Page 59 - ArithBook5thEd ~ BCC

To subtract a signed number A from a signed number B,
add B to the opposite of A:

B − A = B +(−A).

With this definition, there is no longer any real need for a separate operation called subtraction. For
example, instead of subtracting 17 − 9, we could simply add 17 + (−9) (verify that the results are the
same). Despite this, it is convenient to retain the operation of subtraction.

Example 51. (a) Subtract 15 from 9. (b) Subtract 8 from −2.

Solution. (a) 9 − 15 = 9 + (−15). Applying the rule for adding signed numbers with opposite signs,

9+ (−15) = −(15 − 9) = −6.

(b) −2 − 8= −2+ (−8). Applying the rule for adding signed numbers with the same sign,

−2+ (−8) = −(2 + 8) = −10.

Example 52. Subtract −17 from 12.

Solution. 12 − (−17) = 12 + (−(−17)). Remembering that −(−17) = 17 (opposite of the opposite),
we have
12 − (−17) = 12 + 17 = 29.

Example 53. Subtract (−15) from −32.

Solution. −32 − (−15) = −32 + (−(−15)) = −32 + 15. Applying the rule for adding signed numbers
with opposite signs,
−32 − (−15) = −32 + 15 = −(32 − 15) = −17.

Example 54. Perform the subtraction 3359 − 10080.

Solution. 3359−10080 = 3359+(−10080) = −(10080−3359). We perform the subtraction of absolute
values vertically.
10 08 0
− 33 59
67 21

Remembering that the sign was negative, 3359 − 10080 = −6721.

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