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Adding Positive and Negative Numbers

Adding positive numbers, such as 2 + 2, is easy.

When we add a negative number to a positive number, or two negative numbers, that can sometimes seem tricky. However, there are some simple rules to follow and we introduce them here.

Rule 1: Adding positive numbers to positive numbers—it’s just normal addition.

For example: this is what you have learned all along. 3 + 2 are two positive numbers. You can calculate these problems the way you always have: 3 + 2 = 5.

Rule 2: Adding positive numbers to negative numbers—count forward the amount you’re adding.

This is where it gets a little harder. Pay close attention to where the negative signs are placed in the problem.


For example: -6 + 3. This would reading “negative six plus three”. The best way to think about this problem is to use a number line that extends to the negative numbers.


You’re starting with the negative number -6.

adding negative numbers 1
 

 

 

 

 

And you’re adding three to that number, which means you are moving three spots to the right.

adding negative numbers 2
 

 

 

 

 

 

 

 

The answer is -3. -6 + 3 = -3.

Rule 3: Adding negative numbers to positive numbers—count backwards, as if you were subtracting.

Now, let’s look at the reverse equation. When you are adding a negative number to a positive number you are effectively subtracting the second number from the first.
For example, take 4 + (-2). How does that look on the numbers line?


You start at 4.

adding negative numbers 3
 

 

 

 

 

 

And then you add the negative number, which means you are moving to the left – in the negative direction. Basically you are subtracting the 2.

adding negative numbers 4
 

 

 

 

 

 

 

 

The answer is 2. 4 + (-2) = 2.

Rule 4: Adding negative numbers to negative numbers— treat the problem like subtraction (counting backwards).

When you are adding a negative number to a negative number, it becomes subtraction, where you start from a negative point on the numbers line and move left.


For example, -3 + (-2). This reads “negative three plus negative 2”. You need to ignore the plus sign and recognize that the second negative means you are subtracting that number.


We’re starting at -3.

adding negative numbers 5
 

 

 

 

 

 

Then we subtract 2.

adding negative numbers 6
 

 

 

 

 

 

 

The answer is -5. -3 + (-2) = -5.