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Chapter 2—Integers

2-5 Subtracting Signed Integers

When you complete the work for this section, you should be able to:
  • Describe the basic procedure for subtracting signed integers.
  • Demonstrate a mastery of the procedures for subtracting signed integers.

 

Preview
How to Subtract Signed Integers

There are two parts in the procedure for subtracting signed integers:

  1. Change the subtraction sign to the addition sign, and then switch the sign of the subtrahend (the number that immediately follows the operation sign you just changed.
  2. Add the result according to the procedures for adding signed integers.

fig020502.gif (2018 bytes)

Terminology for integer subtraction.

Changing Integer Subtraction to Integer Addition

The purpose of the first step in this subtraction procedure is to change the operation from subtraction to addition. So you begin by changing the symbol of operation from subtraction to addition (from – to +), then switching the sign of the subtrahend (the number immediately following the operation sign you just changed).

Example 1

Here are some examples of changing integer subtraction to integer addition — only the first two steps in the procedure for subtracting signed integers.

1.    (+ 2) – (+ 6) = (+ 2) + (– 6) 2.    (–  8) – (+ 11) = (–  8) + (– 11)
3.    (+ 15) – (– 12) = (+ 15) + (+ 12) 4.    (– 2) – (– 7) = (– 2) + (+ 7)

Examples and Exercises

Completing the Operation

Procedure

Subtracting Signed Integers

  1. Change the subtraction sign to the addition sign, and then switch the sign of the subtrahend (the number that immediately follows the operation sign you just changed.
  2. Add the result according to the procedures for adding signed integers.

It really is as simple as 1-2-3:

  1. Change the subtraction sign to the addition sign, and switch the sign of the subtrahend.
  2. Add the result according to the procedures for adding signed integers.

In these examples, we are not showing the details of the addition portion of the procedure—the second step. You've already seen all that in the previous lesson. But if you are having difficulty or are confused by the addition portion of these examples and exercises, you should carefully review the lesson on adding signed integers.

Example 2

Problem

( +15 ) – ( +12 ) =   ? 

Procedure
  1. Change from subtraction to addition:
  • Change the subtraction sign to the addition sign.
  • Then switch the sign of the number that immediately follows
( +15 ) ( +12 ) (+15 ) + ( –12 )
( +15 ) + ( 
+12 ) (+15 ) + ( 12 )
  1. Add the result
( +15 )  + (  –12 ) = ( +3 )
Solution

( +15 ) + (  –12 ) = ( +3 )

or

15) + (  –12 ) = 3

Example 3

Problem

( – 8 ) – ( – 6 ) =   ?

Procedure
  1. Change from subtraction to addition:
  • Change the subtraction sign to the addition sign.
  • Then switch the sign of the number that immediately follows
( – 8 ) ( –6 ) ( –8 ) + ( –6 )
( – 8 ) + ( 
6 ) ( –8 ) + ( +6 )
  1. Add the result
( –8 ) + ( +6 ) = ( –2)
Solution

( – 8 ) – ( – 6 ) = ( –2)

Examples and Exercises

Subtracting Signed Integers

Use these interactive examples and exercises to strengthen your understanding and build your skills:

David L. Heiserman, Editor

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Revised: June 06, 2015