42 Chapter 1 Real Numbers and Algebraic Expressions �� ������������������������ Addition of Real Numbers ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Add numbers with the same sign. 2. Add numbers with different signs. 3. Solve real-life problems. 4. Troubleshoot common errors. The operating income for Delta Airlines for the years 2002 to 2009 is shown in the table. Find the total operating income for the years 2002–2009. (Source: http://www.airlinefinancials.com/uploads/2002–2009_Delta _ mainline.pdf ) To answer this question, we must know how to perform operations with real numbers. In this section, we will examine addition of real numbers. Adding Numbers with the Same Signs The real number line can help us visualize the process of adding real numbers. Adding two positive Year numbers is a skill that we encounter on a daily basis. For example, if a student enrolls in 6 hr of classes and then adds 4 more hours during the drop/add period, the student enrolls in a total of 6 + 4 = 10 hr of classes. +6 +4 0 1 2 3 4 5 6 7 8 9 10 Adding two negative numbers is not something that we encounter as often as adding two positive numbers. Suppose we owe a friend $5 and then we borrow $2 more. At this point, we owe our friend a total of $7. Mathematically, the total we owe can be represented as -5 + (-2) = -7 On the number line, we can visualize this situation as beginning at 0, moving to the left 5 units, and moving left again 2 units until we arrive at -7. (–2) (–5) –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 While number lines provide us the ability to visualize the operations on the numbers, using them every time we add two numbers can be very time consuming. From the previous examples, we can conclude that adding two positive numbers results in a positive number and adding two negative numbers results in a negative number. ���������������������� Adding Numbers with the Same Sign Step 1: Add the absolute values of the numbers. Step 2: The sign of the result is the same as the sign of the numbers in the original expression. �� ������������������������ ������������������ Add. For parts (a) and (b), use a number line to add the numbers. 1a. 7 + 2 1b. (-1) + (-4) 1c. (-2) + (-7) 1d. (-1.5) + (-3) 1e. 1 5 + 3 10 1f. (-7) + a- 2 3 b 1g. (-8) + (-2) + (-4) Operating Income (in millions) 2002 –$1309 2003 –$ 786 2004 –$5985 2005 –$1605 2006 –$1139 2007 $ 78 2008 –$ 58 Objective 1 ▶ 2009 $ 605 Add numbers with the same sign.
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