Integer Subtraction

If you know how to add integers, I’m sure that you can also subtract integers. The key step is to transform an integer subtraction problem into an integer addition problem. The process is very simple. Here’s how:

Steps on How to Subtract Integers

Step 1: Transform the subtraction of integers problem into the addition of integers problem. Here’s how:

  • First, keep the first number (known as the minuend).
  • Second, change the operation from subtraction to addition.
  • Third, get the opposite sign of the second number (known as the subtrahend)
  • Finally, proceed with the regular addition of integers.

Step 2: Proceed with the regular addition of the integers.

Note that you will eventually add integers. So for your convenience, here’s the quick summary of the rules on how to add integers.

  • Case 1:  Adding two integers having the same sign

Add their absolute values then keep the common sign.

  • Case 2:  Adding two integers with different signs

Subtract their absolute values (larger absolute value minus smaller absolute value) then take the sign of the number with the larger absolute value.


Examples of Integer Subtractions

Example 1: Subtract the integers below.

The difference of negative 13 and positive four which can be written as -3-(+4).

Solution:

We will need to transform the problem from subtraction to addition. To do that, we keep the first number which is –13 , change the operation from subtraction to addition, then switch the sign of 4 to 4.

Negative 13 minus positive 4.
arrow pointing down showing equivalent expression of integer subtraction
Negative 13 minus positive 4 can be expressed as negative 13 plus negative 4.

The final step is to proceed with regular addition. Add their absolute values. Then we determine the sign of the final answer. Since we are adding integers with the same sign, we will keep the common sign which in this case is negative.

-13+(-4)=|-13|+|-4|=13+4=17 implies -17 because the common sign is negative.

Example 2: Subtract the integers below.

Positive 9 subtracted by negative 3 which can be expressed as +9-(-3)

Solution:

Just like before, convert a subtraction problem to an addition problem. Positive 9 remains, switch the operation from “minus” to “plus” then get the opposite sign of the subtrahend (second number) from negative to positive.

+9-(-3)
arrow pointing down to imply that an integer subtraction problem can be converted or transformed into an integer addition problem.
+9-(-3)=+9+(+3)=12

Now, let’s add them. We are adding two positive integers so we expect the answer to be positive as well because the common sign is positive.

+9+(+3)=|+9|+|+3|=9+3=+12

Example 3: Find the difference of the two integers.

Negative 19 subtracted from negative 24

Solution:

I hope you are already getting the hang of it. Let’s make this an addition of integers problem first then proceed with regular addition of integers with different signs.

Negative 19 subtracted from negative 24 can be written as an addition of integer problem which makes it negative 24 added to positive 19.

So we subtract their absolute values first then get the sign of the number with larger absolute value.

Subtracting the absolute values, we have 24 minus 19 which gives us +5. But the final answer is  5 because the sign comes from 24.

-24+(+19)=|-24|-|+19|=24-19=5 but the final answer should be -5 since the number which has a higher absolute value, in this case -24, has a negative sign.

Practice with Worksheets

You might also be interested in:

Integer Addition
Integer Multiplication
Integer Division