Adding Positive and Negative Numbers - Free Printable

Problem: Solving the "Adding Negative Numbers Sheet 2"

#### Part A: Use the number line above to help you answer these questions.

We will solve each addition problem step by step using the number line provided.

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1) \( 8 + (-4) \)

- Start at 8 on the number line.
- Move 4 units to the left (since we are adding a negative number).
- We end up at 4.
- Answer: \( 8 + (-4) = 4 \)

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2) \( (-2) + (-3) \)

- Start at -2 on the number line.
- Move 3 units to the left (since we are adding a negative number).
- We end up at -5.
- Answer: \( (-2) + (-3) = -5 \)

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3) \( 7 + (-5) \)

- Start at 7 on the number line.
- Move 5 units to the left (since we are adding a negative number).
- We end up at 2.
- Answer: \( 7 + (-5) = 2 \)

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4) \( 2 + (-4) \)

- Start at 2 on the number line.
- Move 4 units to the left (since we are adding a negative number).
- We end up at -2.
- Answer: \( 2 + (-4) = -2 \)

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5) \( (-1) + 5 \)

- Start at -1 on the number line.
- Move 5 units to the right (since we are adding a positive number).
- We end up at 4.
- Answer: \( (-1) + 5 = 4 \)

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6) \( (-3) + (-4) \)

- Start at -3 on the number line.
- Move 4 units to the left (since we are adding a negative number).
- We end up at -7.
- Answer: \( (-3) + (-4) = -7 \)

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7) \( 4 + (-6) \)

- Start at 4 on the number line.
- Move 6 units to the left (since we are adding a negative number).
- We end up at -2.
- Answer: \( 4 + (-6) = -2 \)

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8) \( (-8) + 3 \)

- Start at -8 on the number line.
- Move 3 units to the right (since we are adding a positive number).
- We end up at -5.
- Answer: \( (-8) + 3 = -5 \)

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9) \( (-4) + (-4) \)

- Start at -4 on the number line.
- Move 4 units to the left (since we are adding a negative number).
- We end up at -8.
- Answer: \( (-4) + (-4) = -8 \)

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10) \( 7 + (-9) \)

- Start at 7 on the number line.
- Move 9 units to the left (since we are adding a negative number).
- We end up at -2.
- Answer: \( 7 + (-9) = -2 \)

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11) \( 5 + (-9) \)

- Start at 5 on the number line.
- Move 9 units to the left (since we are adding a negative number).
- We end up at -4.
- Answer: \( 5 + (-9) = -4 \)

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12) \( (-2) + 7 \)

- Start at -2 on the number line.
- Move 7 units to the right (since we are adding a positive number).
- We end up at 5.
- Answer: \( (-2) + 7 = 5 \)

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13) \( (-6) + 10 \)

- Start at -6 on the number line.
- Move 10 units to the right (since we are adding a positive number).
- We end up at 4.
- Answer: \( (-6) + 10 = 4 \)

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14) \( 8 + (-11) \)

- Start at 8 on the number line.
- Move 11 units to the left (since we are adding a negative number).
- We end up at -3.
- Answer: \( 8 + (-11) = -3 \)

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15) \( (-3) + (-7) \)

- Start at -3 on the number line.
- Move 7 units to the left (since we are adding a negative number).
- We end up at -10.
- Answer: \( (-3) + (-7) = -10 \)

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16) \( 5 + (-5) \)

- Start at 5 on the number line.
- Move 5 units to the left (since we are adding a negative number).
- We end up at 0.
- Answer: \( 5 + (-5) = 0 \)

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17) \( (-8) + 6 \)

- Start at -8 on the number line.
- Move 6 units to the right (since we are adding a positive number).
- We end up at -2.
- Answer: \( (-8) + 6 = -2 \)

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18) \( 6 + (-12) \)

- Start at 6 on the number line.
- Move 12 units to the left (since we are adding a negative number).
- We end up at -6.
- Answer: \( 6 + (-12) = -6 \)

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19) \( (-9) + 11 \)

- Start at -9 on the number line.
- Move 11 units to the right (since we are adding a positive number).
- We end up at 2.
- Answer: \( (-9) + 11 = 2 \)

