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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)