CHAPTER 9 Introduction to Real Numbers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 9.1Introduction to Algebra 9.2The Real Numbers 9.3Addition of Real Numbers 9.4Subtraction of Real Numbers 9.5Multiplication of Real Numbers 9.6Division of Real Numbers 9.7Properties of Real Numbers 9.8Simplifying Expressions; Order of Operations

OBJECTIVES 9.8 Simplifying Expressions; Order of Operations Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aFind an equivalent expression for an opposite without parentheses, where an expression has several terms. bSimplify expressions by removing parentheses and collecting like terms. cSimplify expressions with parentheses inside parentheses. dSimplify expressions using the rules for order of operations.

9.8 Simplifying Expressions; Order of Operations THE PROPERTY OF –1 Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 9.8 Simplifying Expressions; Order of Operations a Find an equivalent expression for an opposite without parentheses, where an expression has several terms. 1 Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 9.8 Simplifying Expressions; Order of Operations a Find an equivalent expression for an opposite without parentheses, where an expression has several terms. 5 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find an equivalent expression without parentheses.

9.8 Simplifying Expressions; Order of Operations b Simplify expressions by removing parentheses and collecting like terms. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When a sum is added to another expression, we can simply remove, or drop, the parentheses and collect like terms because of the associative law of addition. When a sum is subtracted from another expression, we cannot simply drop the parentheses. However, we can subtract by adding an opposite. We then remove parentheses by changing the sign of each term inside the parentheses and collecting like terms.

EXAMPLE 9.8 Simplifying Expressions; Order of Operations b Simplify expressions by removing parentheses and collecting like terms. 6 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Remove parentheses and simplify.

EXAMPLE 9.8 Simplifying Expressions; Order of Operations b Simplify expressions by removing parentheses and collecting like terms. 9 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Remove parentheses and simplify.

EXAMPLE 9.8 Simplifying Expressions; Order of Operations b Simplify expressions by removing parentheses and collecting like terms. 14 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Remove parentheses and simplify

9.8 Simplifying Expressions; Order of Operations Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When more than one kind of grouping symbol occurs, do the computations in the innermost ones first. Then work from the inside out.

EXAMPLE 9.8 Simplifying Expressions; Order of Operations c Simplify expressions with parentheses inside parentheses. 15 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Simplify.

EXAMPLE 9.8 Simplifying Expressions; Order of Operations c Simplify expressions with parentheses inside parentheses. 19 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Simplify.

9.8 Simplifying Expressions; Order of Operations RULES FOR ORDER OF OPERATIONS Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Do all calculations within grouping symbols before operations outside. 2. Evaluate all exponential expressions. 3. Do all multiplications and divisions in order from left to right. 4. Do all additions and subtractions in order from left to right.

EXAMPLE 9.8 Simplifying Expressions; Order of Operations d Simplify expressions using the rules for order of operations. 22 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 9.8 Simplifying Expressions; Order of Operations d Simplify expressions using the rules for order of operations. 23 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. An equivalent expression with brackets as grouping symbols is This shows, in effect, that we do the calculations in the numerator and then in the denominator, and divide the results: