Whole Numbers

Altering the order of numbers will yield different results.a/b =/= b/a

Any non-zero number divided by itself is one.n/n = 1Any number divided by one remains unchanged.n/1 = n

Zero may be divided by any non-zero number, and will always result in zero.0/n = 0No number may be divided by zero; the result is undefined.n/0 = ???

A remainder occurs when whole numbers do not divide evenly, and is signified with an R.13/4 = 3R1

Operations contained between the symbols ( and ) must supercede other operations.

Numbers with exponents must be multiplied before they may be used for other operations.

After parentheses and exponents have been fulfilled, multiplication and division equally share the next priority; they must be fulfilled from left to right.

After all other operations have been completed, addition and subtraction equally share the lowermost priority; they must be fulfilled from left to right.

Numbers may be added in any order with the same result.a + b = b + a

Any number added to zero will always result in the original number.a + 0 = a

Added numbers may be grouped in any way with the same result.(a + b) + c = a + (b + c)

Because it represents repeated addition, multiplication may be distributed over other addition separated by parentheses.3(2 + 3) = (2 + 3) + (2 + 3) + (2 + 3)Therefor,a(b + c) = ab + ac

Altering the order of numbers will yield different results.a - b =/= b - a

Because it represents repeated addition, multiplication may be distributed over subtraction separated by parentheses.3(4 - 3) = (4 - 3) + (4 - 3) + (4 - 3)Therefor,a(b - c) = ab - ac

Changing the order of factors does not change the product.ab = ba

Changing the grouping of factors does not change the product.(ab)c = a(bc)

Any number multiplied by zero results in zero.n x 0 = 0

Any number multiplied by one will result in the original number.n x 1 = n

Repeated multiplying of the same number may be reduced to a superscript of the amount of times the number appears in the equation. This is read, "to the [#]th power."n x n x n = n^3

Multiplying a number by itself once.n x n

Multiplying a number by itself three times.n x n x n