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Introduction

Father: Shreya! As you compare your and your brother’s heights by subtracting Rohan’s height
from yours height, i.e., 140 cm – 130 cm = 10 cm
And you found that you are 10 cm taller than Rohan.

Thus, finding the difference between two quantities or numbers is a way of comparing two
quantities or numbers.
But, we have another way of comparing two quantities or numbers. In certain situations,

comparison by division makes better sense than comparison by subtraction.

140cm 14
Now, let us divide your height by Rohan’s height, as =
130cm 13
14
Here, we can say that your height is times of your brother’s height. This division is also called
13
the ratio of the heights of both of you.

The method of comparing quantities or numbers by division is also known as ratio.
Concept of Ratio

A ratio is a comparison of two quantities of same kind by division. It can be used to express one
quantity as a fraction of the other one.
It is denoted by the colon (:) and read as ‘is to’.
If a and b are two quantities, the ratio of quantity a to quantity b is written Remember
a a
as or a : b and read as ‘a is to b’. In or a : b, b must not
b b
Here, a and b are called the terms of the ratio. a is called the first term or be 0, i.e., b ≠ 0.
antecedent and b is called the second term or consequent.

a Antecedent
Ratio =
b Consequent

Suppose there are 18 girls and 16 boys in a class, then the ratio of the girls to the boys in the class
18 9
= = = 9: 8 (read as 9 is to 8)
16 8
16 8
Similarly, the ratio of the boys to girls in the class = = = 8: 9 (read as 8 is to 9)
18 9
In the same way, the ratio of the girls to the total students of the class will be
18 18 9
= = = 9 : 17
16 18 34 17
+
16 16 8
And the ratio of the boys to the total students of the class will be = = = 8 : 17.
+
16 18 34 17
Properties of a Ratio

Property 1: The order of the terms in a ratio is very important.
For example: The ratio ‘2 is to 3’ is different from the ratio ‘3 is to 2’.

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