Algebraic Properties Terra Alta/East Preston School Terra Alta, West Virginia

The Commutative Property In addition or multiplication, the order of the terms makes no difference.

Commutative Properties = ( 1) = 1 ( 2) a + b = b + a ab = ba

Associative Property In addition and multiplication, the grouping of terms makes no difference.

Associative Property ( ) + 3 = 1 + ( 2 + 3) (2 X 3 ) X 4 = 2 X ( 3 X 4 ) ( put dots for X) ( a + b ) + c = a + ( b + c) ( ab ) c = a (bc)

Distributive Property 2 ( ) = 2 X X 3 3 ( 4 – 1 ) = 3 X 4 – 3 X 1 a ( b + c ) = ab + ac a ( b – c ) = ab - ac

The Property of Zero 1. Any number times zero is zero 7 x 0 = 0 A x 0 = 0 2. No number can be divided by zero.

The Property of Zero 3. Zero divided by any number (except zero) is zero 4.Adding zero to a number gives that number = 6 N + 0 = N

The Property of Zero 5. Adding and subtracting the same number (adding opposites) is like adding zero. N + 5 – 5 = N + 0 = N

The Property of One 1. Multiplying a number by one gives that number. 6 x 1 = 6 N x 1 = N

The Property of One 2. Any number (except zero) divided by itself is one. 4/4 = 1 n/n =1

The Property of One 3. Any number divided by one is that number 8/1 = 8 a/1 = a