Question

What type of number is $\dfrac{-15}{3}?$

Answer 1

Hint: In the number system, there are negative numbers and positive numbers. Also, there are natural numbers, integers, rational numbers, real numbers, complex numbers, etc. We will find in which category the given number is included.

Complete step by step solution:
We know that there are positive numbers and negative numbers in the number system apart from zero.
We can undoubtedly say that the given number $\dfrac{-15}{3}$ is a negative number since it has a negative sign in front of it. This is just one classification.
We call the numbers from $1$ to infinity the natural numbers. That is, the numbers we use to count are called the natural numbers. So, the given number is not a natural number.
We know that the numbers including the natural numbers, zero and the negative numbers are called integers. We know that $3\times 5=15.$ Therefore, if any one of the numbers is negative, then the product is also negative. So, we will get $\dfrac{-15}{3}=-5.$ Therefore, the given number is an integer.
We know that the number that can be written as $\dfrac{p}{q}$ where $p$ and $q$ are integers are called rational numbers. So, the given number is a rational number.
We can find the given value in the set of real numbers and complex numbers since they are supersets of the set of rational numbers.

Note: The numbers that cannot be written in the form of $\dfrac{p}{q}$ where $p$ and $q$ are called irrational numbers. So, the intersection of the set of rational numbers and the set of irrational numbers is $\phi .$ And their union is the set of real numbers.