# Divide by zero

**Repeated and opposite operations**

Everybody knows that 7 + 7 + 7 is shortened to 3 × 7.

Multiplication is repeated addition.

Subtraction is the opposite operation of addition and

Dividing is the opposite operation of multiplication.

Thus, dividing is a repeated subtraction.

**How may times you can subtract 4 of 12?**

First time: 12 - 4 = 8; second time: 8 - 4 = 4; third time: 4 - 4 = 0.

Then you reached the zero. So it could be done 3 ×.

In short you write 12 : 4 = 3.

**12 : 0 = ?**

Now try to calculate 12 : 0 with the same method.

Then you wonder, how often you can subtract zero of the twelve.

First 12 - 0 = 12. Then 12 - 0 = 12. Following 12 - 0 = 12. ... .

Because you never reach the zero, you can make two remarks.

The first thing is: you can subtract infinite number of times.

The other remark is, that dividing by zero is impossible, because this subtract process never ends.

This number two is more practical, since you never leave the 12 and

you never reaches 0.

In short: **dividing by zero is impossible**.

**An algebraic explanation**

12 : 4 = 3, because 3 × 4 = 12.

In the same way you tackle the problem 12 : 0.

Suppose 12 : 0 = *p*, then *p* × 0 = 12.

However *p* × 0 = 0 and not 12. This is contrary.

Consequently *p* × 0 = 12 has no solution for *p*.

Then 12 : 0 = *p* has no solution as well.

Therefore **dividing by zero is impossible**.

You are not allowed to divide by zero, because you cannot divide by zero.

Any electronic calculator should display: *error* after input '12 : 0 ='