Page 55 - ArithBook5thEd ~ BCC

When two signed numbers are added

• if the numbers have opposite signs,
1. the sign of the sum is the sign of the num-
ber with the larger absolute value;
2. the absolute value of the sum is the differ-
ence between the two individual absolute
values (larger − smaller).

• if the two numbers have the same sign,

1. the sign of the sum is the common sign
of the summands;
2. the absolute value of the sum is the sum
of the individual absolute values.

Example 43. Add 15 + (−18).

Solution. The numbers have opposite signs, so the sign of the sum is the same as the sign of the
number with the larger absolute value (−18), i.e., −. The absolute value of the sum is the difference
| −18 | − | 15 |=18 − 15 = 3. Thus the sum is −3. This reasoning is summarized as

15 + (−18) = −(18 − 15) = −3.

Example 44. Add −7+ (−9).

Solution. The numbers have the same sign, −,so that is also the sign of the sum. The absolute value
of the sum is the sum of the individual absolute values, | −7 | + | −9 |=7 + 9 =16. Thus the sum is
−16. The reasoning is summarized as

−7+ (−9) = −(7 + 9) = −16.

Example 45. Add −36 + 49.

Solution. The numbers have opposite signs, and the number with the larger absolute value (49) deter-
mines the sign of the sum (+). The absolute value of the sum is the difference | 49 | − | −36 |=49−36.
Thus
−36 + 49 = +(49 − 36) = +13 = 13.

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