Question

The simplest form of the ratio $8:12$ is ___ whereas simplest form of the ratio $\frac{1}{8}:\frac{1}{12}$ is ___

Answer 1

Simplest form of $8:12$

$8:12$ can also be written as $\frac{8}{12}$

H.C.F of $8$ and $12$ is $4$

Divide both $8$ and $12$ by $4$

$\frac{8}{12}=\frac{2}{3}$

Hence, Simplest form of $8:12$ is $2:3$

Similarly, Given ratio $\frac{1}{8}:\frac{1}{12}$ is in fraction

L.C.M of denominator $8$ and $12$ is $24$

Multiply both terms by L.C.M $24$

Therefore,

$\frac{1}{8}\times 24:\frac{1}{12}\times 24$ $=3:2$

Hence, Simplest form of $\frac{1}{8}:\frac{1}{12}$ is $3:2$