Subtracting Integers

Subtracting Integers

To subtract Integers, you will convert the problem into an addition problem and use the thinking processes you used for adding Integers. This plan will make it unnecessary to handle multiple cases. Here is the strategy.

When you subtract two Integers, change the problem to addition by taking the opposite of the second number. Then, use the strategy you learned for adding Integers.

Dealing with subtraction requires knowledge of opposites. Opposites have the same distances from zero, or absolute values, but differ in sign. So the opposite of 3 is -3. The opposite of -8 is 8. The notation below says the exact same thing, but is written using mathematical symbols.

-(3) = -3

-(-8) = 8

Example #1: 7 - 5
Even though this problem is simple by most people's standards, getting used to the conversion process will help you deal with harder problems. The strategy says that you must change the problem to addition and take the opposite of the last number. It would change the problem from 7 - 5 to 7 + (-5), because -5 is the opposite of 5. Using your knowledge of handling Positive + Negative numbers, 7 - 5 = 7 + (-5) = 2.
Example #2: -3 - 2
Following the same procedure as the example above; switch to addition. The opposite of 2 is -2. So, -3 - 2 = -3 + (-2). If you review your knowledge of handling Negative + Negative numbers, you will see that the answer is -5. Therefore, -3 - 2 = -5.
Example #3: -6 - (-8)
This problem looks a little more complicated but you still have to switch to addition. The opposite of -8 is 8. So, -6 - (-8) = -6 + 8. If you review your knowledge of handling Negative + Positive numbers, you will see that the answer is 2. Therefore, -6 - (-8) = 2.
Example #4: 10 - (-12)
Once again, you must switch to addition. The opposite of -12 is 12. So, 10 - (-12) = 10 + 12. If you review your knowledge of handling Positive + Positive numbers, which may not be necessary to do, you will see that the answer is 22. Therefore, 10 - (-12) = 22.

To help you reinforce skills with subtracting Integers, use the links below to review adding Integers.

Positive + Positive
Positive + Negative
Negative + Positive
Negative + Negative

Go to Multiplying Integers.
Go to the Frontpage.
Go to MATHguide.

(Updated October 17th, 2004)