Basics of Ratio: Use and Application

This post will discuss some Basics of the Ratio. The ratio is used to compare two quantities of the same kind. Consider in a group of 45 people, 15 of them are females. Let us understand the Basics of the Ratio from an example. We can compare the number of males and the number of females in the group in two different ways,

1. There are 15 more males than females in a group of people. Actually, we are comparing the number of males and the number of females in the group of people by finding their difference.
2. The number of males in a group of people is twice that of females. Actually, we are comparing the number of males and the number of females by finding a fraction consisting of the number of males over the number of females. The fraction is $\frac{30}{15}$.

In the second method, the fraction obtained is an example of the ratio.

A ratio may be written with a colon symbol between the numbers. Therefore, the male-female ratio in the group of people can be written as 30:15 or $\frac{30}{15}$. It can be read as the ratio of 30 is to 15 or simply 30 to 15.

In general, the ratio of $a$ to $b$ can be written as $la:b$ or $\frac{a}{b}$, where $a$ and $b$ represent whole numbers and $b$ should not be zero. Since ratio $\frac{30}{15}=\frac{2}{1}$ or $30:15 = 2:1$. the $30:15$ and $2:1$ are called equivalent ratios.

Note that the order in which the ratio is written is important. A ratio has no measurement units. It is only a number that indicates how many times, one quantity is as great as the other. For example, the male to the female ratio of 2:1 means that the number of males is twice the number of females. It can also be interpreted as the female to male of 1:2 or $\frac{1}{2}$ indicates that there are half as many females as males.

Ratios can also be used to compared more than two quantities. For example, three-man A, B, and C share the profit of a business. They receive say 5000, 3000 and 1000, respectively. The ratio of their share of the profit is 5000:3000:1000 or 5:3:1.

One can also find that either there is an increase or decrease in the ratio. For example, say if the number of teachers in a college is increased from 45 to 55, then the ratio “number of present staff” to “number of old staff” (or number of present staff: number of old staff) = 55:45 = 11:9 or $\frac{\text{no. of present staff}}{\text{no. of old staff}} = \frac{55}{45}=\frac{11}{9}$.
This ratio can be interpreted as the number of teachers has been increased in the ratio 11:9 or $\frac{11}{9}$.