1. Commutative Property of Addition.
a + b = b + a
Examples:
1. real numbers
2 + 3 = 3 + 2
2. algebraic expressions
x 2 + x = x + x 2
2. Commutative Property of Multiplication.
a * b = b * a
Examples:
1. real numbers
5 * 7 = 7 * 5
2. algebraic expressions
(x 3 - 2) * x = x * (x 3 - 2)
3. Associative Property of Addition.
(a + b) + c = a + (b + c)
Examples:
1. real numbers
(2 + 3) + 6 = 2 + (3 + 6)
2. algebraic expressions
(x 3 + 2 x) + x = x 3 + (2 x + x)
4. Associative Property of Multiplication.
(a * b) * c = a * (b * c)
Examples:
1. real numbers
(7 * 3) * 10 = 7 * (3 * 10)
2. algebraic expressions
(x 2 * 5 x) * x = x 2 * (5 x * x)
5. Distributive Properties of Addition Over Multiplication.a * (b + c) = a * b + a * c
and
(a + b) * c = a * c + b * c
Examples:
1. real numbers
2 * (2 + 8) = 2 * 2 + 2 * 8
(2 + 8) * 10 = 2 * 10 + 8 * 10
2. algebraic expressions
x * (x 4 + x) = x * x 4 + x * x
(x 4 + x) x 2 = x 4 * x 2 + x * x 2
6. The reciprocal of a non zero real number a is 1/a.and a*(1/a) = 1
Examples:
1. real numbers
reciprocal of 5 is 1/5 and 5*(1/5) = 1
7. The additive inverse of a is -a.a + (- a) = 0
Examples:
additive inverse of -6 is -(-6) = 6 and - 6 + (6) = 0
8. The additive identity is 0. and a + 0 = 0 + a = a
9. The multiplicative identity is 1.and a * 1 = 1 * a = a
