1. Algebraic Properties

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

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

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

5. 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)

6. 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

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

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

9. 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

10. 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

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

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

13. 4/4 = 1 n/n =1 The Property of One 1. Any number (except zero)
divided by itself is one.
4/4 = n/n =1

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