Question

What is 7 divided by 0?

Answer 1

Hint: Assume the required expression as E. Now, consider 7 as the dividend and write it in the numerator of the fraction while consider 0 as the divisor and write it in the denominator of the fraction of the expression E. Use the fact that the denominator of a fraction cannot be 0 to conclude the result of the expression E.

Complete step-by-step solution:
Here we have been asked to find the value of the expression that will be obtained by the sentence 7 divided by 0. Let us assume the expression as E.
Now, here 7 is being divided by 0 so the dividend is 7 and the divisor is 0. Therefore, the expression will have 7 as the numerator and 0 as the denominator. So we get,
$\begin{align}
  & \Rightarrow E=7\div 0 \\
 & \Rightarrow E=\dfrac{7}{0} \\
\end{align}$
We know that any fraction or you may call a rational number is defined only when its denominator is unequal to 0. This is the definition of a rational number that ‘a number of the form $\dfrac{p}{q}$ where p and q are integers and q is unequal to 0’. But in the above case we have the denominator equal to 0 in the expression E, so the given expression is undefined.
Hence, 7 divided by 0 is undefined.

Note: You may think the result of the given expression will be infinite $\left( \infty \right)$ but remember that infinite is not a real number so the given form of the expression is termed as indeterminate form. These terms are used in the starting chapter of the calculus known as limits. Note that 0 divided by any non – zero number is 0 but any non – zero number divided by 0 is undefined.