1.2 Operations with Real Numbers and Simplifying Algebraic Expressions

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

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

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

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

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

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

1.2 Assignment p. 23 (2,8,12,20,38,76-92even,96,100,120-130 even)