Question

What is 5 divided by 0?

Answer 1

Hint: We need to find the value of 5 divided by 0. We start to perform a division considering number 1 as a dividend and the number 0 as a divisor. Then, we write all the cases encountered during the division to get the desired result.

Complete step by step solution:
The division of a real number P with the real number Q is given as follows.
$\Rightarrow {\displaystyle \frac{P}{Q}}$
Here
P is the dividend of the division
Q is the divisor of the division
Assuming the real number R is the result of the above division.
Writing the expression for the same, we get
$\Rightarrow {\displaystyle \frac{P}{Q}}=R$
Cross-multiplying the number Q to the other side of the equation
$\Rightarrow P=Q\times R$
Now,
According to our question,
Assume that the value of Q is equal to 0
$\Rightarrow Q=0$
if P is the non-zero real number, there is no value of R such that if multiplied by the number $Q=0$, gives a non-zero real number P since the product of any number with the number 0 is always 0.
Even if we consider the value of $P=0$, the real number R can take any number that is multiplied by $Q=0$ to the result as the number 0.
From the above cases
We can say that the division by the number 0 is undefined among the set of real numbers. Therefore, the result of 5 divided by 0 is undefined.

Note: We must remember that the value of 5 divided by 0 is infinity only in the case of Limits. The word infinity signifies the length of the number. In the case of limits, we only assume that the value of limit x tends to something and not equal to something so we consider it infinity.in normal cases, the value of any number divided by 0 is undefined.