Adding and Subtracting

Think of every integer as a move on the number line. Adding a positive steps right; adding a negative steps left.

So 5 + (−3) lands on 2, and −4 + 7 lands on 3.

The one that feels strange is subtracting a negative. Taking away a step backward is the same as stepping forward: 5 − (−3) = 5 + 3 = 8. Subtracting a negative adds. That is not a trick to memorize — it falls straight out of what subtraction means.

Why does a negative times a negative come out positive? Read it as reversing a reversal.

Face north, turn 180°, then turn 180° again — you are back facing north. Each negative flips the sign, and two flips return you to where you started.

That is also why (−4) × (−3) = 12: the two minus signs cancel, and only the size, 12, survives.