B the absolute values of 12 and 9 are 12 and 9 and 12

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Precalculus: Real Mathematics, Real People
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Chapter 2 / Exercise 99
Precalculus: Real Mathematics, Real People
Larson
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b) The absolute values of 12 and 9 are 12 and 9, and 12 9 21. So, ( 12) ( 9) 21. c) Add the absolute values of 3.5 and 6.28, and put a negative sign on the sum. Remember to line up the decimal points when adding decimal numbers: 3.50 6.28 9.78 So ( 3.5) ( 6.28) 9.78. d) 1 2 1 4 2 4 1 4 3 4 Now do Exercises 1–10
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Precalculus: Real Mathematics, Real People
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Chapter 2 / Exercise 99
Precalculus: Real Mathematics, Real People
Larson
Expert Verified
28 Chapter 1 Real Numbers and Their Properties 1-28 To understand the sum of a positive and a negative number that are not additive inverses of each other, consider the following situation. If you have a debt of $6 and $10 in cash, you may have $10 in hand, but your net worth is only $4. Your assets exceed your debts (in absolute value), and you have a positive net worth. In symbols, 6 10 4. Note that to get 4, we actually subtract 6 from 10. If you have a debt of $7 but have only $5 in cash, then your debts exceed your assets (in absolute value). You have a negative net worth of $2. In symbols, 7 5 2. Note that to get the 2 in the answer, we subtract 5 from 7. As you can see from these examples, the sum of a positive number and a negative number (with different absolute values) may be either positive or negative. These examples help us to understand the rule for adding numbers with unlike signs and different absolute values. Sum of Two Numbers with Unlike Signs (and Different Absolute Values) To find the sum of two numbers with unlike signs (and different absolute values), subtract their absolute values. The answer is positive if the number with the larger absolute value is positive. The answer is negative if the number with the larger absolute value is negative. U Helpful Hint V We use the illustrations with debts and assets to make the rules for adding signed numbers understand- able. However, in the end the carefully written rules tell us exactly how to per- form operations with signed num- bers, and we must obey the rules. For any number a , a and its opposite, a , have a sum of zero. For this reason, a and a are called additive inverses of each other. Note that the words “negative,” “opposite,” and “additive inverse” are often used interchangeably. Additive Inverse Property For any number a , a ( a ) 0 and ( a ) a 0. E X A M P L E 2 Finding the sum of additive inverses Evaluate. a) 34 ( 34) b) 1 4 1 4 c) 2.97 ( 2.97) Solution a) 34 ( 34) 0 b) 1 4 1 4 0 c) 2.97 ( 2.97) 0 Now do Exercises 11–14
1-29 1.3 Addition and Subtraction of Real Numbers 29 U 3 V Subtraction of Signed Numbers Each subtraction problem with signed numbers is solved by doing an equivalent addition problem. So before attempting subtraction of signed numbers be sure that you understand addition of signed numbers. We can think of subtraction as removing debts or assets, and addition as receiv- ing debts or assets. Removing a debt means the debt is forgiven. If you owe your E X A M P L E 3 Adding numbers with unlike signs Evaluate.

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