The Distributive Property

Multiplication is distributive over addition and subtraction. 
If a, b, and c are represented by real numbers, then


a + ( b + c ) = ( a + b ) + c


a ( b + c ) = ( ab) * (ac)




Example: 


Is this statement true or false?
5 ( 3 + 7 ) = ( 5 * 3 ) + ( 5 * 7 )


Since 5 ( 3 + 7 )  
5 * 10
50


And 
( 5 * 3 ) + ( 5 * 7 )

15 + 35
50


Therefore this equation is true by the distributive property

Let's look at another example: 


Is this statement true or false:
5 ( 3 * 4 ) = ( 5 * 3 )  * ( 5 * 4 )


First half of the equation:
5 ( 3 * 4 )
3 * 4 = 12
5 * 12 = 60


Second half of the equation:
First half of the second half of the equation:
( 5 * 3 )                ( 5 * 4 )
15            *          20
300
60 does not equal 300 
Therefore the statement is false
You cannot distribute over multiplication.
You can only distribute over addition and subtraction.

Example:

Is the following statement true or false?

5 ( 4 - 2 ) = ( 5 * 4 ) - ( 5 * 2 )


First equation:
( 4 - 2 ) 
2
5 * 2
10


Second equation: 
( 5 * 4 ) - ( 5 * 2 )
( 5 * 4 )
20


First half of the second equation
( 5 * 2 )
10


Second half of the second equation
20 - 10
10

This statement is true by the distributive property.

Classwork: 

State whether the statement is true or false.
Name the property that states that the statement is true.


1) 2 + 3 = 3 + 2
2) 5 + 4 = 4 + 5
3) ( 2 + 3 ) + 4 = 2 + ( 3 + 4 )
4) ( 1 + 6 ) + 4 = 1 + ( 6 + 4 )
5) 5 - 3 = 3 - 5
6) 4 - 7 = 7 - 4
7) ( a + b ) + c = a + ( b + c )
8) ( r + s ) + t = r + ( s + t )
9) a / b = b / a
10) x / y = y / x
11) ax = xa
12) pn = np
13) 2 + ( - 5 ) = ( - 5 ) + 2
14) ( - 8 ) + 5 = 5 + ( - 8 )
15) ( 3 * 4 ) * 5 = 3 * ( 4 * 5 )
16) ( 2 * 4 ) * 6 = 2 * ( 4 * 6 )
17) 3 ( 4 + 5 ) = ( 3 * 4 ) + ( 3 * 5 )
18) 4 ( 2 + 3 ) = ( 4 * 2 ) + ( 4 * 3 )
19) 3 ( 4 * 5 ) = ( 3 * 4 ) ( 3 * 5 )
20) 4 ( 2 * 3 ) = ( 4 * 2 ) ( 4 * 3 )
21) - 3 + 0 = -3
22) 5 + 0 = 5
23) 4 + - 4 = 0
24) 2 + -2 = 0
25) a ( x + y ) = ax + ay
26) 5 ( 3 - 2 ) = ( 5 * 3 ) - ( 5 * 2 )
27) 9 * 0 = 0
28) 4 * 0 = 4
29) 3 + ( 5 + 7 ) = ( 3 + 5 ) + 7 
30) 2 * ( 5 * 7 )  = 2 * ( 7 * 5 )
31) 3 * ( 5 + 7 ) = 3 * ( 7 + 5 )
32) 2 ( 6 + 8 ) = 2 ( 8 + 6 )


Once you have completed these problems, turn to page 39 in the Beginning Algebra textbook and complete the problems for Set 2.