How to Add and Subtract Negatives

Step-by-Step Guide

1. 1

   Step 1: Draw your number line.

   Draw a long, horizontal line.
   
   Mark a short vertical line in the middle and label it "0." Make more marks to the right of 0 and label them 1, 2, 3, and so on in that order.
   
   Those are the positive numbers.
   
   Negative numbers go the opposite direction.
   
   Starting at 0 and moving left, draw more marks and label them
   -1,
   -2,
   -3, and so on.
2. 2

   Step 2: Start with the first number in your problem.

   Let's say you want to solve the problem
   -8 +
   3.
   
   Find the first number,
   -8, on the number line.
   
   Draw a thick dot at that number. , On the number line, adding a positive number moves you to the right.
   
   For example, if you start at
   -8 and add 3, you move 3 marks to the right.
   
   The answer is where you end up:
   -5.
   
   This works no matter which number we start with. , Subtracting a positive number moves you to the left of the number line.
   
   For example, you know that
   -8
   - 3 =
   -11, because
   -11 is three marks left of
   -8. , Now let's try the other way around.
   
   This time, start at +5 on the number line and solve the problem 5 + (-2).
   
   Because the second number is negative, we change the direction we move on the number line.
   
   Adding normally moves to the right, but adding a negative number moves to the left instead.
   
   Start at +5, move 2 spaces to the left, and you end up at +3.
   
   So 5 + (-2) =
   3.
   
   Here's another way to think of it: adding a negative number is the same as subtracting a positive number. 5 + (-2) = 5
   -
   2. , Now try subtracting a negative number: 5
   - (-2).
   
   Again, we're going to switch the normal direction, and move right instead of left.
   
   Start at +5, move two the right, and you end up at
   7.
   
   Subtracting a negative number is the same as adding a positive number. 5
   - (-2) = 5 +
   2. , Let's solve
   -6 + (-4).
   
   Start at
   -6 on the number line.
   
   Addition moves to the right, but the negative sign in front of the 4 changes our direction, so we move to the left instead.
   
   Move four spaces left of
   -6 and you'll land on
   -10, so
   -6 + (-4) =
   -10.
   
   Don't get confused by where you start on the number line.
   
   The first number only tells you where to begin on the number line.
   
   You'll always move right or left based on the type of problem and the second number. , Now let's solve
   -10
   - (-3).
   
   Start at
   -10.
   
   Subtraction moves to the left but the negative in front of the 3 changes direction to the right instead.
   
   Move 3 places to the right and land on
   -3.
   
   The solution is
   -10
   - (-3) =
   -7.
   
   Here's a memory aid: it takes two lines to draw the two negative signs.
   
   It also takes two lines to draw a plus sign, so
   -
   - is the same as +, moving to the right.
3. 3

   Step 3: Review how to add positive numbers.

4. 4

   Step 4: Subtract positive numbers by moving left.

5. 5

   Step 5: Add a negative number.

6. 6

   Step 6: Subtract a negative number.

7. 7

   Step 7: Add two negative numbers.

8. 8

   Step 8: Subtract two negative numbers.

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