Question

Express each of the given ratio in its simplest form:

$\left(viii\right)$ $6$ months $:1\frac{1}{3}$ years

Answer 1

Step: Express the ratio in simplest form:

Since $1$ year $=12$ months,

Therefore,
$1\frac{1}{3}$ years $=12\times 1\frac{1}{3}=12\times \frac{4}{3}=16$ months

Now,
$6$ months $:1\frac{1}{3}$ years $=\frac{6\text{months}}{16\text{months}}$

Above ratio or fraction can be converted to its simplest form by dividing numerator and denominator by their $\text{HCF}$ equal to $3$,

we get,
$\frac{6}{16}=\frac{6÷2}{16÷2}=\frac{3}{8}$

Hence, the simplest form of the given ratio is $3:8$.