Algebraic Properties

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

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

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

Associative Property ( ab ) c = a (bc) ( 1 + 2 ) + 3 = 1 + ( 2 + 3) (2 ● 3 ) ● 4 = 2 ● ( 3 ● 4 ) ( a + b ) + c = a + ( b + c) ( ab ) c = a (bc)

Distributive Property When two or more numbers are being multiplied by the same factor, you can multiply and then add or add and then multiply

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

Zero Property of Multiplication Any number times zero is zero 7 ● 0 = 0 A ● 0 = 0

1. No number can be divided by zero Zero divided by any number Attributes of Zero 1. No number can be divided by zero Zero divided by any number (except zero) is zero

3. Adding and subtracting the same number (adding Attributes of Zero 3. Adding and subtracting the same number (adding opposites) is like adding zero N + 5 – 5 = N + 0 = N

Identity Property of Addition Adding zero to a number gives that number 6 + 0 = 6 N + 0 = N

Identity Property of Multiplication Multiplying a number by one gives that number 6 ● 1 = 6 N ● 1 = N

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

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