Properties of Real Numbers

Properties of Real Numbers

Commutative Property

Change Order – The order doesn’t matter; you will get the same answer.
         

 Commutative of Addition:  $3+5=5+3$  
           

Commutative of Multiplication:  $3\left(8\right)=8\left(3\right)$  

Multiple Choice

Use the commutative property to re-write the expression

 $123+x+9$  

•  $x+9+123$  

•  $\left(123+x\right)+9$  

Associative Property

Associative Property: Grouping Changes – The parenthesis will move but you will get the same answer


Associative of Addition:  $\left(3+7\right)+9=3+\left(7+9\right)$  
         

Associative of Multiplication:   $\left(4x\right)9=4\left(x9\right)$  

Multiple Choice

Which correctly applies the associative property to the expression

 $\left(x+5\right)+7$  

•  $\left(5+x\right)+7$  

•  $x+\left(5+7\right)$  

•  $7+\left(5+x\right)$  

Identity Property

Additive Identity Property: Any # plus 0 equals the original number.
           Example:  $5+0=5$  
Multiplicative Identity Property: Any number multiplied by 1 equals the original number
           Example:  $8\cdot1=8$  

Multiple Choice

Which correctly represents the identity property?

• $x-x=0$

• $x+3=3$

• $x\cdot1=x$

Inverse Property

Multiplicative Inverse: Any number multiplied by its reciprocal equals 1.
           Example:  $8\cdot\frac{1}{8}=1$  


Additive Inverse Property: Any number plus its opposite equals 0.
           Example:  $5+-5=0$  

Multiple Choice

Which correctly shows the inverse property?

• $x+-x=0$

• $x\cdot1=x$

• $a+x=x+a$

Property of Zero

Multiplicative Property of Zero: Any number multiplied by 0 equals 0

           Example:  $4\cdot0=0$  

Multiple Choice

Is this the property of zero?

• $3-0=3$

• $6+0=6$

• $1-1=0$

• $9\cdot0=0$

Distributive Property 

Distributive Property: A number multiplied by the sum or difference of two numbers is equivalent to the number multiplied by the first added (or subtracted) to the number multiplied by the second.

           Example:  $3\left(x+4\right)=3x+12$  

Multiple Choice

Is this a correct use of the distributive property?

 $5\left(x-8\right)=5x-8$  

• Yes

• No