1-4 Properties of Real Numbers notes algebra

1-4 Properties of Real Numbers algebra

How do we identify and perform the properties of real numbers?

Commutative Property of Addition

 $2+3=3+2$  

How will I remember?
- changes order of the terms.

Commutative Property of Multiplication

 $2\bullet3=3\bullet2$  

How will I remember?
- changes order of the terms.

Multiple Select

Put a check next to the equations that show the Commutative Property.

• 
  

  $1+2=2+1$
  

• $3\bullet4=4\bullet3$

• $1+\left(2+3\right)=1+\left(3+2\right)$

• $1+\left(2+3\right)=\left(1+2\right)+3$

Associative Property of Addition

 $\left(4+5\right)+6=4+\left(5+6\right)$  

How will I remember?
- who you group/associate with

Associative Property of Multiplication

 $\left(4\bullet5\right)\bullet6=4\bullet\left(5\bullet6\right)$  

How will I remember?
- who you group/associate with

Multiple Select

Mark the equations that show the Associative Property.

•  $7+\left(8+9\right)=\left(7+8\right)+9$  

• $3\bullet4=4\bullet3$

•  $1\bullet\left(2\bullet3\right)=1\bullet\left(3\bullet2\right)$ 

•  $1\bullet\left(2\bullet3\right)=\left(1\bullet2\right)\bullet3$ 

Inverse Property of Addition

 $7+\left(-7\right)=0$  

 $-8+8=0$  

How will I remember? 
- to invert (opposite/upside down)

Inverse Property of Multiplication

 $7\bullet\frac{1}{7}=1$  

 $\frac{7}{8}\bullet\frac{8}{7}=1$  

How will I remember? 
- to invert (opposite/upside down)

Multiple Select

Mark the equations that show the Inverse Property.

• $1+\left(-1\right)=0$

• 
  

  $-4+4=0$
  

• $\frac{3}{4}\bullet\frac{3}{4}=1$

• $2\bullet\frac{1}{2}=1$

Identity Property of Addition

 $9+0=9$  

 $-9+0=-9$  

How will I remember?
- you get yourself back

Identity Property of Multiplication

 $9\bullet1=9$  

 $-9\bullet1=-9$  

How will I remember?
- you get yourself back

Multiple Select

Mark the equations that show the Identity Property.

• $\frac{10}{10}=1$

• $10-10=0$

• 
  

  $10\bullet1=10$
  

• $10+0=10$

Distributive Property

 $2\left(x+3\right)=2x+6$  

 $-4\left(3x-5\right)=-12x+20$  

 $3\left(x^2+5x-1\right)=3x^2+15x-3$  

How will I remember?
- parentheses disappear

Multiple Select

Mark the equations that show the Distributive Property.

• 
  

  $3\left(x-2\right)=3x-6$
  

• $3\left(x+1\right)=3x+1$

• $-2\left(4x+1\right)=-8x-2$

• $4\bullet\left(5-2\right)=4\left(5\right)-4\left(2\right)$

Multiple Choice

When solving the equation

 $12x^2-7x=6-2\left(x^2-1\right)$ , Evan wrote  $12x^2-7x=6-2x^2+2$  as his first step. Which property justifies this step?

• subtraction property of equality

• multiplication property of equality

• associative property of multiplication

• distributive property of multiplication over subtraction

Multiple Choice

A part of Jennifer's work to solve the equation  $2\left(6x^2-3\right)=11x^2-x$  is shown below.
Given:  $2\left(6x^2-3\right)=11x^2-x$  
Step 1:  $12x^2-6=11x^2-x$  
Which property justifies her first step?

• identify property of multiplcation

• multiplication property of equality

• distributive property of multiplication over subtraction

• commutative property of multiplication

Addition Property of Equality

 $x-2=6$ 
 $\ \ \ \ +2\ \ \ +2$  

 $\ \ \ \ \ x=8$  

Subtraction Property of Equality

 $x+2=6$ 
 $\ \ \ \ -2\ \ \ -2$  

 $\ \ \ \ \ x=4$  

Multiplication Property of Equality

Division Property of Equality