Study Guide

Basic Operations - Adding Integers

Adding Integers

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.

-5 + 7 table

There are two + left, representing the answer of +2.

Examples:

Different Examples Table

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.

Number Line (-5) + 7

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:

Number Line

(-3) + (-2)
Start at –3. Jump 2 places in the negative direction. You land on the answer, –5.
-4 + 3
Start at –4. Jump 3 places in the positive direction. You land on the answer, –1.
2 + -2
Start at +2. Jump 2 places in the negative direction. You land on the answer, 0.
4 + -1
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.

  • -6 + -10 = -16 
    Since both are negative, the answer is negative.
     
  • 7 + 12 = +19
    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.

  • -15 + 3 = -12
    Since there are 15 negatives and only 3 positives, our answer will be negative.
     
  • -3 + 8 = 5
    Since there are 3 negatives and 8 positives, our answer will be positive.