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CHAPTER 2 Introduction to Integers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2.1Integers and the Number Line 2.2Addition of Integers 2.3Subtraction of Integers 2.4Multiplication of Integers 2.5Division of Integers and Order of Operations 2.6Introduction to Algebra and Expressions 2.7Like Terms and Perimeter 2.8Solving Equations

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OBJECTIVES 2.3 Subtraction of Integers Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aSubtract integers and simplify combinations of additions and subtractions. bSolve applied problems involving addition and subtraction of integers.

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2.3 Subtraction of Integers THE DIFFERENCE Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The difference a – b is the number that when added to b gives a.

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EXAMPLE 2.3 Subtraction of Integers a Subtract integers and simplify combinations of additions and subtractions. 1 Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Think: 5 – 8 is the number that when added to 8 gives 5. What number can we add to 8 to get 5? The number must be negative. The number is –3: 5 – 8 = –3. That is, 5 – 8 = –3 because 8 + (–3) = 5. Subtract: 5 – 8.

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2.3 Subtraction of Integers a Subtract integers and simplify combinations of additions and subtractions. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The definition of a – b does not always provide the most efficient way to subtract.

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2.3 Subtraction of Integers SUBTRACTING BY ADDING THE OPPOSITE Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To subtract, add the opposite, or additive inverse, of the number being subtracted:

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EXAMPLE 2.3 Subtraction of Integers a Subtract integers and simplify combinations of additions and subtractions. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Equate each subtraction with a corresponding addition. Then write the equation in words. Negative twelve minus thirty is negative twelve plus negative thirty.

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EXAMPLE 2.3 Subtraction of Integers a Subtract integers and simplify combinations of additions and subtractions. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Negative twenty minus negative seventeen is negative twenty plus seventeen.

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EXAMPLE 2.3 Subtraction of Integers a Subtract integers and simplify combinations of additions and subtractions. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Subtract.

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EXAMPLE 2.3 Subtraction of Integers a Subtract integers and simplify combinations of additions and subtractions. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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2.3 Subtraction of Integers a Subtract integers and simplify combinations of additions and subtractions. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When several additions and subtractions occur together, we can make them all additions. The commutative law for addition can then be used.

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EXAMPLE 2.3 Subtraction of Integers a Subtract integers and simplify combinations of additions and subtractions. 10 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 2.3 Subtraction of Integers b Solve applied problems involving addition and subtraction of integers. 11Temperature Changes. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Denver, Colorado, experienced its greatest temperature change in one day on January 25, 1872. From the low of –20 F(degrees Fahrenheit), the temperature increased 66. If it later decreased 10, what was the final temperature? Source: Based on information from www.examiner.com

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EXAMPLE 2.3 Subtraction of Integers b Solve applied problems involving addition and subtraction of integers. 11Temperature Changes. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We let T represent the final temperature.

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Integers and Introduction to Solving Equations

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