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Solution. We add all the positive numbers,

43
69
+1 5 8

270
and the absolute values of all the negative numbers,

5
13 5
13 4
+1 6 2

436

Treating the subtotal associated with the negative numbers as negative, we add 270 + (−436). By the
rule for adding signed numbers with opposite signs,

270 + (−436) = −(436 − 270) = −166.

If we think of positive numbers as “profits,” and negative numbers as “losses,” then signed number
addition is like “balancing the books.” There is a net gain if the total profits are larger than the total
losses (in absolute value); otherwise there is a net loss.

2.3.5 Exercises

Perform the additions.

1. 1 + (−1) + 1 + (−1) + 1 + (−1)

2. −82 + (−1985) + 82

3. 44 + (−55) + 288 + 36 + (−191) + (−8)

4. 123 + (−78) + (−143) + 78 + 15 + (−6) + 50

5. Find the average noon temperature for the first week of January in Barrow, Alaska if the noon
◦
◦
◦
temperatures were: Monday: −8 F, Tuesday: 2 F, Wednesday: −3 F, Thursday: −5 F, Friday:
◦
1 F, Saturday: 4 F, Sunday: 9 F.
◦
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2.4 Subtracting signed numbers
The phrase “subtract A from B” indicates the operation B − A. We extend subtraction to signed
numbers by defining it in terms of addition.

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