Page 127 - ArithBook5thEd ~ BCC

Solution. The numbers have opposite signs, and the number with the larger absolute value (4.9) de-
termines the sign of the sum (+). The absolute value of the sum is the difference | 4.9 | − | −3.6 |=
4.9 − 3.6. Thus
−3.6 + 4.9 = +(4.9 − 3.6) = +1.3 = 1.3.

Example 158. Add: 43.6 + (−5.8) + (−135) + 69.5 + (−134) + 158.7 + (−162.3)

Solution. We add all the positive numbers,

43 . 6
69 . 5
+1 5 8 . 7

27 1. 8
and the absolute values of all the negative numbers,

5. 8
13 5.
13 4.
+1 6 2 . 3

43 7. 1
Treating the subtotal associated with the negative numbers as negative, we add 271.8 + (−437.1). By
the rule for adding signed numbers with opposite signs,

271.8 + (−437.1) = −(437.1 − 271.8) = −165.3.

Example 159. Subtract: 3.359 − 10.08.

Solution. 3.359− 10.08 = 3.359+ (−10.08) = −(10.08− 3.359). We first subtract the absolute values,
and affix the negative sign at the end.

10 . 08 0
− 3. 3 59

6. 72 1
Remembering that the sign was negative, 3.359 − 10.08 = −6.721.

Example 160. Last week, a business received checks from clients in the amounts of $350.65, $461.00
and $900.78, and paid bills in the amounts of $261.50, $551.00 and $78.70. What was the net profit
or loss for the week?

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