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