Properties of Equality

Multiple of Zero

6 x 0 = 0

Addition Subtraction Multiplication and Division

Allow you to add, subtract, multiply, and/or divide the same to both sides of an equation

Addition Property

For all real numbers if x=y x=y , then x+z=y+zx+z=y+z .

Subtraction Property

For all real numbers if x=y x=y , then x−z=y−z x−z=y−z .

Reflexive Property

For all real numbers xx , x=xx=x . A number equals itself.

Multiplication Property

For all real numbers, if x=y x=y , then xz=yz xz=yz .

Division Property

For all real numbers, if x=yx=y , and z≠0z≠0 , then xz=yzxz=yz .

Symmetry Property

For all real numbers, if x=yx=y , then y=xy=x . Order of equality does not matter.

Substitution Property

For all real numbers, if x=yx=y , then yy can be substituted for xx in any expression.

Transitive Property

For all real numbers, if x=yx=y and y=zy=z , then x=zx=z . Two numbers equal to the same number are equal to each other.

Distributive Property

For all real numbers, x(y+z)=xy+xz

Identity Property of Addition

The sum of any number and zero is the original number. For example 5 + 0 = 5.

Associative property of Addition

You can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'

Reflexive Property

a=a

Inverse Property of Addition

any number added to its opposite will equal zero. 3 + -3 = 0

Identity Property of Multiplication

any time you multiply a number by 1, the result, or product, is that original number. For example, 2 x 1 = 2

Commutative Property of Addition

moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2.

Communicative Property of Multiplication

two numbers can be multiplied in either order. 2 x 6 = 12 and 6 x 2 = 12