Question

What is 0 divided by 1?

Answer 1

Hint: We can use the property that if any number is divided by 1, the result is always the same number. Alternatively, we can also use the property that when 0 is divided by any number, except 0 itself, the result is always equal to 0.

Complete step-by-step solution:
We all know very well that when any number is divided by 1, then the result is the same number.
And so, if a is any number, either real or imaginary, rational or irrational, positive or negative, the result is always a. In mathematical form,
$\dfrac{a}{1}=a$
So, by using this property of definition and potting the value of a = 0, then we get
$\dfrac{0}{1}=0$.
We can also get the same result using other properties.
We also know the property that when 0 is divided by any number (except 0 itself), then the result is always 0. Mathematically, we can say that
if a is any number not equal to 0, then $\dfrac{0}{a}=0$ .
Hence, we can see that we get the same result using this property as well.
Let us once more verify this by the division process.
We know that for $\dfrac{0}{1}$ , the divisor is 1, and the dividend is 0.
So, the division process will look like,
$\begin{align}
  & 1\overset{0}{\overline{\left){0}\right.}} \\
 & \underline{\text{ }0} \\
 & \text{ }0 \\
\end{align}$
Here, we get the remainder as 0. And the quotient is 0.
Hence, we can say that $\dfrac{0}{1}=0$ .
Thus, we have verified by using three different approaches that 0 divided by 1 is 0.
Hence, the required answer is 0.

Note: We must remember that $\dfrac{a}{a}$ = 1, $\dfrac{0}{a}$ = 0, when a is not equal to 0. We must also keep in mind that if a is not equal to zero, then $\dfrac{a}{0}$ = Not Defined. Also, $\dfrac{0}{0}$ is indeterminate. This is indeterminate so that the basic properties of division are not contradicted.