Math Properties

The Commutative Property deals with an order change.  For example 3 + 5 = 5 + 3.  The 3 and the 5 switched order, yet the two expressions are equal.  Also, 4(6) = 6(4).  The commutative property holds for both addition and multiplication, but not for subtraction or division.

The Associative Property deals with a grouping change.  For example 6 +(3+4) = (6+3)+4.  Notice that order did not change, but rather how the numbers were grouped.  The associative property holds for both addition and multiplication.

The Identity Property states that zero may be added to any number, or one multiplied to any number and the original number keeps its identity … 5+0=5 and 5(1)=5.

The Inverse Property states that every number has an additive inverse and a multiplicative inverse, which when applied will result in the identity elements of respectively 0 and 1 …  5+(-5)=0 and 5(1/5)=1.  -5 is called the additive inverse and 1/5 is called the multiplicative inverse (sometimes referred to as the reciprocal.)

The Distributive Property uses the number in front of the parenthesis (including the sign of the number) to multiply all numbers (and their signs) within the parenthesis.  For example, 5(3+4) = 5(3)+5(4).

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 19-Sep-2007