Question

Reduce each of the following ratios to their lowest terms:

(iii) $3$ years $4$ months : $5$ years $5$ months

Answer 1

Expressing in the Lowest form

We know that $1$ year = $12$ months

Therefore,
$3$ years $4$ months
$=3\times 12+4=36+4=40$ months

And,
$5$ years $5$ months
$=5\times 12+5=60+5=65$months

We have:
$3$ years $4$ months : $5$ years $5$ months

$=\frac{3years4months}{5years5months}=\frac{40months}{65months}=\frac{40}{65}$

Simplifying the above ratio or fraction into its lowest form by dividing numerator and denominator by 5, we get

$\frac{40}{65}=\frac{40÷5}{65÷5}=\frac{8}{13}=8:13$

Therefore, the simplest form of the ratio $3$ years $4$ months : $5$ years $5$ months is $8:13$