Basics of Ratios: Use and Application (2021)

This post will discuss some Basics of Ratios. The ratio is used to compare two quantities of the same kind. Consider in a group of 45 people, 15 of whom are females. Let us understand the Basics of Ratios from an example.

Example of Ratios

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. We are comparing the number of males and the number of females in the group of people by finding their differences.
2. The number of males in a group of people is twice that of females. 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.

Application of Ratios

Ratios can also be used to compare more than two quantities. For example, three-men 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 $\frac{11}{9}$.

The application of ratios in various fields are:

1. Finance (Financial rations, investment analysis)
2. Business and Management (inventory management, marketing and sales, and human resources)
3. Science and Engineering (Concentration and Ratios in Chemistry, Mixture Ratios, Scale and Proportion
4. Everyday Applications (Recipes, Maps and Scales)
5. Mathematics (Rates and Unit Costs, Proportions)

Remember, ratios are a versatile tool, and their specific applications can vary depending on the field and situation. However, their core principle of comparing quantities remains constant, making them a valuable asset for anyone seeking to analyze and understand the world around them.

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