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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 2.2 Addition of Integers Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aAdd integers without using the number line.

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2.2 Addition of Integers a Add integers without using the number line. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 2.2 Addition of Integers a Add integers without using the number line. 1 Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 2.2 Addition of Integers a Add integers without using the number line. 2 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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2.2 Addition of Integers ADDING NEGATIVE INTEGERS Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To add two negative integers, add their absolute values and change the sign (making the answer negative).

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EXAMPLE 2.2 Addition of Integers a Add integers without using the number line. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Add.

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2.2 Addition of Integers a Add integers without using the number line. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. When the number 0 is added to any number, that number remains unchanged. For this reason, the number 0 is referred to as the additive identity.

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EXAMPLE 2.2 Addition of Integers a Add integers without using the number line. 6 Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Add.

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2.2 Addition of Integers ADDING POSITIVE AND NEGATIVE INTEGERS Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To add a positive integer and a negative integer, find the difference of their absolute values. a) If the negative integer has the greater absolute value, the answer is negative. b) If the positive integer has the greater absolute value, the answer is positive.

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EXAMPLE 2.2 Addition of Integers a Add integers without using the number line. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Add.

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For any integer a, (The sum of any number and its additive inverse, or opposite, is 0.) 2.2 Addition of Integers ADDING OPPOSITES Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 2.2 Addition of Integers a Add integers without using the number line. 13 Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Add.

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2.2 Addition of Integers RULES FOR ADDITION OF INTEGERS Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Positive numbers: Add the same way as arithmetic numbers. The answer is positive. 2. Negative numbers: Add absolute values. The answer is negative.

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2.2 Addition of Integers RULES FOR ADDITION OF INTEGERS Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. A positive and a negative number: Subtract absolute values. a) If the positive number has the greater absolute value, the answer is positive. b) If the negative number has the greater absolute value, the answer is negative. c) If the numbers have the same absolute value, they are additive inverses and the answer is One number is zero: The sum is the other number.

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EXAMPLE 2.2 Addition of Integers a Add integers without using the number line. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Add.

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2.2 Addition of Integers a Add integers without using the number line. Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Suppose we wish to add several numbers, positive and negative. Because of the commutative and associative laws for addition, we can group the positive numbers together and the negative numbers together and add them separately. Then we add the two results.

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EXAMPLE 2.2 Addition of Integers a Add integers without using the number line. 17 Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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EXAMPLE 2.2 Addition of Integers a Add integers without using the number line. 17 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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