Explain how you know that 45 divided 0 cannot be done.

I'll give you what I know that is an undefined problem.

You can't divide something by nothing.

one has to understand what division really is

e.g. 12/3 = ??

12-3 = 9
9-3 = 6
6-3 = 3
3-3 = 0

how many times did I subtract the 3 so that nothing was left ?
4 times
so 12/3=4

so 45/0 = ??
45-0 = 45
45-0=45
45-0=45
...
how many times will I have to do this before nothing is left???
I guess I could keep this up for all eternity

so we say 45/0 is infinitely large or undefined

another way:
24/4 = 6 because 4*6 = 24
then 45/0 = x because x*0=45
but anything times zero is zero!
so x cannot be a number as we know it.
so 45/0 does not have an answer as we know it, so we call it undefined.

To understand why dividing by zero is not possible, we need to look at the basic principles of division. Division is essentially the process of dividing a quantity into equal parts.

When we divide a number by another number, we are essentially asking "how many times does the divisor fit into the dividend?" For example, if we have 10 apples and we want to divide them into groups of 2, we would have 5 groups because 10 divided by 2 equals 5.

However, when it comes to dividing by zero, the concept breaks down. This is because zero does not represent any specific value or quantity. It is considered an undefined concept in mathematics.

Mathematically, dividing any number by zero leads to contradictions and inconsistencies. For example, if we were to calculate 45 divided by 0, we would need to find a number that, when multiplied by 0, gives us 45. However, no such number exists since any number multiplied by zero is always zero, not 45.

Additionally, dividing by zero violates the fundamental properties of arithmetic, such as the distributive property and associative property, which rely on the assumption that division is defined for all non-zero numbers.

Overall, dividing by zero is not possible because it leads to mathematical inconsistencies and contradicts the basic principles of division.