Question

Do \[10\] divide by \[0\] and \[0\] divide by \[10\] have the same answer?

Answer 1

Hint: To find that if \[10\] divide by \[0\] and \[0\] divide by \[10\] are equal, we will first try to divide \[10\] by \[0\] and then \[0\] divide by \[10\]. In the first case we will consider \[10\] as a dividend and \[0\] as a divisor and in the second case we will consider \[0\] as a dividend and \[10\] as a divisor. We will check if by dividing \[10\] by \[0\] and \[0\] by \[10\] the answer is the same or not.

Complete step by step answer:
We know from the definition of an operation of division that \[a\] divided by \[b\] is a number \[c\] such that \[a = b \times c\].
First consider \[10\] divide by \[0\] i.e., \[\dfrac{{10}}{0}\] also must be a number which when multiplied by \[0\] gives 10. But we know any number multiplied by \[0\] gives \[0\].
As, there is not any such number which on multiplication with zero gives any number other than zero.
Therefore, \[\dfrac{{10}}{0}\] is undefined.
Now, consider \[0\] divided by \[10\] i.e., \[\dfrac{0}{{10}}\] is a number which when multiplied by \[10\] gives \[0\].
As we know, anything multiplied by \[0\] gives the result as \[0\]. Any other number multiplied by \[10\] will not give the result \[0\].
Therefore, \[\dfrac{0}{{10}}\] is \[0\].
Hence, we can see that \[\dfrac{{10}}{0}\] is undefined whereas \[\dfrac{0}{{10}}\] is \[0\].
Therefore, \[10\] divide by \[0\] and \[0\] divide by \[10\] do not have the same answer.

Note:
In normal cases the value of any number divided by \[0\] is undefined. The value of \[10\] 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 tends to something and not equal to something. So, we consider it to be infinity.