Add the Opposite

Every subtraction can be turned into an addition: subtracting a number is adding its opposite. So $4-9$ is $4 + \left(-9\right)$. You already know how to add numbers with different signs: 9 - 4 is 5, and -9 is further from zero, so the answer is -5.

On the number line, start at 4 and take 9 steps left. Four steps reach zero, and the other five go below it, ending at -5. Whenever you take away more than you have, you cross zero, so a smaller number minus a bigger one is always negative.

Why does this work? Taking away 9 dollars and adding a debt of 9 dollars change your total in exactly the same way. Reading every subtraction as adding the opposite means one set of rules covers both operations.