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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 4.2 Addition, Order, and Applications Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aAdd using fraction notation when denominators are the same. bAdd using fraction notation when denominators are different. cUse to form a true statement with fraction notation. dSolve problems involving addition with fraction notation.

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4.2 Addition, Order, and Applications a Add using fraction notation when denominators are the same. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Addition using fraction notation corresponds to combining or putting like things together, just as when we combined like terms.

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Title 4.2 Addition, Order, and Applications Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To add when denominators are the same, a) add the numerators, b) keep the denominator, and c) simplify, if possible.

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EXAMPLE 4.2 Addition, Order, and Applications a Add using fraction notation when denominators are the same. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Add and, if possible, simplify.

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4.2 Addition, Order, and Applications a Add using fraction notation when denominators are the same. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We may need to add fractions when combining like terms.

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EXAMPLE 4.2 Addition, Order, and Applications a Add using fraction notation when denominators are the same. 5 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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Title 4.2 Addition, Order, and Applications Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To add when denominators are different: a) Find the least common multiple of the denominators. That number is the least common denominator, LCD. b) Multiply by 1, writing 1 in the form of n/n, to find an equivalent sum in which the LCD appears in each fraction. c) Add the numerators, keeping the same denominator. d) Simplify, if possible.

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EXAMPLE 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 6 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. a) Since 4 is a factor of 8, the LCM of 4 and 8 is 8. Thus, the LCD is 8. b) We need to find a fraction equivalent to with a denominator of 8:

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EXAMPLE 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 6 Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 7 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 9 Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 10 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 10 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.2 Addition, Order, and Applications b Add using fraction notation when denominators are different. 10 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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4.2 Addition, Order, and Applications c Use to form a true statement with fraction notation. Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When two fractions share a common denominator, the larger number can be found by comparing numerators. For example, 4 is greater than 3, so

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EXAMPLE 4.2 Addition, Order, and Applications c Use to form a true statement with fraction notation. 11 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.2 Addition, Order, and Applications c Use to form a true statement with fraction notation. 11 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A contractor uses two layers of subflooring under a ceramic tile floor. First, she installs a -in. layer of oriented strand board (OSB). Then a -in. sheet of cement board is mortared to the OSB. The mortar is -in. thick. What is the total thickness of the two installed subfloors?

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EXAMPLE 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We let t = the total thickness of the subfloors.

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EXAMPLE 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate.

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EXAMPLE 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve.

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EXAMPLE 4.2 Addition, Order, and Applications d Solve problems involving addition with fraction notation. 13 Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. We check by repeating the calculation. 5. State. The total thickness of the installed subfloors is in.

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