Once the number line stretches into the negative numbers, adding and subtracting still work exactly the same way — you just keep moving along the line, even past zero.

Adding moves right. Subtracting moves left. That single rule never changes. So if you start at 2 and subtract 5, you take five steps left — straight through zero and out the other side:

And starting in the negatives is fine too. From -1, adding 4 means four steps right, which carries you back up past zero:

Press play, then replay it: each time the marker starts somewhere new and hops for a calculation that crosses zero, reading each number aloud — minus signs and all.

There is one more move to learn: subtracting a negative. Taking away a debt makes you richer, so subtracting a negative turns into adding — it moves you right. The two minus signs cancel:

That is the famous rule: two minuses make a plus. Whenever you see a minus sign right next to a negative, swap the pair for a single plus and carry on.

Khan Academy works through these moves here: