Download Properties of Real Numbers

Properties of Real Numbers
• Commutative Property of Addition
a+b=b+a
Ex) (- 7) + ( 3) = ( 3) + ( -7) = - 4
Ex) 2 + 9 + 1 = 2 + 1 + 9
Commutative Property of Multiplication
ab = ba
Ex) ( 4)(-3) = ( -3)(4) = - 12
Order doesn’t matter.
Associative Property of
Addition
(a + b) + c = a + ( b + c)
Ex) ( 3 + 6) + ( - 4) =
3 + ( 6 + (-4))
9 + ( -4 ) =
3 + ( 2)
5
=
5
True
Because of this property, we can leave off
the parentheses when doing Addition.
Associative Property of
Multiplication
Ex)
(ab)c= a(bc)
(3  4)  2  3(4  2)
(12)  2  3(8)
24  24
Is this an example of Commutative
or Associative Properties?
• Ex)
5(7  6)  5(6  7)
Commutative
• I didn’t Regroup, I only rearranged the order
inside the Parenthese.
• Ex) ( 4 + 9) + 7 = 4 + ( 7 + 9)
• Associative and Commutative
• I regrouped the numbers and I rearranged
the order of the 9 and 7.
Identity Properties
Addition
Ex) 4 + 0 = 4
a + 0 = a and 0 + a = a
Multiplication
a( 1) = a and ( 1)a = a
Ex) We use this property to find Equivalent Fractions.
2  5  10
  
3  5  15
Inverse Properties
Additive Inverse
Ex) 5 + ( -5) = 0
a + ( - a) = 0
Multiplicative Inverse
Ex)
Ex)
1
9   1
9
1
a    1
a
2 3
 1
3 2
Distributive Property
a ( b + c ) = ab + ac
a ( b – c ) = ab – ac
Ex) Verify 3( 9 – 4 ) = 3(9) – 3 (4)
3 ( 5)
= 27 – 12
15
= 15
More Examples
6( x + 4) = 6x + 6(4) = 6x + 24
- ( 4x – 8) = - 4x + 8
8 ( 3x + 2) + 7 = 8( 3x) + 8(2) + 7
= 24x + 16 + 7 = 24x + 23
5(x) – 5(y) = 5 ( x – y )
Use a Property to Simplify the
Expressions
• Ex) 9 + ( 13) + ( -9) + 7
• Ex) 2999 + ( 47) + 1 + ( - 7)
• Ex) x + (-x ) + (2/3)(3/2)
• Ex) 9.8x + 7 – 7 – 9.8x
More Examples
• Rewrite each expression using the
Distributive Property.
8( x – 5) =
9x + 9y + 9z =
- ( 7x - 2y + 3z ) =