Download Algebraic Properties

Algebraic Properties
Commutative Property of Addition
The order in which two numbers are added does not change their sum.
Example
4+2=2+4
Commutative Property of Multiplication
The order in which to numbers are multiplied does not change their product.
Example
7x5=5x7
Associative Property of Addition
The way in which numbers are grouped when adding does not change their sum.
Example
2 + (6 + 9) = (2 + 6) + 9
Associative Property of Multiplication
The way in which numbers are grouped when multiplying does not change their product.
Example
(7 x 2) x 3 = 7 x (2 x 3)
Identity Property of Addition
The sum of a number and zero is the number.
Example
21 + 0 = 21
Identity Property of Multiplication
The product of a factor and one is the factor.
Example
1 x 32 = 32
Inverse Property of Addition
The sum of a number and its opposite is 0.
Example
3 + -3 = 0
Inverse Property of Multiplication
The product of a number and its reciprocal is 1.
Example
6 x 1/6 = 1
Zero Property of Multiplication
The product of any factor and zero is zero.
Example
12 x 0 = 0
Distributive Property – The product of a number and a sum is equal to the sum of the individual products and the
number. That is, a(b + c) = ab + ac.
Example
3(5 + 7) = 3(5) + 3(7)
The product of a number and a sum
3(5 + 7)
is equal to
=
sum of the individual products and the number
3(5) + 3(7)