When adding 3 and -9, how do you know that the sum is negative?

You know it is negative because you are adding a small number and a bigger negative number. At first number lines are helpful to visualize it.

Step-by-step explanation:

Maybe this will help:

Let's say you are borrowing money from a friend and need to pay them back. You own your friends $9, but you only have 3. So, you give them your $3. This leaves you owning $6.

3-9=-6

negative = owes money