Question

Reduce in standard form: $\dfrac{{36}}{{ - 24}}$.

Answer 1

Hint: In this question, the numerator of the given fraction is $36$ and the denominator is equal to $ - 24$ and we have to simplify this fraction. When the numerator and the denominator are in the form of prime factors and don’t have any common factor, the fraction is said to be simplified. We can find whether the given fraction is simplified or not by writing both the numerator and the denominator as a product of their prime factors, and thus simplify the fraction if it is not in the simplified form.

Complete step by step solution:
Prime factorization of $36$ is:
$36 = 2 \times 2 \times 3 \times 3$
Prime factorization of $24$ is:
$24 = 2 \times 2 \times 2 \times 3$
We see that powers of numbers, $2$ and $3$ are the prime factors of both the numerator and the denominator, so we have ${2^2}$ and $3$ as common factors, and thus we divide the numerator and the denominator by ${2^2} \times 3$.
So, we get, $ - \dfrac{{36}}{{24}} = - \dfrac{{2 \times 2 \times 3 \times 3}}{{2 \times 2 \times 2 \times 3}}$
$ \Rightarrow - \dfrac{{36}}{{24}} = - \dfrac{3}{2}$
Now, the numerator and the denominator are both prime numbers and don’t have any common factor, so it cannot be simplified further.
Hence, the simplified form of $\dfrac{{36}}{{ - 24}}$ is $\left( { - \dfrac{3}{2}} \right)$. So, $\dfrac{{36}}{{ - 24}}$ can be reduced in the standard form as $\left( { - \dfrac{3}{2}} \right)$.
So, the correct answer is “$\left( { - \dfrac{3}{2}} \right)$”.

Note: When a horizontal line divides a term into two parts such that there is one number above the horizontal line and one below it, the part above the horizontal line is called the numerator and the denominator is the lower part. The process of writing a number as a product of the prime factors is known as its prime factorization.