Question

What is the set of numbers to which $\dfrac{18}{3}$ belong?

Answer 1

Hint: First simplify the given fraction by cancelling the common factors of the numerator and the denominator. Now, check if we can include this simplified form of the fraction in the set of natural numbers, whole numbers, integers, rational numbers etc. All the sets in which it can be included will be the answer.

Complete step by step solution:
Here we have been provided with the fraction $\dfrac{18}{3}$ and we are asked the set to which it belongs. First we need to simplify this fraction if there are common factors in the numerator and the denominator. So we have,
$\begin{align}
 & \Rightarrow \dfrac{18}{3}=\dfrac{3\times 6}{3\times 1} \\
 & \therefore \dfrac{18}{3}=6 \\
\end{align}$
Now, clearly we can include 6 in the set of natural numbers as it is a counting number, it can be considered as a whole number and integer. Also, we can write 6 as $\dfrac{6}{1}$ because we know that any number divided by or multiplied with 1 given the number itself. We know that any number of the form $\dfrac{p}{q}$ where p and q are integers and q is unequal to 0 is called a rational number. Therefore, we can say that 6 or $\dfrac{6}{1}$ is a rational number.

Hence, $\dfrac{18}{3}$ belongs to the sets of natural numbers (N), whole numbers (W), integers (Z) and rational numbers (R).

Note: Note that all natural numbers, whole numbers, integers, rational numbers and irrational numbers are the subsets of real numbers. 6 is not an irrational number because irrational numbers are non – terminating and non – repeating. There are bigger sets than real numbers also like the set of complex numbers which include all real and imaginary numbers. You must remember the definitions of all the types of sets.