Question

What is the set of numbers to which $\dfrac{36}{6}$ belong?

Answer 1

Hint: In order to find out in which set(s) does the given number belong, we will first simplify the given number, so that we obtain the new number in its simplest form. Now, we will look at this number and decide in which set(s) does this number belong. We shall proceed like this to get our answer.

Complete step by step solution:
Let us first assign some terms that we are going to use in our solution. Let the fraction given to us be denoted by ‘x’, such that, our first step towards solving this problem will be to find the simplest value of ‘x’. This can be done as follows:
$\begin{align}
  & \Rightarrow x=\dfrac{36}{6} \\
 & \therefore x=6 \\
\end{align}$
Therefore, we get the simplest form of ‘x’ as 6. Now, we will see in which set(s) of numbers does 6 belong.

First of all, we can say that 6 is a Real number and not a complex number as there is no complex term in it so it belongs in the set of Real numbers. So, $6\in R$.
The second set of numbers is the set of Integers. 6 being an integer belongs to the set of integers. This can be represented as: $6\in I$.
The third is the set of whole numbers, as 6 is a positive whole number. So, $6\in W$.
The fourth set of numbers is the set of Positive integers or Counting numbers or Natural numbers. Since, 6 is a positive integer, it belongs to this set. So, $6\in N$.
The fifth and the last set of numbers is the set of rational numbers. 6 is a rational number, so it belongs in this set. This can be written as: $6\in Q$.
Hence, the sets of numbers to which $\dfrac{36}{6}$ belong are Real numbers (R), Integers (I), Whole numbers (W), Natural numbers (N) and Rational numbers (Q).

Note: The difference between the set of Natural numbers and the set of Whole numbers is only of a zero. This is because the set of Whole numbers contains zero in it and the set of Natural numbers does not contain zero in it. This could be represented as: $W-\left\{ 0 \right\}=N$ .