Download Algebraic Expressions and Properties

Unit 1 Algebraic Expressions and Properties
Monday, June 01, 2009
8:49 PM
Make sure you get a good start on Unit 1 Variables and Expressions. Algebra is one of those classes
where it's important to learn the stuff as you go. Each new unit builds on the last one.
So here we go……
In Unit 1 it's important to know:
Algebraic Expressions
o
What's an Algebraic Expression?
An algebraic expression consists of one or more numbers and variables along with one or more
arithmetic operations.
Some examples might be:
o
6x
5-2x
Convert a word phrase to an expression?
Example: four times the sum of a variable x plus 3 --- >>> 4(x+3)
And back again….
Example:
Important Properties of Algebra
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
Understand each of the following properties:
Commutative Property

a + b = b + a …. Examples: 3+ 4 = 4 + 3

ab = ba
…. Examples: 3(4) = 4(3)
x+7 = 7 + x
x(7) = 7(x) = 7x
Remember just Addition and Multiplication are commutative. Subtraction and Division
are NOT!!!!

Associative Property
(a + b) + c = a + (b + c) ….Examples: (x + 3) + 4 = x + (3 + 4)
(ab)c = a(bc)
….Examples: (3x)4 = 3(4x)


Addition
(4 + 5) + 8 = 4 + (5 + 8)
9 + 8 = 4 + 13
17 = 17
Multiplication
(4 ∙ 5) ∙ 8 = 4 ∙ (5 ∙ 8)
20 ∙ 8 = 4 ∙ 40
160 = 160

Distributed Property




by multiplying the sum of numbers
or by multiplying each number individually and then adding.
a(b + c) = ab + ac
a(b – c) = ab – ac
Example
Addition
2(4 + 5) = 2(4) + 2(5)
2(9) = 8 + 10
18 = 18
Subtraction
8(6 – 3) = 8(6) – 8(3)
8(3) = 48 – 24
24 = 24
Another Example:
Simplify: 4(x + 3) + 5x
4x + 12 + 5x
9x + 12

Order of Operations
Always do:
 Parentheses (Groups, Brackets, Division Bars, etc.) First!!!
then
 Exponents
and then
 Multiplication & Division, Left to Right
finally
 Addition & Subtraction, Left to Right
Laws of Algebra