Operations with Real Numbers and Simplifying Algebraic Expressions

1
1.2
Operations with Real Numbers and Simplifying
Algebraic Expressions
2
Finding Absolute Value
Absolute value is used to describe how to operate
with positive and negative numbers.
Geometric Meaning of Absolute Value The absolute
value of a real number a, denoted
is the distance from 0 to a on the number line.
This distance is always nonnegative.
The absolute value of -5 is 5 because -5 is 5
units from 0 on the number line.
The absolute value of 3 is 3 because 3 is 3
units from 0 on the number line.
Blitzer, Algebra for College Students, 6e Slide
2 Section 1.2
3
Order of Operations
EXAMPLE
Simplify.
SOLUTION
Evaluating exponent
Multiply
Divide
Subtract
Blitzer, Algebra for College Students, 6e Slide
3 Section 1.2
4
Order of Operations
EXAMPLE 2
Simplify.
SOLUTION
Blitzer, Algebra for College Students, 6e Slide
4 Section 1.2
5
Basic Algebraic Properties
Property Examples
Commutative 2 3 3 2 2(3) 3(2) 10 4 4 10 4(10) 10(4) 8 7 7 8 7(8) 8(7)
Associative 4 (3 2) (4 3) 2 (6 4)11 6(4 11) 3(2 5) (3 2)5
Distributive 7(2x 3) 14x 21 5(3x-2-4y) 15x 10 20y (2x 7)4 8x 28
Blitzer, Algebra for College Students, 6e Slide
5 Section 1.2
6
Combining Like Terms
EXAMPLE 3
Simplify 3a (2a 4b 6c) 2b 3c
SOLUTION
3a (2a 4b 6c) 2b 3c
Distributive Property
3a 2a - 4b 6c 2b 3c
(3a 2a) (2b - 4b) (6c 3c)
Comm. Assoc. Prop.
(3 2)a (2 - 4)b (6 3)c
Distributive Property
1a - 2b 3c
Subtract
Simplify
a - 2b 3c
Blitzer, Algebra for College Students, 6e Slide
6 Section 1.2
7
Combining Like Terms
EXAMPLE 4
Simplify 8x 25 -(x-3)
SOLUTION
6x 16
Blitzer, Algebra for College Students, 6e Slide
7 Section 1.2
8
1.2 Assignment
p. 23 (2,8,12,20,38,76-92even,96,100,120-130 even)