Page 179 - Maths Class 06

Ratio, Proportion and

Unitary Method

Introduction

Everyday in our life we come across many situations where a need is arise to compare two quantities of
same type in terms of their measurements, etc.
Suppose the heights of Shilpa and Shamita are 160 and 156 cm respectively. We can compare their
heights in two different ways:

(i) We can say that Shilpa is (160 cm – 156 cm) 4 cm taller than Shamita.
Here, we compare the two numbers by taking difference, so, this process is known as
comparison by difference.
Height of Shilpa 160 40
(ii) We can write = = or
Height of Shamita 156 39

40
So, we can say height of Shilpa = times the height of Shamita.
39
In this process, two numbers are compared by taking the help of division method. So, this process is
known as comparison by division.

Thus, in this way, when two similar quantities are compared by the method of division, a ratio is obtained
which shows relation between the two quantities. We use the symbol ‘:’ to express a ratio.
For example, the ratio of height of Shilpa to the height of Shamita is written as ‘40 : 39’ and is read as ‘40
is to 39’.
Important : Comparison is done on the similar kind or unit. We cannot compare 20 books with 3 tickets or
7 girls with 5 pens.

Ratio

Ratio is a way of comparing numbers by division, or we can say that the ratio of two quantities in the same
units is a fraction that one quantity is of the other.
The ratio between two quantities say x and y may be written as x : y or as a division x ¸ y or as the
x
fraction .
y
Here, x is called as ‘first term’ or antecedent and y is called the ‘second term’ or consequent.

NOTE

The names of units are not used in a ratio.
The two quantities compared in a ratio must be expressed in the same unit.

179 Mathematics-6