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.