1.6
Properties
of Real Numbers
and
Simplifying Expressions
Concept #1:
Commutative Property of
Addition
a + b = b
+ a
Commutative Property of Multiplication
ab = ba
Concept
#2:
Associative Property of Addition
(a
+ b) + c = a + (b + c)
Associative Property of Multiplication
(ab)c = a(bc)
Concept
#3:
Identity Property of Addition
a
+ 0 = a
Identity Property of Multiplication
a 
1 =
a
Inverse Property of Addition
a
+ (-a) = 0
Inverse Property of Multiplication
a (1/a) =
1
Concept
#4:
Distributive Property
a(b + c) = ab + ac
Examples:
3(2x + 1)
=
3(2x) +
3(1) =
6x + 3
4(3a
+ 2b 5) =
4(3a) +
4(2b) 4(5) =
12a + 8b
20
-2(5x
3) =
-2(5x)
(-2)(3) =
-10x + 6
-(2x + 8) =
-1(2x + 8)
=
-1(2x) +
-1(8) =
-2x + -8 =
-2x 8
-(5x 3) =
-1(5x 3)
=
-1(5x)
(-1)3 =
-5x + 3
ACTIVITY: DISTRIBUTIVE PROPERTY
Concepts
#5 & #6:
Simplifying Algebraic Expressions ; Clearing Parentheses and Combining Like Terms
Definition: Terms
are the expressions we are adding together.
Note: In the
expression above, one of the operations is subtraction. But since subtraction
means adding the opposite of, we can consider 3yz as a term. Notice that the minus sign applies to the 3yz
and not to the 8.
How many terms are in 5x2 + 4x - 6y2
+ 2x - 3x2 + 12y2?
What is the third term?
Combining Like
Terms:
We can combine any terms that contain exactly the
same variables taken to the same powers.
In 5x2 + 4x - 6y2 + 2x
- 3x2 + 12y2,
the 5x2 and the -3x2 are like terms.
What are some other like terms?
Each set of like terms can be combined.
5x2+(-3x2)
= 2x2 and so on.
ACTIVITY: Combining Like
Terms - Part 1
ACTIVITY: Combining Like
Terms - Part 2
Clearing Parentheses and Combining Like Terms:
In the following problems, clear the parentheses using the distributive property and then combine like terms.
2 + 3(4x+1)
5x 2(3x+7)
8k 4(k-1) + 7 k
Assignment for 1.6
Page 102: 43-67 odd, 69-77 all,
89-93 odd, 99-109 odd