Integer Addition Rules worksheet with examples and exercises for learning how to add positive and negative integers.

You're working on Integer Addition Rules, and the worksheet gives you clear rules to follow:

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## ✔ Integer Addition Rules Recap:

1. Same Sign? → Add the absolute values, keep the same sign.
- Example: `2 + 6 = 8` (both positive → sum is positive)
- Example: `-3 + (-5) = -8` (both negative → sum is negative)

2. Different Signs? → Subtract the smaller absolute value from the larger one. The answer takes the sign of the number with the larger absolute value.
- Example: `-9 + 2 = -7` (|−9| > |2| → answer is negative)
- Example: `1 + (-7) = -6` (|−7| > |1| → answer is negative)

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## 📝 Let’s Solve the Problems Step-by-Step

We’ll go row by row.

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🔹 First Row (Determine the sign of the sum):

> Use integer addition rules to determine if the answer to each problem will be positive or negative. The first one has been done for you.

| Problem | Sign |
|----------------|------|
| `-6 + 8` | `+` ✔️ (8 > 6, positive wins) |
| `5 + 2` | `+` (same sign → positive) |
| `-7 + (-3)` | `-` (same sign → negative) |
| `1 + (-4)` | `-` (|−4| > |1| → negative) |
| `-8 + (-9)` | `-` (same sign → negative) |

✔ Answers: +, -, -, -

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🔹 Second Row:

| Problem | Sign |
|----------------|------|
| `10 + (-7)` | `+` (|10| > |−7| → positive) |
| `-20 + (-6)` | `-` (same sign → negative) |
| `-11 + 4` | `-` (|−11| > |4| → negative) |
| `-2 + (-18)` | `-` (same sign → negative) |
| `12 + (-5)` | `+` (|12| > |−5| → positive) |

✔ Answers: +, -, -, -, +

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🔹 Third Row:

| Problem | Sign |
|----------------|------|
| `-24 + (-2)` | `-` (same sign → negative) |
| `18 + (-15)` | `+` (|18| > |−15| → positive) |
| `-19 + 27` | `+` (|27| > |−19| → positive) |
| `15 + (-11)` | `+` (|15| > |−11| → positive) |
| `-16 + (-23)` | `-` (same sign → negative) |

✔ Answers: -, +, +, +, -

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## 🧮 Now, Solve the Problems — “Solve each problem. Use integer addition rules to help!”

Let’s compute each one using the rules.

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🔸 First Row:

1. `-4 + (-5)` → same sign → add → `-(4+5) = -9`
2. `6 + (-7)` → different signs → |7| > |6| → subtract → `7 - 6 = 1`, sign is negative → `-1`
3. `-2 + (-3)` → same sign → `-(2+3) = -5`
4. `-7 + 8` → different signs → |8| > |7| → `8 - 7 = 1`, sign positive → `+1`

✔ Answers: -9, -1, -5, 1

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🔸 Second Row:

5. `1 + (-8)` → |8| > |1| → `8 - 1 = 7`, negative → `-7`
6. `-9 + 1` → |9| > |1| → `9 - 1 = 8`, negative → `-8`
7. `-5 + (-3)` → same sign → `-(5+3) = -8`
8. `8 + (-12)` → |12| > |8| → `12 - 8 = 4`, negative → `-4`

✔ Answers: -7, -8, -8, -4

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🔸 Third Row:

9. `-10 + (-4)` → same sign → `-(10+4) = -14`
10. `-4 + 11` → |11| > |4| → `11 - 4 = 7`, positive → `+7`
11. `13 + (-2)` → |13| > |2| → `13 - 2 = 11`, positive → `+11`
12. `-14 + (-2)` → same sign → `-(14+2) = -16`

✔ Answers: -14, 7, 11, -16

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🔸 Fourth Row:

13. `20 + (-3)` → |20| > |3| → `20 - 3 = 17`, positive → `+17`
14. `-15 + 17` → |17| > |15| → `17 - 15 = 2`, positive → `+2`
15. `-18 + (-2)` → same sign → `-(18+2) = -20`
16. `-22 + (-23)` → same sign → `-(22+23) = -45`

✔ Answers: 17, 2, -20, -45

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## ✔ Final Answer Key:

Part 1: Determine the sign

Row 1: `+ , - , - , -`
Row 2: `+ , - , - , - , +`
Row 3: `- , + , + , + , -`

Part 2: Solve each problem

Row 1: -9, -1, -5, 1
Row 2: -7, -8, -8, -4
Row 3: -14, 7, 11, -16
Row 4: 17, 2, -20, -45

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## 💡 Tip for Success:
Always ask yourself:
- Are the signs the same? → Add, keep the sign.
- Are the signs different? → Subtract, take the sign of the bigger number (by absolute value).

This rule works every time!

Let me know if you’d like a printable version or flashcards for practice! 😊