Teach Math Interactive
  • GED
    • Answers
  • Home
    • Resources
    • Word Problems >
      • Answers to Geometry Word Problems
    • Problems of the Day >
      • Projects
      • Money Problems
  • Mathematics
    • Absolute Value
    • Adding and Subtracting Decimals
    • Divisibility Rules
    • Fractions
    • Integers
    • Least Common Multiple/Greatest Common Factor
    • Order of Operations >
      • Order of Operations Answer Key
    • Percents and Ratios >
      • Ratio
    • Prime and Composite Numbers
    • Numbers >
      • Properties of Real Numbers
      • Decimals
  • Algebra
    • Combining Like Terms
    • Create and evaluate expressions
    • Discover One Step Functions
    • Distributive Property >
      • The Distributive Property
    • Equations
    • Exponents >
      • Finding Powers of Signed Numbers
      • Exponential and Logarithmic Functions
    • Linear Equations
    • Mean, Median and Mode
    • Probability
    • Properties of Real Numbers >
      • Properties Answer key
    • Simplify Equations
    • Solve Equations with Variables on Both Sides
    • Systems of Two Linear Equations
    • Two Step Equations
    • Writing Terms in Algebraic Terms
  • Geometry
    • Angles and Lines
    • Conversions
    • Coordinate Geometry
    • Daily Lesson for Geometry
    • Identify and Plot Points on a Coordinate Plane
    • Polygons
    • Proofs
    • Surface Area of Prisms and Cylinders
    • Triangles
  • Misc
    • Logic
    • Test Problems >
      • Answers
    • CAHSEE >
      • Answers
    • Test Prep >
      • Answers
    • Careers
    • Mathography >
      • Journal Entries Lesson Plans
  • Money/Economics
    • Checks - Writing Dollars and Cents
    • 5 Tips to Save Money
  • Engineering
  • Telling Time

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.

Powered by Create your own unique website with customizable templates.