All of mathmatics, every last bit of it, ultimately comes down to arithmetic. In fact, it may be argued that all of arithmetic ultimately comes down to addition.

Addition is pretty well understood:

2 + 2 = 4

4 + 4 = 8

8 + 8 = 16

16 + 16 = 32

The answer to an addition problem is called the “sum”.

Subtraction is the reverse of addition. The following are equivalent mathematical “sentences”:

3 + 4 = 7

7 – 4 = 3

Subtraction can also be considered as addition with negative numbers (this is how computers do it). The following are also equivalent mathematical “sentences”:

7 – 4 = 3

7 + (-4) = 3

The answer to a subtraction problem is called the “difference.”

Mulitiplication is simply adding a number to itself mulitple times:

2 x 3 = 2 + 2 + 2 = 6

4 x 5 = 4 + 4 + 4 + 4 + 4 = 20

The answer to a multiplication problem is called the “product.”

Division is the reverse of multiplication. When you ask, “What is 12 divided by 3?”, you are asking, “What number do I multiply by 3 to get 12?” The following are equivalent mathmatical “sentences”:

12 / 3 = 4

3 x 4 = 12

The answer to a division problem is called the “quotient.”

Division may also be considered as multiple subtractions, as in, “How many times do I subtract 3 from 12 until I reach 0?”

12 – 3 – 3 – 3 – 3 = 0 (4 subtractions of 3)

Or:

12 + (-3) + (-3) + (-3) + (-3) = 0

And there you have it. These 4 operations (which really all boil down to addition) form the basis of all mathematics. It truly need not be any more complicated than this.

This it is, and nothing more.