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CHAPTER 4 Fraction Notation: Addition, Subtraction, and Mixed Numerals Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.1Least Common Multiples 4.2Addition, Order, and Applications 4.3Subtraction, Equations, and Applications 4.4Solving Equations: Using the Principles Together 4.5Mixed Numerals 4.6Addition and Subtraction of Mixed Numerals; Applications 4.7Multiplication and Division of Mixed Numerals; Applications 4.8Order of Operations and Complex Fractions

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OBJECTIVES 4.8 Order of Operations and Complex Fractions Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aSimplify expressions containing fraction notation using the rules for order of operations. bSimplify complex fractions.

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4.8 Order of Operations and Complex Fractions a Simplify expressions containing fraction notation using the rules for order of operations. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Like expressions containing integers, expressions containing fraction notation follow the rules for order of operations.

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Title 4.8 Order of Operations and Complex Fractions Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Do all calculations within parentheses ( ), brackets [ ], braces { }, absolute-value symbols, numerators, or denominators. 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.

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EXAMPLE 4.8 Order of Operations and Complex Fractions a Simplify expressions containing fraction notation using the rules for order of operations. 1 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.8 Order of Operations and Complex Fractions a Simplify expressions containing fraction notation using the rules for order of operations. 1 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.8 Order of Operations and Complex Fractions a Simplify expressions containing fraction notation using the rules for order of operations. 3 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Simplify. The parentheses here are not grouping symbols, so we begin by evaluating the exponential expression.

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EXAMPLE 4.8 Order of Operations and Complex Fractions a Simplify expressions containing fraction notation using the rules for order of operations. 3 Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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4.8 Order of Operations and Complex Fractions b Simplify complex fractions. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A complex fraction is a fraction in which the numerator and/or denominator contain one or more fractions. Since a fraction bar represents division, complex fractions can be rewritten using the division symbol

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EXAMPLE 4.8 Order of Operations and Complex Fractions b Simplify complex fractions. 4 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Simplify.

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EXAMPLE 4.8 Order of Operations and Complex Fractions b Simplify complex fractions. 4 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.8 Order of Operations and Complex Fractions b Simplify complex fractions. 4 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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4.8 Order of Operations and Complex Fractions b Simplify complex fractions. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When the numerator or denominator of a complex fraction consists of more than one term, first simplify the numerator and/or denominator separately.

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EXAMPLE 4.8 Order of Operations and Complex Fractions b Simplify complex fractions. 6 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.8 Order of Operations and Complex Fractions b Simplify complex fractions. 6 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.8 Order of Operations and Complex Fractions b Simplify complex fractions. 6 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.8 Order of Operations and Complex Fractions b Simplify complex fractions. 7Harvesting Walnut Trees. Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A woodland owner decided to harvest five walnut trees in order to improve the growing conditions of the remaining trees. The logs she sold measured What is the average length of the logs?

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EXAMPLE 4.8 Order of Operations and Complex Fractions b Simplify complex fractions. 7Harvesting Walnut Trees. Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Recall that to compute an average, we add the numbers and then divide the sum by the number of addends.

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EXAMPLE 4.8 Order of Operations and Complex Fractions b Simplify complex fractions. 7Harvesting Walnut Trees. Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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