Question

What is 6 divided by 0?

Answer 1

Hint: To find the quotient when 6 is divided by 0, we have to first represent it in the form $\dfrac{6}{0}$ . We have to equate $\dfrac{6}{0}$ to x . We have to solve for x if possible. If we cannot solve for x, then the quotient will be undefined.

Complete step by step solution:
We have to find the quotient when 6 is divided by 0. Here, we can see that 6 is the dividend and 0 is the divisor. Let us represent this as $\dfrac{6}{0}$ .
Any number (except 0) when divided by 0 is undefined. We can prove this fact by equating $\dfrac{6}{0}$ to x.
$\Rightarrow \dfrac{6}{0}=x$
Let us take the denominator of LHS to RHS.
$\Rightarrow 6=x\times 0$
We know that when a number is multiplied 0 is always 0. Hence, we can write the above equation as
$\Rightarrow 6=0$
The above form is not possible because 6 is not equal to 0. Therefore, any number when divided by 0 is undefined except for 0.

Therefore, the result when 6 is divided by 0 is undefined.

Note: We have seen that any number when divided by 0 is undefined except for 0. Let us consider the case of $\dfrac{0}{0}$ . We have to equate $\dfrac{0}{0}$ to x.
$\Rightarrow \dfrac{0}{0}=x$
Let us take 0 from the denominator of LHS to the RHS.
$\begin{align}
  & \Rightarrow 0=x\times 0 \\
 & \Rightarrow 0=0 \\
\end{align}$
The above form is possible. Thus the value of $\dfrac{0}{0}$ is not undefined but is equal to any number.