Some of the properties of any mathematical equation include the addition property of equality, the subtraction property of equality, the division property of equality and the multiplication property of equality. Each of these properties show that inverse operations performed on both sides of a mathematical equation produce the same results.
The addition property equality asserts that adding the same number to both sides of an equation produces an equivalent equation. The subtraction property of equality states that subtracting the same number from both sides of an equation produces an equivalent equation. The division property of equality asserts that dividing each side of any equation with the same nonzero number produces an equivalent equation. The multiplication property of equality states that both sides of any equation, multiplied by the same nonzero number, produce an equivalent equation.
The use of the number zero is an important factor in the differences between properties of addition and subtraction and properties of multiplication and division. For example, multiplying by zero no longer produces an equivalent equation, and dividing by zero creates nonsensical results.
An additional property of mathematical equations is the reflexive property of equality. This property states that any quantity must be equal to itself. The symmetric property of equality asserts that two equal quantities must be represented by an equal number.