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Chapter 2 Integers 2-4 Adding Signed Integers Preview
How to Add Signed Integers The exact procedure for adding signed integers depends upon whether the addends have the same sign or opposite signs. When the addends have the same sign (both + or both – ): Step 1: Add the absolute values of the addends
Step 2. Give the result the sign that is common to the addends When the addends have opposite signs (one is + and the other is –): Step 1: Subtract the absolute values of the addends
Step 2. Give the result the sign of the addend that has larger absolute value | | 
Figure 2-x. Terminology for integer addition. | 2-4.1 Adding Integers Having the Same Sign Procedure When adding integers that have the same sign (both positive or both negative): Step 1: Add the absolute values of the addends
Step 2. Give the result the sign that is common to the addends | Adding Positive Integers When adding integers that are both positive: Step 1: Add the absolute values of the addends
Step 2. Give the result a + sign Notes - Q: "Why do we have to take the absolute values of the addends when numbers are already positive?"
A: It's the procedure that is important--as you will soon discover. - Adding negative integers will always produce a positive sum.
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Adding positive integers.
| Example (+2) + (+3) = ? | The Problem | | (+2) + (+3) = ? | Step 1: Add the absolute values of the addends. | |+2| + |+3| = 2 + 3 = 5 | | Step 2. Give the result the sign that is common to the addends | Both addends are positive, so the result is positive, +5 | | | The Solution | | (+2) + (+3) = (+5) Or more simply as
2 + 3 = 5 | Adding Negative Integers When adding integers that are both negative: Step 1: Add the absolute values of the addends
Step 2. Give the result a – sign Notes - This is an addition problem. So even though the addends both have negative values, you still add their absolute values.
- Adding negative integers will always produce a negative sum.
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Adding negative integers.
| Example (– 6) + (– 3) = ? | The Problem | | (– 6) + (– 3) = ? | Step 1: Add the absolute values of the addends. | | – 6 | + | – 3 | = 6 + 3 = 9 | | Step 2: Assign the common sign to the sum. | Both addends are negative, so the result is negative, – 9 | | | The Solution | | (– 6) + (– 3) = (– 9) This can be expressed more simply as
– 6 + (– 3) = – 9 | Exercises Add these signed integers.
Click the ? symbol to see the correct answer. | 1. (+5) + (+4) = ? | 2. (+4) + (+9) = ? | | 3. (-7) + (-4) = ? | 4. (-6) + (-7) = ? | 2-4.2 Adding Integers Having Opposite Signs Procedure When adding integers that have opposite signs: Step 1: Subtract the absolute values of the addends
Step 2. Give the result the sign of the addend that has larger absolute value | Example (+ 5) + (– 2) = ? | The Problem | | (+ 5) + (– 2) = ? | Step 1: Subtract the absolute values of the addends | |+ 5| – |– 2| = 5 – 2
5 – 2 = 3. | | Step 2: Give the result the sign of the addend that has larger absolute value. | The addend with the larger absolute value is 5, and the sign of this addend is +. So sum is a positive value, +3 | | | The Solution | | (+ 5) + (– 2) = (+ 3) You might see this expressed more simply as: - 5 + (– 2) = 3
- or
- 5 – 2 = 3
| Example (– 8) + (+ 2) = ? The Problem | | (– 8) + (+ 2) = ? | Step 1:Subtract the absolute values of the addends | |– 8| – |+ 2| = 8 – 2
8 – 2 = 5 | | Step 2: Give the result the sign of the addend that has larger absolute value | The addend of the larger absolute value is 8, and the sign of this addend is –. So the sum is a negative value, – 6 | | | The Solution | | (– 8) + (+ 2) = (– 6) Or you might see it expressed more simply as: – 8 + 2 = – 6 | Exercise Add the following signed integers.
Click the ? symbol to see the correct answer. | 1. (+6) + (-5) = ? | 2. (+12) + (-16) = ? | | 3. (+8) + (-3) = ? | 4. (-10) + (+7) = ? |
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