Subtracting Signed Numbers

To subtract 7 from 12, you can answer the question: "What number added to 7 gives 12?" The same kind of question subtracts 8 from 15, or 25 from 43, or any number a from any number b. (The missing-number exercises in the last lesson were really subtraction problems.) This shows how closely subtraction is tied to addition.

A shortcut

If you try the subtractions in this lesson both ways, by answering the question and by changing the sign of the number being subtracted and then adding, you'll get the same answers every time. That illustrates two important principles:

1. Subtracting a positive number has the same effect as adding a negative number with the same absolute value. A decrease of $100 in a man's assets is the same as an increase of $100 in his debts, as far as his real financial standing goes.
2. Subtracting a negative number has the same effect as adding a positive number with the same absolute value. A decrease of $75 in his debts is the same as an increase of $75 in his assets.

Rule. Change the sign of the subtrahend (if it's +, make it -; if it's -, make it +), then find the algebraic sum of the changed subtrahend and the minuend.

This rule turns algebraic subtraction into algebraic addition. For example: 8 - (-5) = 8 + (+5) = 13, \qquad -12 - (+3) = -12 + (-3) = -15