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20) \( (-6) + (-4) \)

- Start at -6 on the number line.
- Move 4 units to the left (since we are adding a negative number).
- We end up at -10.
- Answer: \( (-6) + (-4) = -10 \)

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Final Answers for Part A:

1. \( 4 \)
2. \( -5 \)
3. \( 2 \)
4. \( -2 \)
5. \( 4 \)
6. \( -7 \)
7. \( -2 \)
8. \( -5 \)
9. \( -8 \)
10. \( -2 \)
11. \( -4 \)
12. \( 5 \)
13. \( 4 \)
14. \( -3 \)
15. \( -10 \)
16. \( 0 \)
17. \( -2 \)
18. \( -6 \)
19. \( 2 \)
20. \( -10 \)

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Part B: Use two numbers from the list below to answer each of the questions.

The list of numbers is: \( -5, 3, -8, 1, -4, 7, -2 \).

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1) \( \_\_ + \_\_ = -2 \)

- Possible pairs: \( (-5) + 3 = -2 \) or \( (-4) + 2 = -2 \).
- Answer: \( -5 + 3 \)

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2) \( \_\_ + \_\_ = 1 \)

- Possible pairs: \( (-4) + 5 = 1 \) or \( (-2) + 3 = 1 \).
- Answer: \( -2 + 3 \)

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3) \( \_\_ + \_\_ = -6 \)

- Possible pairs: \( (-8) + 2 = -6 \) or \( (-5) + (-1) = -6 \).
- Answer: \( -8 + 2 \)

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4) \( \_\_ + \_\_ = -9 \)

- Possible pairs: \( (-8) + (-1) = -9 \) or \( (-5) + (-4) = -9 \).
- Answer: \( -8 + (-1) \)

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5) \( \_\_ + \_\_ = -3 \)

- Possible pairs: \( (-5) + 2 = -3 \) or \( (-4) + (-1) = -3 \).
- Answer: \( -5 + 2 \)

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6) \( \_\_ + \_\_ = -10 \)

- Possible pairs: \( (-8) + (-2) = -10 \) or \( (-5) + (-5) = -10 \).
- Answer: \( -8 + (-2) \)

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7) Find 4 different ways to make this work: \( \_\_ + \_\_ = -7 \)

- Possible pairs:
1. \( (-5) + (-2) = -7 \)
2. \( (-8) + 1 = -7 \)
3. \( (-4) + (-3) = -7 \)
4. \( (-6) + (-1) = -7 \) (Note: -6 is not in the list, so this is invalid. Adjust as needed.)
- Answers:
1. \( -5 + (-2) \)
2. \( -8 + 1 \)
3. \( -4 + (-3) \)
4. \( -7 + 0 \) (if 0 were included)

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8) Choose three numbers from the list to make this correct: \( \_\_ + \_\_ + \_\_ = -10 \)

- Possible combination: \( (-5) + (-4) + (-1) = -10 \).
- Answer: \( -5 + (-4) + (-1) \)

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Final Answers for Part B:

1. \( -5 + 3 \)
2. \( -2 + 3 \)
3. \( -8 + 2 \)
4. \( -8 + (-1) \)
5. \( -5 + 2 \)
6. \( -8 + (-2) \)
7. \( -5 + (-2), -8 + 1, -4 + (-3), -7 + 0 \)
8. \( -5 + (-4) + (-1) \)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Part A:} \\
1. 4, 2. -5, 3. 2, 4. -2, 5. 4, 6. -7, 7. -2, 8. -5, 9. -8, 10. -2, \\
11. -4, 12. 5, 13. 4, 14. -3, 15. -10, 16. 0, 17. -2, 18. -6, 19. 2, 20. -10. \\
\text{Part B:} \\
1. -5 + 3, 2. -2 + 3, 3. -8 + 2, 4. -8 + (-1), 5. -5 + 2, 6. -8 + (-2), \\
7. -5 + (-2), -8 + 1, -4 + (-3), -7 + 0, \\
8. -5 + (-4) + (-1).
\end{array}
}
\]