Properties of Real Numbers

 

 

 

Commutative Property of Addition

 

 

 

a + b = b + a                          Example: 12 + 4 = 4 + 12

 

 

 

Commutative Property of Multiplication

 

 

a ∙ b = b ∙ a                            Example: 8 ∙ 3 = 3 ∙ 8

 

 

Associative Property of Addition

 

 

 

a + (b + c) = (a + b) + c         Example: 2 + (5 + 7) = (2 + 5) + 7

 

 

 

Associative Property of Multiplication

 

 

a ∙ (b ∙ c)=(a ∙ b) ∙ c               Example: 5 ∙ (2 ∙ 7)= (5 ∙ 2) ∙ 7

 

 

Identity PropertyofAddition

 

 

 

  a + 0 = a                                Example: 9 + 0 = 9

 

 

Identity Property of Multiplication

 

 

a ∙ 1 = a                                  Example: 3 ∙ 1 = 3

 

 

Inverse Property of Addition

 

 

a + (-a) = 0                           Example: 6 + (-6) = 0

 

 

Inverse Property of Multiplication

 

 

a ∙ (1/a) = 1                           Example: 7 ∙ (1/7) = 1

 

 

 

 

If you are still having trouble, view this youtube video...

 

 

 

 

  Now try on your own to identify these properties of real numbers...

 

1)  3 + 6 = 6 + 3                                        6)  8 ∙ 1 = 8

 

2)  4 ∙ 0 = 0                                               7)  1 + ( 5 + 2 ) = ( 1 + 5) + 2 

 

3)  -7 + 7 = 0                                            8)  6 âˆ™  (1/6) = 1 

 

4)  4 ∙ (5 ∙ 9) = (4 ∙ 5) ∙ 9                          9) -8 + 8 = 0

 

5)  2 ∙ 9 = 9 ∙ 2                                         10) 5 ∙ 5 = 5 ∙ 5 

 

Answers...

 

1. Commutative Property of Addition                  6. Identity Property of Multiplication

 

2. Identity Property of Addition                         7. Associative Property of Multiplication

 

3. Inverse Property of Addition                          8. Inverse Property of Multiplication

 

4. Associative Property of Multiplication            9. Inverse Property of Addition 

 

5. Commutative Property of Multiplication         10. Commutative Property of Multiplication