# 5.2.8 Rules for Negatives

As you first learn how to work with negative numbers and develop your skills, a number line will be very helpful—but it can sometimes be tedious. Let’s create a few rules that can help us perform addition and subtraction when negative numbers are involved. Remember that you can always use a number line if you find it useful or if you’re unsure of your answer!

## Rule 1:

If you are adding two numbers that have the same sign, like , momentarily ignore the signs, and add the numbers together. Then, place the sign in front of the sum.

We think of as , which equals 7. Since both numbers were negative, we place a negative sign in front of the answer. Thus, . You can verify this using a number line.

## Rule 2:

If you are adding two numbers that have different signs, such as , momentarily ignore the signs. Then SUBTRACT the numbers and place the sign of the “larger” number (we are ignoring signs!) in front of the difference.

We ignore the signs in and subtract: , which equals 6. Since the “larger number” is 8, and it has a negative sign in front of it, the overall answer is also negative: .

## Rule 3:

If you are subtracting a positive number, like , then rewrite it as addition of the negative number and then use the rules for addition.

So, . For help visualizing this example, look at the number line below.

## Rule 4:

If you are subtracting a negative number, such as , then rewrite it as addition of the positive number and then use the rules for addition.

So, . Check out the number line below to see the addition.

Of course if you feel comfortable adding and subtracting negative without these rule there is no need to use them.

### Activity: Adding and Subtracting Negative Numbers Using the Four Strategies

Try these questions again using the four strategies above.

(a)

#### Discussion

Look at rule 2.

#### Answer

(a) We are adding two numbers with different signs. Ignore the signs and subtract the numbers 20 – 5 and use the sign from the larger number in the answer. So

(b)

#### Discussion

Look at rule 1.

#### Answer

(b) We are adding two numbers with the same sign. Ignore the signs and add the numbers, 20 + 5 and put back the sign from the numbers. So

(c)

#### Discussion

Look at rule 4.

#### Answer

(c) Re-write as addition of a positive number, 20 + 5

(d)

#### Answer

(d) Re-write as addition of a positive number, -20 + 5. Then follow rule 2. Ignore the signs and subtract the numbers 20 – 5 and use the sign from the larger number in the answer.

If you’d like a little more explanation on subtracting negative numbers, you can check out this video:

5.2.7 Adding and Subtracting Negative Numbers