Question

Express the ratio $20:60$ in their simplest form.
A) $3:1$
B) $2:6$
C) $1:3$
D) $10:30$

Answer 1

Hint:The simplest form of any ratio contains either two distinct prime numbers in numerator and denominator or the numerator and denominator are co-prime numbers. The simplest form of any ratio can be determined by expressing both numerators and denominators as product of prime factors and then eliminating the common factors. The simplest form is the one for which we cannot divide the ratio further.

Complete step-by-step answer:
We will consider numerator and denominator separately.
We have to find the common factors from both so we will first factorize numerator and denominator into its prime factors.
First consider the numerator.
We will factorize numerator into its prime factors as follows:
$20 = 2 \times 2 \times 5$
Similarly, we will factorize denominators as well.
So, consider the denominator:
$60 = 2 \times 2 \times 3 \times 5$
Therefore, we have now got the prime factorization of both numerators and denominators.
Now express the ratio $20:60$ in the fraction form by writing it as follows:
$\dfrac{{20}}{{60}} = \dfrac{{2 \times 2 \times 5}}{{2 \times 2 \times 3 \times 5}}$
Now on the right-hand side if you observe closely then it is easier to see that the factor $2 \times 2 \times 5$ is common in both numerator as well as denominator.
Therefore, we can cancel it out.
Thus, we are left with:
$\dfrac{{20}}{{60}} = \dfrac{1}{3}$
Now express the fraction in the ratio form as $1:3$ .

So, the correct answer is “Option C”.

Note:The final answer is in the simplest form meaning we can’t divide it further. We have used prime factorisation to solve the problem but it is not the only way. One can simply divide denominator by the numerator to reach the result. Finally, understand why all the other options are not right.