A ratio compares quantities by division. For like quantities, first express them in the same units.

Question

A ratio compares quantities by division. For like quantities, first express them in the same units. The ratios $a:b$ and $ma:mb$ are equivalent when $m\ne0$; division by a common factor also requires that factor to be nonzero. The fraction $a/b$ requires $b\ne0$.

The ratio of $a$ is to $b$ is written as $a:b$ and it has no units.

Conversion of fraction to ratio,

$\frac ab\leftrightarrow a:b$, where $b\ne0$.

Equivalent ratios are obtained by multiplying or dividing all parts by the same nonzero number.

$a:b=ma:mb=\frac an:\frac bn$, where $m\ne0$ and $n\ne0$.

Accepted Answer

Express quantities in the same unit before comparing them. The ratio of $a$ to $b$ is $a:b$, and multiplying or dividing both terms by the same non-zero number gives an equivalent ratio.

Concept of Ratio

Concept of Ratio

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