# Number Properties

 Commutative Property of Additiona + b = b + aExample: 3 + 2 = 2 + 3Let, LHS, 3 + 2 = 5RHS, 2 + 3 = 5Therefore, LHS = RHS. Commutative Property of Multiplicationa • b = b • aExample: 2 x 3 = 3 x 2Let, LHS, 3 x 2 = 6RHS, 2 x 3 = 6Therefore, LHS = RHS. Associative Property of Addition a + ( b + c ) = ( a + b ) + c Example: 2 + (3 + 4) = (2 + 3) + 4Let, LHS, 2 + (3 + 4) = 2 + (7) = 9RHS, (2 + 3) + 4 = 5 + 4 = 9Therefore, LHS = RHS. Associative Property of Multiplication a • ( b • c ) = ( a • b ) • cExample: 2 x (3 x 4) = (2 x 3) x 4Let, LHS, 2 x (3 x 4) = 2 x (12) = 24RHS, (2 x 3) x 4 = 6 x 4 = 24Therefore, LHS = RHS. Distributive Propertya • ( b + c ) = a • b + a • cExample: 2 x (3 + 4) = (2 x 3) + (2 x 4)LHS, 2 x (3 + 4) = 2 x (7) = 14RHS, (2 x 3) + (2 x 4) = 6 + 8 = 14Therefore, LHS = RHS. Additive Identity Propertya + 0 = aExample: 2 + 0 = 2LHS = 2 + 0 = 2 = RHS Multiplicative Identity Property a •  1 = aExample: 2 x 1 = 2LHS = 2 x 1 = 2 = RHS Additive Inverse Property a + ( -a ) = 0Example: 2 + (-2) = 0LHS = 2 + (-2) = 2 – 2 = 0 = RHS Multiplicative Inverse Property a x a-1 = 1Note: a cannot = 0Example: 2 x 2-1 = 1LHS = 2 x 1/2 = 1 = RHS Zero Propertya • 0 = 0Example: 2 x 0 = 0LHS = 2 x 0 = 0 = RHS