Question

If an integer is divided by a nonzero integer, then the quotient will be always _____.

• A. a whole number
• B. a rational number
• C. a natural number
• D. an integer

Answer 1

The correct option is B a rational number

Let the two integers be $“a”$ and $“b”$, where $b\ne 0$.

1. If $b$ is a factor of $a$, then $a÷b$ will have no reminder and will be an integer. If $“a”$ is $0$, then $a÷b$ will also be $0$ and so it will be a whole number. If $a÷b$ is greater than $0$, then it is also a natural number.

• Let a = 6 and b = 3. So, $a÷b$ = $6÷3$ = 2.

1. If $b$ is not a factor of $a$, then $a÷b$ is not an integer. It can neither be a whole number or a natural number. But by definition, it is still a rational number. And it will always be a rational number.

• Let $a=6$ and $b=5$. So, $a÷b=6÷5=1.2$.

In all these situations, the quotient is a rational number, where the integer is divided by a nonzero integer.