How to add two positive integers:
You add the numbers like you normally would. There's no trick even though it seems like a trick question.
Example: 3+5 = 8
In that example, you can think of like starting at 3 on the number line. Then you move 5 units to the right to arrive at 8 on the number line.
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How to add two negative integers:
Treat the negative numbers as their positive version of themselves. Next, you add those positive counterparts like normal. The last thing you do is make the result negative.
For example,
-9 + (-12) = -21
which we can think of like this
9+12 = 21
Then we just make everything negative to get that first equation mentioned.
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How to add positive and negative integers:
This will depend on which has larger absolute value. In other words, which is further away from 0 on the number line.
In any event, you basically subtract the positive version of each number. Then the one furthest from 0 will determine if the result is positive or negative.
Examples:
-8 + 9 = 1
7 + (-12) = -5
In the first example, we can think of it like 9-8 = 1. I'm subtracting the two numbers 8 and 9, but doing so large - small and only focusing on the positive versions so far. Because 9 is further away from 0 compared to -8, this ultimately means the result is positive (since 9 is positive).
In the second example, we would say 12-7 = 5. Then note how -12 is farther away from 0 compared to 7. This means the negative side wins, so to speak, and the final result is negative.