Ratio and Proportion

Ratio: The ratio of two quantities a and b of the same kind and in the same units is the fraction ~ written as $a : b$, read as $\text{ 'a is to b'}$.

Terms of a ratio: In the ratio $a : b$, we call \$latex a as the first term or antecedent and b as the second term or consequent.

Thus, in the ratio $2 : 5$, the antecedent is $2$·and the consequent is $5$.

An Important Property

If both the terms of a ratio are multiplied or divided by the same non-zero quantity, then the ratio remains unchanged.

i.e., if $\displaystyle m \neq 0$, then

$\displaystyle \frac{a}{b}=\frac{ma}{mb} \text{ or we can say } a:b=ma:mb$

$\displaystyle \frac{a}{b}=\frac{\frac{a}{m}}{\frac{b}{m}} \text{ or we can say } a:b= \frac{a}{m}:\frac{b}{m}$

Ratio in Simplest Form

A ratio $a : b$ is said to be in simplest form, if the H. C. F. of a and b is 1.