Question

Express the ratio 36:90 in its simplest form.

Answer 1

Hint: In this question, we use the concept of HCF. To find the ratio in simplest form so we divide each number with HCF of both the numbers. So, we will get the required answer.

Complete step-by-step answer:

For Convert 36:90 in simplest form so we have to divide each number by HCF of 36 and 90 .
Now, HCF of 36 and 90
The Highest Common Factor (HCF) of two or more numbers is the highest number by which all the given numbers are divisible without leaving any remainders
The factor of $36 = 2 \times 2 \times 3 \times 3$
The factor of $90 = 2 \times 3 \times 3 \times 5$
HCF of 36 and 90 $ = 2 \times 3 \times 3 = 18$
Now, divide 36:90 by the HCF of 36 and 90.
$ \Rightarrow \dfrac{{36}}{{90}}$
Divide by 18 in numerator and denominator.
$ \Rightarrow \dfrac{{\dfrac{{36}}{{18}}}}{{\dfrac{{90}}{{18}}}} = \dfrac{2}{5}$
So, the simplest form of ratio 36:90 is 2:5.

Note: Whenever we face such types of problems we use some important points. Like first we find the HCF of two numbers then divide each number by the HCF. So, using this concept we can easily convert ratio into simplest form.