Page 227 - Start Up Mathematics_6

12 Ratio, Proportion and

Unitary Method

We often come across situations where we need to compare two quantities in terms of their
magnitudes. Let’s compare the ages of Ali and Gurpreet, who are 12 and 10 years old. This
comparison could be done in two ways:

(i) Comparison by Difference: The difference in their ages is 2 years (i.e., 12 – 10 = 2 years).
Hence, we say that Ali is 2 years older to Gurpreet.
(ii) Comparison by Division:

Ali’s age 12 6
Gurpreet’s age = 10 = 5

6
i.e., Ali’s age = cm times Gurpreet’s age
5
This comparison by division is called ratio. Ratio is denoted by the symbol ‘:’
In the above example, ratio of Ali’s age to Gurpreet’s age is 6 : 5.

Ratio
The ratio of two quantities of the same kind and expressed in same units is a fraction that shows
how many times one quantity is of the other.
The ratio of any two non-zero numbers a and b is a ÷ b = a . Symbolically, ratio between two
b
numbers is denoted by a : b. The numbers a and b are called the terms of the ratio a : b. The first
term a is the antecedent and second term b is the consequent.

• The ratio a : b and b : a are not equal. They are equal only if a = b.
• The ratio a : b has no units. It is independent of the units of a and b.
• The ratio a : b is defined only if a and b are non-zero numbers.
• Ratio can be expressed as a fraction.

Simplest Form of Ratio
A ratio is in its simplest form if the terms of the ratio have no common factors other
than 1. For example, the simplest form of the ratio 20 : 15 is 4 : 3.

Equivalent Ratios

Multiplying or dividing the first and second term of the ratio by the same non-zero number gives
equivalent ratios.
Consider the ratio 8 : 6.

We have, 8 = 8 ÷ 2 = 4 , also, 8 = 83× = 24 .
6 6 ÷ 2 3 6 63× 18
Therefore, 4 : 3 and 24 : 18 are equivalent ratios of 8 : 6.