Page 127 - Start Up Mathematics_7

8 Percentage and Its Applications

In our everyday life, we often need to compare two quantities in terms of their magnitudes.
Comparison between two things can either be done by finding their ratio or by calculating their
percentage.
Suppose we need to compare the speed of a helicopter with that of a fighter jet.

Helicopter Fighter jet
Speed of helicopter = 300 km/h Speed of fighter jet = 2,120 km/h

The speed of the fighter jet is approximately seven times the speed of the helicopter. Equivalently,
1
the speed of the helicopter is times the speed of the fighter jet.
7

We can compare two quantities if and only if their units are same.

Ratio

The ratio of two quantities expressed in the same units and of the same kind is a fraction that
shows how many times one quantity is of the other.
a
The ratio of any two non-zero numbers a and b is a ÷ b = . The usual notation to represent ratio
b
of a and b is a : b.

Simplest form of ratio

A ratio is said to be in its simplest form when the terms of the ratio are co-prime, i.e., they have

no common factors other than 1. For example, the simplest form of the ratio 20 : 15 is 4 : 3.

Equivalent ratios

Equivalent ratios are obtained by multiplying or dividing the terms of the ratio by the same constant
non-zero number. For example, the ratio 1 : 2 is equivalent to 2 : 4 or 5 : 10.