How Do You Subtract Integers?

Subtracting integers involves a simple process of converting the subtraction problem into an addition problem using the concept of additive inverse. Here’s a step-by-step guide on how to do it, based on the references:

Steps to Subtract Integers

Here’s a breakdown of the procedure, clearly outlining each step with examples:

1. Keep the First Integer: The first number in your subtraction problem remains unchanged.

   • Example: In the problem 5 - 3, the number 5 stays as 5.
     
     

2. Change Subtraction to Addition: Convert the subtraction operation into addition. The core idea here is that subtraction is the same as adding the opposite.

   • Example: 5 - 3 becomes 5 + ( ).
     
     

3. Change the Sign of the Second Integer: Take the second number and change its sign to its opposite. If it's positive, make it negative; if it's negative, make it positive. This is equivalent to finding the additive inverse.

   • Example: The +3 in 5 + (3) becomes -3, resulting in 5 + (-3).
     
     

4. Add the Two Integers: Finally, perform the addition operation with the transformed numbers. This will give you the result of the original subtraction problem.

   • Example: 5 + (-3) = 2.

Example Table

Here’s a table illustrating the process with various subtraction problems:

Original Problem	Step 1: Keep First Integer	Step 2: Change to Addition	Step 3: Change Sign of Second Integer	Step 4: Add Integers	Answer
7 - 4	7	7 +	7 + (-4)	7 + (-4)	3
10 - (-2)	10	10 +	10 + (2)	10 + 2	12
-3 - 5	-3	-3 +	-3 + (-5)	-3 + (-5)	-8
-8 - (-1)	-8	-8 +	-8 + (1)	-8 + 1	-7

Key Takeaway

Subtraction of integers can be simply viewed as adding the additive inverse of the second integer to the first integer, transforming subtraction problems into equivalent addition problems. This simplifies the calculation and makes it easier to understand integer operations.