Integer Addition worksheet (A) with problems resulting in positive, negative, or zero sums, from Math-Drills.com.

Let's solve the Integer Addition (A) worksheet step by step and explain the process.

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🔢 Understanding Integer Addition

When adding a positive number and a negative number:
- You are essentially subtracting the absolute value of the negative number from the positive one.
- The sign of the result depends on which number has the greater absolute value.

#### Rules:
1. If the positive number is larger → positive result
2. If the negative number is larger (in absolute value) → negative result
3. If they are equal → zero

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We'll go through each section.

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## ✔ Part 1: These questions result in positive sums

These are cases where the positive number is larger than the absolute value of the negative number.

| Problem | Solution |
|--------|----------|
| 7 + (–6) = | 7 – 6 = 1 |
| 5 + (–1) = | 5 – 1 = 4 |
| 3 + (–2) = | 3 – 2 = 1 |
| 9 + (–6) = | 9 – 6 = 3 |
| 4 + (–1) = | 4 – 1 = 3 |
| 8 + (–7) = | 8 – 7 = 1 |
| 5 + (–4) = | 5 – 4 = 1 |
| 9 + (–4) = | 9 – 4 = 5 |
| 8 + (–6) = | 8 – 6 = 2 |
| 8 + (–3) = | 8 – 3 = 5 |
| 5 + (–2) = | 5 – 2 = 3 |
| 6 + (–3) = | 6 – 3 = 3 |
| 3 + (–1) = | 3 – 1 = 2 |
| 8 + (–5) = | 8 – 5 = 3 |
| 7 + (–4) = | 7 – 4 = 3 |
| 6 + (–5) = | 6 – 5 = 1 |
| 9 + (–8) = | 9 – 8 = 1 |
| 8 + (–2) = | 8 – 2 = 6 |
| 8 + (–1) = | 8 – 1 = 7 |
| 8 + (–4) = | 8 – 4 = 4 |

✔ All results are positive, as expected.

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## ✘ Part 2: These questions result in negative sums

Here, the absolute value of the negative number is greater than the positive number.

| Problem | Solution |
|--------|----------|
| 2 + (–8) = | 2 – 8 = –6 |
| 1 + (–3) = | 1 – 3 = –2 |
| 8 + (–9) = | 8 – 9 = –1 |
| 5 + (–9) = | 5 – 9 = –4 |
| 1 + (–8) = | 1 – 8 = –7 |
| 3 + (–7) = | 3 – 7 = –4 |
| 2 + (–3) = | 2 – 3 = –1 |
| 3 + (–4) = | 3 – 4 = –1 |
| 1 + (–7) = | 1 – 7 = –6 |
| 5 + (–7) = | 5 – 7 = –2 |
| 3 + (–8) = | 3 – 8 = –5 |
| 1 + (–5) = | 1 – 5 = –4 |
| 1 + (–4) = | 1 – 4 = –3 |
| 2 + (–4) = | 2 – 4 = –2 |
| 3 + (–5) = | 3 – 5 = –2 |
| 4 + (–8) = | 4 – 8 = –4 |
| 4 + (–7) = | 4 – 7 = –3 |
| 4 + (–5) = | 4 – 5 = –1 |
| 5 + (–6) = | 5 – 6 = –1 |
| 2 + (–9) = | 2 – 9 = –7 |

✔ All results are negative, as expected.

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## ⚠️ Part 3: These questions could have negative, positive, or zero sums

Now we consider all possibilities.

| Problem | Solution |
|--------|----------|
| 5 + (–2) = | 5 – 2 = 3 |
| 8 + (–7) = | 8 – 7 = 1 |
| 7 + (–2) = | 7 – 2 = 5 |
| 2 + (–7) = | 2 – 7 = –5 |
| 3 + (–7) = | 3 – 7 = –4 |
| 6 + (–7) = | 6 – 7 = –1 |
| 7 + (–9) = | 7 – 9 = –2 |
| 6 + (–8) = | 6 – 8 = –2 |
| 4 + (–4) = | 4 – 4 = 0 |
| 7 + (–5) = | 7 – 5 = 2 |
| 5 + (–7) = | 5 – 7 = –2 |
| 7 + (–3) = | 7 – 3 = 4 |
| 4 + (–9) = | 4 – 9 = –5 |
| 9 + (–4) = | 9 – 4 = 5 |
| 3 + (–2) = | 3 – 2 = 1 |
| 9 + (–2) = | 9 – 2 = 7 |
| 1 + (–5) = | 1 – 5 = –4 |
| 8 + (–1) = | 8 – 1 = 7 |
| 3 + (–6) = | 3 – 6 = –3 |
| 9 + (–1) = | 9 – 1 = 8 |

✔ Mixed results: positive, negative, and zero — as expected.

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✔ Final Answer Summary

Here’s the complete solution:

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#### Positive Sums:
```
7 + (–6) = 1 5 + (–1) = 4 3 + (–2) = 1 9 + (–6) = 3
4 + (–1) = 3 8 + (–7) = 1 5 + (–4) = 1 9 + (–4) = 5
8 + (–6) = 2 8 + (–3) = 5 5 + (–2) = 3 6 + (–3) = 3
3 + (–1) = 2 8 + (–5) = 3 7 + (–4) = 3 6 + (–5) = 1
9 + (–8) = 1 8 + (–2) = 6 8 + (–1) = 7 8 + (–4) = 4
```

#### Negative Sums:
```
2 + (–8) = –6 1 + (–3) = –2 8 + (–9) = –1 5 + (–9) = –4
1 + (–8) = –7 3 + (–7) = –4 2 + (–3) = –1 3 + (–4) = –1
1 + (–7) = –6 5 + (–7) = –2 3 + (–8) = –5 1 + (–5) = –4
1 + (–4) = –3 2 + (–4) = –2 3 + (–5) = –2 4 + (–8) = –4
4 + (–7) = –3 4 + (–5) = –1 5 + (–6) = –1 2 + (–9) = –7
```

#### Mixed Sums:
```
5 + (–2) = 3 8 + (–7) = 1 7 + (–2) = 5 2 + (–7) = –5
3 + (–7) = –4 6 + (–7) = –1 7 + (–9) = –2 6 + (–8) = –2
4 + (–4) = 0 7 + (–5) = 2 5 + (–7) = –2 7 + (–3) = 4
4 + (–9) = –5 9 + (–4) = 5 3 + (–2) = 1 9 + (–2) = 7
1 + (–5) = –4 8 + (–1) = 7 3 + (–6) = –3 9 + (–1) = 8
```

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📝 Explanation Recap:

- Adding a negative number is like subtracting its absolute value.
- Compare the two numbers: if the positive is bigger → positive result; if negative is bigger → negative result; if equal → zero.
- Always use absolute values to determine magnitude.

This method helps avoid confusion when dealing with integers.

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