Lesson Objectives
  • Demonstrate an understanding of how to add integers
  • Learn how to convert a subtraction operation into addition of the opposite
  • Learn how to subtract one integer from another
  • Learn how to perform subtraction with more than two integers

How to Subtract Integers


In our last lesson, we learned how to perform addition with integers. In this lesson, we will learn how to perform subtraction with integers. The subtraction process will only take on two additional steps from the addition process. When we subtract one integer from another:
  • Note: Leave the Minuend or leftmost number unchanged
  • Change the subtraction operation into addition
  • Change the subtrahend or number being subtracted away into its opposite (change the sign)
  • Find the sum of the two integers
Let's take a look at a few examples.
Example 1: Subtract each.
-11 - 5
  • Change the subtraction operation into addition
  • -11 - 5 » -11 + 5
  • Change the subtrahend or number being subtracted away into its opposite (change the sign)
  • -11 + 5 » -11 + (-5)
  • Find the sum of the two integers
  • -11 + (-5) = -16
-11 - 5 = -16
Example 2: Subtract each.
-8 - (-12)
  • Change the subtraction operation into addition
  • -8 - (-12) » -8 + (-12)
  • Change the subtrahend or number being subtracted away into its opposite (change the sign)
  • -8 + (-12) » -8 + 12
  • Find the sum of the two integers
  • -8 + 12 = 4
-8 - (-12) = 4
Example 3: Subtract each.
-29 - (-15)
  • Change the subtraction operation into addition
  • -29 - (-15) » -29 + (-15)
  • Change the subtrahend or number being subtracted away into its opposite (change the sign)
  • -29 + (-15) » -29 + 15
  • Find the sum of the two integers
  • -29 + 15 = -14
-29 - (-15) = -14

Subtracting More than two Integers

We previously learned that addition is commutative. This means we can add any number of addends in any order and not change the result. The same is not true for subtraction. Subtraction is not commutative; when we work with the subtraction operation, the order matters. If we are faced with a problem with multiple subtraction operations, we can change the subtraction into addition of the opposite. Once this is done, we can add in any order and obtain the correct result. To subtract more than two integers:
  • Note: Leave the leftmost number unchanged
  • Change each subtraction operation into addition
  • Change each number being subtracted away into its opposite (change the sign)
  • Find the sum of the integers
Let's take a look at a few problems:
Example 4: Subtract each.
-4 - (-8) - 5 - (-6)
  • Change each subtraction operation into addition
  • -4 - (-8) - 5 - (-6) » -4 + (-8) + 5 + (-6)
  • Change each number being subtracted away into its opposite (change the sign)
  • -4 + (-8) + 5 + (-6) » -4 + 8 + (-5) + 6
  • Find the sum of the integers
  • -4 + 8 + (-5) + 6 = -4 + (-5) + 8 + 6 = -9 + 14 = 5
-4 - (-8) - 5 - (-6) = 5
Example 5: Subtract each.
7 - 9 - (-24) - 19 - (-2)
  • Change each subtraction operation into addition
  • 7 - 9 - (-24) - 19 - (-2) » 7 + 9 + (-24) + 19 + (-2)
  • Change each number being subtracted away into its opposite (change the sign)
  • 7 + 9 + (-24) + 19 + (-2) » 7 + (-9) + 24 + (-19) + 2
  • Find the sum of the integers
  • 7 + (-9) + 24 + (-19) + 2 = 7 + 24 + 2 + (-9) + (-19) = 33 + (-28) = 5
7 - 9 - (-24) - 19 - (-2) = 5

Skills Check:

Example #1

Find each difference.

218 - 966

Please choose the best answer.

A
684
B
748
C
-805
D
-748
E
-684

Example #2

Find each difference.

-539 - 297

Please choose the best answer.

A
836
B
914
C
-836
D
-914
E
-641

Example #3

Find each difference.

-366 - (-321) - (-23)

Please choose the best answer.

A
22
B
-22
C
32
D
-710
E
710
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