Question

Find the ratio of the following:
81 to 108

Answer 1

Hint: Convert the numbers in both the numerator and denominator as the multiples of a same number and cancel them. Repeat this method until you obtain the least possible value of the numbers.

Complete step-by-step answer:

We have to find the ratio 81 to 108 which can be written by \[\dfrac{{81}}{{108}}\]
Now, rewriting the numbers in numerators and denominator as the multiples of 3, we have
\[\dfrac{{81}}{{108}} = \dfrac{{3 \times 27}}{{3 \times 36}} = \dfrac{{27}}{{36}}\]
Then, rewriting the numbers in numerators and denominator as the multiples of 3, we have
\[\dfrac{{81}}{{108}} = \dfrac{{3 \times 9}}{{3 \times 12}} = \dfrac{9}{{12}}\]
Again, rewriting the numbers in numerators and denominator as the multiples of 3, we have
\[\dfrac{{81}}{{108}} = \dfrac{{3 \times 3}}{{3 \times 4}} = \dfrac{3}{4}\]
Thus, the ratio of 81 to 108 is \[3:4\].

Note: In these types of question, \[a{\text{ to }}b\] can be written as \[\dfrac{a}{b}\] and the ratio of \[\dfrac{x}{y}\] can be written as \[x:y\]. Remember that we can only cancel the common numbers or terms in both the numerator and denominator.