Question

Find the ratio of the following $81$ to $108$

Answer 1

Hint: In this question first do the prime factorization of the numbers then take the $HCF$ i.e. highest common factor.Divide both numerator and denominator with H.C.F and we will get the required answer.

Complete step-by-step answer:
According to the question we have to find the ratio of $\dfrac{{81}}{{108}}$ , So
$1)$ Write $81$ and $108$ product prime.
$2)$ Find the $HCF$ of $81$ and $108$
Hence,
$
  81 = 3 \times 3 \times 3 \times 3 \\
  108 = 3 \times 3 \times 3 \times 4 \\
$
Now, the $HCF$ of $81$ and $108$$ = 3 \times 3 \times 3$$ = 27$
Ratio$ = \dfrac{{81}}{{108}}$
 Hence to find the ratio we need to divide the denominator and numerator with $HCF$.
$ = $$\dfrac{{81}}{{27}} \times \dfrac{{27}}{{108}}$
$ = \dfrac{3}{4}$
Hence, the ratio of $\dfrac{{81}}{{108}}$ is $\dfrac{3}{4}$

Note: For such type of ratio and proportion questions it is advisable to be thorough with the concept of $HCF$ i.e. the highest common factor to solve the question easily and to save time.Factorise to find the highest common factor.One more approach is there for finding ratio of numbers i.e by cancellation method.Cancelling is a way to simplify fractions before we multiply which gives ratio of two numbers.