Question

How do you simplify $24:36?$

Answer 1

Hint: First of all we will convert the given ratio in the form of the fraction then we will find the prime factors of the given numbers and when the factors are placed in the fraction we will remove common factors from the numerator and the denominator for the resultant value.

Complete step-by-step answer:
First of all we will rewrite the given ratio in the form of the fraction. Fraction is the term which is expressed in the form of numerator upon the denominator.
$24:36 = \dfrac{{24}}{{36}}$ .... (A)
Find out the factors of the above fraction.
Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $1$ and which are not the product of any two smaller natural numbers. For Example: $2,{\text{ 3, 5, 7,}}......$ $2$ is the prime number as it can have only $1$ factor.
So, start dividing the given number with the least prime number and then continue dividing with the greater prime numbers. Start with $2$ if it is not divisible by $2$ then move to $3$ and so on...
So, the prime factors of $24 = 2 \times 2 \times 2 \times 3$ .... (B)
Similarly, the prime factors of $36 = 2 \times 2 \times 3 \times 3$ .... (C)
Place the values of equation (B) and (C) in the equation (A)
$24:36 = \dfrac{{2 \times 2 \times 2 \times 3}}{{2 \times 2 \times 3 \times 3}}$
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
$24:36 = \dfrac{2}{3}$
This is the required solution.

Note: Be good in multiples and remember at least $20$. Know the difference between the prime numbers and the composite numbers. Always convert the given number in the prime factors and not the composite to find out the common factors and remove them.