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 Simplify. Evaluating exponent Multiply Divide
EXAMPLE
Simplify.
SOLUTION
Evaluating exponent
Multiply
Divide
Subtract
Blitzer, Algebra for College Students, 6e – Slide #3 Section 1.2

4. Order of Operations Simplify. EXAMPLE #2 SOLUTION
Blitzer, Algebra for College Students, 6e – Slide #4 Section 1.2

5. Basic Algebraic Properties
Property
Examples
Commutative
2 + 3 = (3) = 3(2)
= (10) = 10(4)
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 Simplify: 3a – (2a + 4b – 6c) +2b – 3c
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 Simplify: 8x + 2[5 -(x-3)] 6x + 16 EXAMPLE #4
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, even)