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.
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.
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.
Rule #1: If the signs are the same, add the two numbers together and keep the same sign.
Rule #2: If the signs are different, subtract the two numbers and keep the sign of the number that's further from zero.