Section 1.2 Operations with Real Numbers and Algebraic Expressions 15 SECTION 1.2 Operations with Real Numbers and Algebraic Expressions From 2004 to 2010, the number of active users (in millions) of Facebook can be modeled by the expression 4.3x4 - 32.5x3 + 80.9x2 - 55.5x + 2.2 where x is the number of years after 2004. According to the model, how many visitors were there in 2009? (Source: http://www.facebook.com/press/info.php?timeline) To answer this question, we must know how to perform operations with real numbers and how to evaluate algebraic expressions. In this section, we will review these skills. Adding Real Numbers Adding and subtracting real numbers is a skill that we encounter on a daily basis. Situations in which we must perform these operations involve balancing a checkbook, tracking changes in the stock market, calculating federal taxes, calculating net worth, and understanding changes in temperature, sea level, and altitude. The list could continue. The rules for addition are illustrated next. Signs Are the Same Both signs are positive: Jan enrolls in 6 semester credit hours and then adds 4 more credit hours. So, Jan enrolls in a total of 10 credit hours. We represent this numerically and graphically as shown. 6 + 4 = 10 +4 Both signs are negative: Jason owes a credit card company $100 and then makes another charge of $50. So, Jason owes the credit card company a total of $150. We represent this numerically and graphically as shown. -100 + (-50) = -150 ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Add and subtract real numbers. 2. Multiply and divide real numbers. 3. Simplify exponential expressions. 4. Use the order of operations to simplify an expression. 5. Evaluate algebraic expressions. 6. Solve applications involving operations on real numbers and algebraic expressions. 7. Troubleshoot common errors. Objective 1 ▶ Add and subtract real numbers. 3 4 5 6 7 8 9 10 11 12 13 –180 –170 –160 –150 –140 +(–50) –130 –120 –110 –100 –90 –80 Signs Are Different Number with the larger absolute value is negative: Maria owes a credit card company $100 and makes a payment of $80. After the payment, she owes the company $20. We represent this numerically and graphically as shown. -100 + 80 = -20 +80 –110 –100 –90 –80 –70 –60 –50 –40 –30 –20 –10 Number with the larger absolute value is positive: The temperature in Boston, Massachusetts at 7 a.m. is -5°F. The temperature rises 20°F in 6 hr. So, the
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