| Chapter 2 Integers 2-5 Subtracting Signed Integers Procedure Subtracting Signed Integers Step 1: Change the subtraction sign to the addition sign.
Step 2. Switch the sign of the subtrahend.
Step 3. Add the result according to the procedures for adding signed integers. | | 
Figure 2-x. Terminology for integer subtraction. | The basic procedure for subtracting signed integers is to change the operation to addition, and then complete the addition. You have already learned how to add signed integers, so you only need some instruction for changing the operation from subtraction to addition. - Change From Addition to Subtraction
- Step 1: Change the subtraction sign to the addition sign.
Step 2. Switch the sign of the subtrahend. - Complete the Addition Operation
- Step 3. Add the result according to the procedures for adding signed integers.
Changing Integer Subtraction to Integer Addition | The purpose of the first two steps in this subtraction procedure is to change the operation from subtraction to addition. So you begin by changing the symbol of operation from subraction to addition (from – to +), then switching the sign of the subtrahend (the integer immediately following the operation sign you just changed). | Changing a subtraction operation to an addition operation. | Examples 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) | Exercises Change these subraction operations to addition. Do not do the final addition step at this time.
Click the ? symbol to see the correct answer. | 1. ( +3) – ( +2) = ? | 2. ( +6) – ( +1) = ? | | 3. ( –5) – ( +3) = ? | 4. ( +10) – ( –3) = ? | | 5. ( –7) – ( –4) = ? | Completing the Operation It really is as simple as 1-2-3: - Change the subtraction sign to the addition sign.
- Switch the sign of the subtrahend.
- 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 third 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. |
Subtracting signed integers.
| Example (+15) – (+12) = ? | The Problem | | (+15) – (+12) = ? | Step 1. Change the subtraction operation to addition. | (+15) + ( –12) | | Step 2: Switch the sign of the subtrahend. | (+15) – ( –12) | | Step 3. Add the result | (+15) + ( –12) = (+3) | | | The Solution | | (+15) – (+12) = (+3)
or
15 – 12 = 3 | Example (– 8) – (– 6) = ? | The Problem | | (– 8) – (– 6) = ? | Step 1. Change the subtraction operation to addition | (– 8) + (– 6) | | Step 2: Switch the sign of the subtrahend. | (– 8) + (+ 6) | | Step 3. Add the result | (– 8) + (+ 6) = (– 2) | | | The Solution | | (– 8) – (– 6) = (– 2) Or you might see it expressed more simply as: – 8 – (– 6) = – 2 | Example ( +12) – ( –20) = ? | The Problem | | ( +12) – ( –20) = ? | Step 1. Change the subtraction operation to addition | (+12) + (– 20) | | Step 2: Switch the sign of the subtrahend. | (+ 12) – (+ 20) | | Step 3. Add the result | (+ 12) + (+ 20) = (+ 32) | | | The Solution | | (+ 12) – (– 20) = (+ 32) Or you might see it expressed more simply as: 12 – (– 20) = 32 | Note Much of the confusion about subtracting signed integers is the result of having to use the same symbols for two entirely different purposes: The + is used for indicating both the addition operation and a positive integer value. The – is used for indicating both the subtraction operation and a negative integer value. What can be done about this source of confusion? Nothing. You have to consider the signs very carefully until the differences become second nature. | Examples | 1. | Problem: (– 7) – (+ 3) = ? Procedure: (– 7) – (+ 3) = (– 7) + (– 3)
(– 7) + (– 3) = (– 10) Solution: (– 7) – (+ 3) = (– 10) | 2. | Problem: (+ 7) – (– 3) = ? Procedure: (+ 7) – (– 3) = (+ 7) + (+ 3)
(+ 7) + (+ 3) = (+ 10) Solution: (+ 7) – (– 3) = (+ 10) | | | | | | 3. | Problem: (– 3) – (+ 7) = ? Procedure: (– 3) – (+ 7) = (– 3) + (– 7)
(– 3) + (– 7) = (– 10) Solution: (– 7) – (+ 3) = (– 10) | 4. | Problem: (+ 3) – (– 7) = ? Procedure: (+ 3) – (– 7) = (+ 3) + (+ 7)
(+ 3) + (+ 7) = (+10) Solution: (+ 7) – (– 3) = (+10) | Exercises Complete these subtraction operations.
Click the ? symbol to see the correct answer. | 1. ( + 8) – ( + 6) = ? | 2. (+ 3) – (+ 12) = ? | | 4. (– 2) – (– 7) = ? | 3. (– 18) – (– 12) = ? | | 5. (– 7) – (+ 5) = ? | 6. (– 3) – (+ 9) = ? | | 7. (+ 19) – (– 7) = ? | 8. (+ 4) – (– 13) = ? |
|
