Chapter 8 - XYZ Custom Plus

Introduction . . .Addition with Negative NumbersSuppose you are in Las Vegas playing blackjack and youlose $3 on the first hand and then you lose $5 on the nexthand. If you represent winning with positive numbers andlosing with negative numbers, how will you represent theresults from your first two hands? Since you lost $3 and $5for a total of $8, one way to represent the situation is withaddition of negative numbers:(2$3) 1 (2$5) 5 2$8From this example we see that the sum of two negativenumbers is a negative number. To generalize addition of positive and negativenumbers, we can use the number line.AAdding with a Number lineWe can think of each number on the number line as having two characteristics:(1) a distance from 0 (absolute value) and (2) a direction from 0 (positiveor negative). The distance from 0 is represented by the numerical part of thenumber (like the 5 in the number 25), and its direction is represented by the 1or 2 sign in front of the number.We can visualize addition of numbers on the number line by thinking in termsof distance and direction from 0. Let’s begin with a simple problem we know theanswer to. We interpret the sum 3 1 5 on the number line as follows:1. The first number is 3, which tells us “start at the origin, and move 3 units in thepositive direction.”2. The 1 sign is read “and then move.”3. The 5 means “5 units in the positive direction.”Start3 units 5 unitsJ♣♣JEnd8.2ObjectivesA u se the number line to add positiveand negative numbers.B Add positive and negative numbersusing a rule.C Solve applications involvingaddition with positive and negativenumbers.NoteExamples now playing atMathTV.com/booksThis method of addingnumbers may seema little complicated atfirst, but it will allow us to addnumbers we couldn’t otherwiseadd.−8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8FIGuRE 1Figure 1 shows these steps. To summarize, 3 1 5 means to start at the origin(0), move 3 units in the positive direction, and then move 5 units in the positivedirection. We end up at 8, which is the sum we are looking for: 3 1 5 5 8.ExAmplE 1Add 3 1 (25) using the number line.sOlutiON We start at the origin, move 3 units in the positive direction, andthen move 5 units in the negative direction, as shown in Figure 2. The last arrowends at 22, which must be the sum of 3 and 25. That is:3 1 (25) 5 22prACtiCE prOBlEms1. Add: 2 1 (25)EndStart3 units5 units−8 −7 −6 −5 −4 −3 −2 −1 1 0 1 23 4 5 6 7 8FIGuRE 28.2 Addition with Negative NumbersAnswer1. 23459