Subtracting Integers by Adding the Opposite

Subtracting integers by adding the opposite is a fundamental and very effective rule. It simplifies integer subtraction by transforming it into an addition problem, making calculations easier.

The following figures show how to subtract integers by adding the opposite. Scroll down the page for more examples and solutions.

 

Integer Rules Lesson
Check out the following lesson for the integer addition, subtraction, multiplication, and division.
Integer Rules

Integer Worksheets
Practice your integer skills with the following integer worksheets:
Online & Printable Integer Worksheets

The Rule:
To subtract an integer, you add its opposite. To find the opposite of an integer, we just change its sign. If it is negative, change to positive. If it is positive change to negative.

Mathematically:
a - b = a + (-b)
a - (-b) = a + b
Where:
‘a’ is the first integer (the minuend).
‘b’ is the second integer (the subtrahend).
‘-b’ is the opposite of ‘b’.

Steps to Subtract Integers by Adding the Opposite:

1. Keep the first integer the same. Don’t change the sign of the number you are subtracting from.
2. Change the subtraction sign to an addition sign. The operation now becomes addition.
3. Change the sign of the second integer to its opposite.
   If the second integer was positive, make it negative.
   If the second integer was negative, make it positive.
   
4. Apply the rules for adding integers.

For eg.
3 − 2 = 3 + (−2)
3 − (−2) = 3 + (+2)
Then, we use the same rules as adding integers.

The rules for adding integers are:

1. If the signs are the same, add the absolute value of the numbers and keep the sign.
2. If the signs are different,
   • subtract the smaller absolute value from the greater absolute value.
   • the sign will follow the number with the greater absolute value.

How to subtract integers?
Subtracting integers same as adding the opposite.
To subtract integers, first rewrite the subtraction as adding the opposite and then complete the addition.
Examples:
-8 - 5 =
8 - 12 =
-7 - 7 =
6 - 2 =
-(-3) =
10 - (-3) =
-4 - (-9) =
-8 - (-4) =
7 - (-7) =

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Subtracting Integers
This video goes through four examples on subtracting integers.
To subtract integers remember to change it into an addition problem. The first number plus the opposite of the second number.
Examples:
5 - 8 =
15 - (-4) =
-32 - 7 =
-21 - (-3) =

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Rule for subtracting integers
Add the opposite
Examples:
-9 - -8 =
-10 - +7 =
-10 - -18 =

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How to subtract integers by adding the opposite?
Examples:
-4 - 3 =
-4 - (-3) =

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Positive and negative integers are subtracted using the “add the opposite” method
Number lines and integer counters are also used to model each example problem.
Examples:
-2 - 6 =
4 - (-5) =
-5 - (-3) =
3 - 6 =

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Why Does This Work?
Subtracting a quantity is conceptually the same as adding the removal of that quantity. The opposite of a number represents its removal or the reversal of its effect. By adding the opposite, you are essentially performing the subtraction operation in terms of addition.

This method provides a consistent and reliable way to handle integer subtraction, especially when dealing with negative numbers. It reduces the complexity by relying on the rules you already know for addition.

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