Question

If we divide a positive integer with another positive integer then what is the resulting number?

Answer 1

Hint: In this problem, we have to think about the resulting number when we divide a positive integer with another positive integer. We know that the division of two positive integers will give the positive number. We will consider the different cases for two positive integers and then we divide them. Then, we will observe the resulting numbers.


Complete step-by-step answer:
We know that the division of two positive integers will give the positive number. Let us consider $a$ and $b$ are two positive integers. In this problem, we will consider the different cases for two positive integers and then we divide them.
Case I: If the integer $a$ is exactly divisible by $b$ then we can say that $\dfrac{a}{b}$ will be the positive integer. For example, let us take $a = 8$ and $b = 4$. Note that here $a$ and $b$ are positive integers. We know that the integer $8$ is exactly divisible by the integer $4$. That is, $\dfrac{a}{b} = \dfrac{8}{4} = 2$. Here we can say that the resulting number is a positive integer.
Case II: If the integer $a$ is not exactly divisible by $b$ then we can say that $\dfrac{a}{b}$ will be the positive rational. For example, let us take $a = 9$ and $b = 4$. Note that here $a$ and $b$ are positive integers. We know that the integer $9$ is not exactly divisible by the integer $4$. That is, $\dfrac{a}{b} = \dfrac{9}{4}$. Here we can say that the resulting number is positive rational.
From above cases, we can say that if we divide a positive integer with another positive integer then the resulting number will be either positive integer or positive rational number. In other words, we can say that the resulting number will be either a positive whole number or positive rational number.


Note: Remember that division of two negative integers will give a positive number. In the given problem, if we consider the division of a negative integer by another negative integer then the resulting number will be either positive integer or positive rational number. The rational number is of the form $\dfrac{p}{q}$ where $p$ is an integer and $q$ is natural number.