Here's the secret to adding integers: one positive and one negative added together cancel each other out.
Think about it like this: if you bonk your sister on the head (a negative), then you give her a hug (a positive), your actions cancel each other out. Neutral. Neither bad nor good. (Don't try this at home!)
Let's try it with pictures. In this section, we'll use symbols (+) and (-) to represent each problem.
For the problem (-5) + 7, we've got five minuses and seven pluses. Each pair of pluses and minuses cancels out.
There are two + left, representing the answer of +2.
Examples:
Using a Number Line to Add Integers
Use a number line to solve (-5) + 7.
Start at -5 and jump 7 places in the positive direction (to the right). You'll land on the answer, +2.
Look Out: sometimes you may see parentheses around negative numbers. These do not mean that we need to multiply; they're just used so that we don't confuse negatives with subtraction.
Examples:
 Start at –3. Jump 2 places in the negative direction. You land on the answer, –5. |  Start at –4. Jump 3 places in the positive direction. You land on the answer, –1. |
 Start at +2. Jump 2 places in the negative direction. You land on the answer, 0. |  Start at +4. Jump 1 place in the negative direction. You land on the answer, +3. |
Remember these rules for addition:
Rule #1: If the signs are the same, add the two numbers together and keep the same sign.
Since both are negative, the answer is negative.
Since both are positive, the answer is positive.
Rule #2: If the signs are different, subtract the two numbers and keep the sign of the number that's further from zero.
Since there are 15 negatives and only 3 positives, our answer will be negative.
Since there are 3 negatives and 8 positives, our answer will be positive.