Who is asking: Student
Level: Secondary

Why can't I divide a number by zero. When I put in my calculater 0 divided by 7 it equals 0. But when I put 7 divided by zero my calculater say's error. Why can't this be solved? What is the answer? Is there a paper on it? Help?


Hi Josh

There are two answers:

(a) The question

What is 7 divided by 0?

can be rephrased as

What number, multiplied by 0, gives 7?

That is, consider the equation:

0 x = 7.

Every ordinary number I try for x in FAILS

0 x = 0!

So I can say there is NO REAL ANSWER. The calculator can't find one to give.

However, you can figure out answers - provided you include INFINITE numbers. That is a whole other subject, involving limits etc. as well. Still don't be surprised that a later course will 'make more sense' out of this although your calculator will still confidently say there is no REAL NUMBER answer.

(b) The second answer comes from attempting to divide zero by zero. Consider the multiplictions:

0 x 1 = 0
0 x 2 = 0

Now what should be the answer to 0/0? 1, 2, .... , -100, .... When something has multiple possible real answers, we don't give an answer, or else we look more deeply for ADDITIONAL information which would pick out a single answer. For this situation of 0/0, the study of limits, l'hopital's rule etc. in calculus is such a 'search for additional information' that sometimes gives extra information which picks out a single answer.

It is clear however that the calculator has no way to pick one answer instead of the others - so it just gives an 'error' message'. (In the old days of mechanical calculators, they would spin their gears until you unplugged them!)

A key point is that case (a) no real answer - but specific infinite answers and (b) - multiple answers which check; are very different. They just lead outside of the system where there is a single real number which the calculator can give.

Walter Whiteley


We have received this question before and Chris gave a different wording of the same answer.

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