Question

Evaluate the following:
$\left( { - 36} \right) \div \left( { - 9} \right)$

Answer 1

Hint: As we can clearly see that the question given requires us to divide $ - 36$ by $ - 9$. Whenever we see a question like this, our approach should be to simplify it. Thus, we need to write it in division format as a complex fraction and then expand and work on it. Then, we write the fraction in the simplest form after cancelling the common factor between numerator and denominator.

Complete step by step answer:
In the given problem, we are required to find the quotient when $ - 36$ is divided by $ - 9$.
So, we know that the division of a number by another number is as good as multiplying the number by the multiplicative inverse of the same number.
We know that the multiplicative inverse of a number is equal to its reciprocal. So, the multiplicative inverse of the number $ - 9$ is \[\left( {\dfrac{1}{{ - 9}}} \right)\].
Hence, we multiply the given number $ - 36$ by \[\left( {\dfrac{1}{{ - 9}}} \right)\] to get the desired answer of the given problem.
So, we first write it in fraction format by multiplying the numerators as: $ - 36 \times \left( {\dfrac{1}{{ - 9}}} \right) = \left( {\dfrac{{ - 36}}{{ - 9}}} \right)$.
Firstly, we cancel the negative sign in both numerator and denominator, we get,
$ \Rightarrow \left( {\dfrac{{ - 36}}{{ - 9}}} \right) = \left( {\dfrac{{36}}{9}} \right)$
Now, we can notice that $9$ is a common factor in both numerator and denominator. Expressing the numerator and denominator after factoring out $9$, we get,
\[ \Rightarrow \left( {\dfrac{{9 \times 4}}{9}} \right)\]
Cancelling the common factors in numerator and denominator, we get,
\[ \Rightarrow 4\]
Hence, the quotient obtained on division of $ - 36$ by $ - 9$ is $4$.

Note:
Numerator and denominator never get cut through while division, they only get cut in multiplication. Also, division of a number by a rational number is as good as multiplying the number by the multiplicative inverse of the same rational number. Lastly, it is good to convert your answer from improper fraction to decimal form or mixed fraction form even if it is not mentioned in the question otherwise.