Fundamentals of Mathematics, 2008a

595
-6. Also, notice that the sign of the number with the larger absolute value is negative and that the sign of
the resulting sum is negative.
Adding Numbers with Unlike Signs
Addition of numbers with unlike signs: To add two real numbers that have unlike signs, subtract the smaller
absolute value from the larger absolute value and associate with this dierence the sign of the number with
the larger absolute value.
10.5.4.1 Sample Set B
Find the following sums.
Example 10.23
7 + (−2)
|7| = 7
} {{ }
Larger absolute
value. Sign is positive.
| − 2| = 2
} {{ }
Smaller absolute
value.
Subtract absolute values: 7 − 2 = 5.
Attach the proper sign: "+."
Thus, 7 + (−2) = +5 or 7 + (−2) = 5.
Example 10.24
3 + (−11)
|3| = 3
} {{ }
Smaller absolute
value.
| − 11| = 11
} {{ }
Larger absolute
value. Sign is negative.
Subtract absolute values: 11 − 3 = 8.
Attach the proper sign: "−."
Thus, 3 + (−11) = −8.
Example 10.25
The morning temperature on a winter's day in Lake Tahoe was -12 degrees.
temperature was 25 degrees warmer. What was the afternoon temperature?
The afternoon
We need to nd −12 + 25.
| − 12| = 12
} {{ }
Smaller absolute
value.
|25| = 25
} {{ }
Larger absolute
value. Sign is positive.
Subtract absolute values: 25 − 12 = 16.
Attach the proper sign: "+."
Thus, −12 + 25 = 13.
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