Integer Addition – Positive and Negative Numbers
Integers include all positive whole numbers, negative whole numbers, and zero. Adding them requires understanding how positive and negative values interact.
Positive + Positive
This is ordinary addition. The result is always positive.
(+5) + (+3) = +8 or simply 5 + 3 = 8
Negative + Negative
Adding two negatives makes the result more negative. Think of it as going further into debt — you owe more.
(−4) + (−6) = −10
Rule: Add the absolute values, keep the negative sign.
Positive + Negative (or Negative + Positive)
The numbers partially cancel each other. The result takes the sign of the number with the larger absolute value.
(+7) + (−3) = +4 (7 is larger, so the result is positive; 7−3=4)
(−8) + (+5) = −3 (8 is larger in absolute terms, so the result is negative; 8−5=3)
Summary of Rules
| Signs | Method | Example | Result |
|---|---|---|---|
| + and + | Add, keep + | (+6)+(+4) | +10 |
| − and − | Add absolute values, keep − | (−6)+(−4) | −10 |
| + and − | Subtract absolute values, take sign of larger | (+8)+(−3) | +5 |
| − and + | Subtract absolute values, take sign of larger | (−8)+(+3) | −5 |
Using the Number Line
On a number line: adding a positive moves right; adding a negative moves left.
Start at −2, add +5: move right 5 steps → land on +3
Start at +4, add −7: move left 7 steps → land on −3
Key Takeaways
- Same signs: add the values, keep that sign.
- Different signs: subtract the smaller from the larger, keep the sign of the larger.
- Adding a negative is the same as subtracting a positive.
- The number line provides a visual check for integer addition.
Practice Questions
- Calculate (−3) + (−7).
- Calculate (+9) + (−4).
- Calculate (−5) + (+12).
- Calculate (−6) + (−6) + (+8).
- A diver is at −15 m. She rises 9 m. What is her new depth?