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CHAPTER 1 Introduction to Real Numbers and Algebraic Expressions Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 1.1Introduction to Algebra 1.2The Real Numbers 1.3Addition of Real Numbers 1.4Subtraction of Real Numbers 1.5Multiplication of Real Numbers 1.6Division of Real Numbers 1.7Properties of Real Numbers 1.8Simplifying Expressions; Order of Operations

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OBJECTIVES 1.8 Simplifying Expressions; Order of Operations Slide 3Copyright 2011, 2007, 2003, 1999 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.

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For any real number a, 1 a = a (Negative one times a is the opposite, or additive inverse, of a.) 1.8 Simplifying Expressions; Order of Operations The Property of –1 Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE (–1)(4x) +(–1)(5y) + (–1)(2) Use the property of 1 Use the distributive law Use the property of 1 –(4x + 5y + 2) 1.8 Simplifying Expressions; Order of Operations a Find an equivalent expression for an opposite without parentheses, where an expression has several terms. AFind an equivalent expression without parentheses. Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. –1(4x + 5y + 2) (–1)(4x) +(–1)(5y)(–1)(4x) –4x – 5y – 2

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EXAMPLE 2x – 7y + 6 –(–2x + 7y – 6) 1.8 Simplifying Expressions; Order of Operations a Find an equivalent expression for an opposite without parentheses, where an expression has several terms. BFind an equivalent expression without parentheses. Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Use the distributive law to change the sign of each term 2x – 7y2x2x

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EXAMPLE 8x – 4x + 5y + 2y + 6 – 3 8x – 4x + 5y + 2y + 6 8x – 4x + 5y + 2y 8x – 4x + 5y 8x – 4x (8x + 5y – 3) – (4x – 2y – 6) 1.8 Simplifying Expressions; Order of Operations b Simplify expressions by removing parentheses and collecting like terms. CRemove parentheses and simplify. Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 8x + 5y – 3 4x – 4x + 2y + 6– 4x + 2y– 4x 8x + 5y + 2y – y+ 34x + 7y + 3 Distributive Law Collect like terms PEMDAS

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EXAMPLE (3a + 4b – 8) – 3(–6a – 7b + 14) 1.8 Simplifying Expressions; Order of Operations b Simplify expressions by removing parentheses and collecting like terms. DRemove parentheses and simplify. Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 21a + 25b – 50 3a + 18a– 8 – 42 3a + 4b – 8+ 18a + 21b – b + 21b

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When more than one kind of grouping symbol occurs, do the computations in the innermost ones first. Then work from the inside out. 1.8 Simplifying Expressions; Order of Operations c Simplify expressions with parentheses inside parentheses. Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE a. 5(3 + 4) – {8 – [5 – (9 + 6)]} 1.8 Simplifying Expressions; Order of Operations c Simplify expressions with parentheses inside parentheses. ESimplify. (continued) Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 35 – {8 – [ –10]} 17 5(7) – {8 – [5 – 15]} 35 – 18 Compute (3+4) and (9+6) Compute5(7) and (5 – 15) Compute 8 – [–10] 35 – {8 +10} Compute – {8+10)

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EXAMPLE b. [6(x + 3) – 4x] – [4(y + 3) – 8(y – 4)] [ ] – [ ] 2x + 18 – 4y y x + 18 – 4x 1.8 Simplifying Expressions; Order of Operations c Simplify expressions with parentheses inside parentheses. ESimplify. Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. – 8y + 32 Collect like terms Remove brackets Collect like terms 2x + 4y – y – 44 2x + 4y + 18 – 44

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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. 1.8 Simplifying Expressions; Order of Operations Rules for Order of Operations Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution Simplifying Expressions; Order of Operations d Simplify expressions using the rules for order of operations. FSimplify. (continued) Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution Simplifying Expressions; Order of Operations d Simplify expressions using the rules for order of operations. FSimplify. Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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EXAMPLE Solution 1.8 Simplifying Expressions; Order of Operations d Simplify expressions using the rules for order of operations. GSimplify: Slide 15Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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