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This module contains a chart of the properties of real numbers from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.

Commutative property

Addition

a + b = b + a
3 + 4 = 4 + 3

Multiplication

a b = b a
4 · 3 = 3 · 4

Associative property

Addition

a + ( b + c ) = ( a + b ) + c
4 + ( 3 + 5 ) = ( 4 + 3 ) + 5

Multiplication

a ( bc ) = ( ab ) c
4 ( 3 · 5 ) = ( 4 · 3 ) 5

Distributive property

a ( b + c ) = a b + a c
4 ( x + 3 ) = 4x + 12
( b + c ) a = a b + b c
( x + 3 ) 4 = 4x + 12

Properties of zero

a · 0 = 0
0 · a = 0 If a 0 , then 0 a = 0 and 0 a = 0 is undefined.

Double negative property

- ( - a ) = a

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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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