the same coin. When two ratios are equal in value, then they are said to be in proportion. In simple words, it compares two ratios. Proportions are denoted by the symbol  ‘::’ or ‘=’.


Ratio and Proportion Formula

Suppose we have two quantities or two numbers or two entities and we have to find the ratio of these two, then the formula for ratio is defined as;

a : b ⇒ a/b

where, a and b could be any two quantity. You can also learn ratio formula completely here.

Now, let us assume that, in proportion, the two ratios are a:b & c:d. The two terms ‘b’ and ‘c’ are called as ‘means or mean term,’ whereas the terms ‘a’ and ‘d’ are known as ‘extremes or extreme terms.’

 a/b = c/d or  a : b :: c : d

Let us consider one more example of a number of students in a classroom. Our first ratio of the number of girls to boys is 3:5 and that of the other is 4:8, then the proportion can be written as

3 : 5 ::  4 : 8 or 3/5 = 4/8

Here 3 & 8 are the extremes, while 5 & 4 are the means.

Ratio and Proportion Tricks With Example Questions

Question 1: Are the ratios 4:5 and 8:10 said to be in Proportion?


4:5= 4/5 = 0.8 and 8: 10= 8/10= 0.8

Since both the ratios are equal, they are said to be in proportion.

Question 2: Are the two ratios 8:10 and 7:10 in proportion?


8:10= 8/10= 0.8 and 7:10= 7/10= 0.7

Since both the ratios are not equal, they are not in proportion.

Continued Proportion

Consider two ratios to be a:b and c:d.

Then in order to find the continued proportion for the two given ratio terms, we convert the means to a single term/number. This would, in general, be the LCM of means.

For the given ratio, the LCM of b & c will be bc.

Thus, multiplying the first ratio by c and second ratio by b, we have

First ratio- ca:bc

Second ratio- bc: bd

Thus, the continued proportion can be written in the form of ca:bc:bd

Example: Given ratio are-

a:b = 2:3

b:c = 5:2

c:d = 1:4

Find a:b:c.

Solution: Multiplying the first ratio by 5, second by 3 and third by 6, we have

a:b = 10: 15

b:c = 15 : 6

c:d = 6 : 24

In the ratio’s above, all the mean terms are equal, thus

a:b:c:d = 10:15:6:24

Likewise, ratio and proportion are used to solve many real-world problems. Get NCERT solutions for Ratios and Proportion in detail and step-by-step procedure to all questions in NCERT textbooks at BYJU’S.

Practise This Question

Draw a line AB. At A, draw an arc of length 3cm using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure QAB. What is the value of QAB.