# Ratio

A method of comparing two quantities of same kind is defined as Ratio.

Comparison of two quantities which belong to group, is actually performed in mathematics to know the first quantity, how many times to second quantity and vice-versa.

## How to compare

Division method is used to evaluate the comparison of the two quantities of same kind.

The antecedent (the value in numerator) and consequent (the value in denominator) both should be at their minimum terms while performing the division to evaluate the ratio of two quantities. It is possible when same multiplying factors are there in both antecedent and consequent.

### How to use

Consider a class in a school. Totally, $20$ students are there in that class, in which $12$ students are boys and $8$ students are girls. Boys and girls both are human beings and it is their common property. So, we can compare them by the concept of ratio.

There are two possible methods to calculate the ratio between them. One is to calculate the ratio of number of boys to number of girls and the second one is to calculate the ratio of number of girls to number of boys.

Let us first find the ratio of number of boys to number of girls.

$⇒Ratio=\frac{12}{8}$

Both numerator and denominator can be expressed as multiplying factors in order to get ratio in minimum terms.

$⇒Ratio=\frac{2×2×3}{2×2×2}$

There are two $2$ in both numerator and denominator multiplicatively. So, they can be cancelled each other mathematically.

$⇒Ratio=\frac{\overline{)2}×\overline{)2}×3}{\overline{)2}×\overline{)2}×2}=\frac{3}{2}$

The ratio of number of boys to number of girls in a class is $\frac{3}{2}$. It is written as $3:2$. It is read as either $3$ is to $2$ or $3$ to $2$. The meaning of this ratio is, for every $3$ boys admission, $2$ girls should be admitted in the class. In this pattern, the whole class is formed with $20$ students.

Similarly, the ratio of number of girls to number of boys can be calculated by applying the same procedure.

$⇒Ratio=\frac{8}{12}=\frac{2×2×2}{2×2×3}=\frac{\overline{)2}×\overline{)2}×2}{\overline{)2}×\overline{)2}×3}=\frac{2}{3}$

The ratio of number of girls to number of boys in the class is $\frac{2}{3}$. It is expressed as $2:3$. It is read as either $2$ is to $3$ or $2$ to $3$. It means, for every $2$ girls admission, $3$ boys should get admission in the class. Thus, the class is formed with $20$ students.

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