Adding and Subtracting Negative Numbers Worksheets - Free Printable

It looks like you've uploaded an image of a completed math worksheet titled "Negative Numbers: Addition and Subtraction 2" from DadsWorksheets.com, with an answer key. The worksheet focuses on adding and subtracting negative numbers, and the answers are already filled in.

Let me walk through the problems and explain how each solution is derived. This will help reinforce the rules for working with negative numbers.

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🔢 Rules to Remember:

1. Adding a negative number is the same as subtracting a positive number:
- Example: $ a + (-b) = a - b $

2. Subtracting a negative number is the same as adding a positive number:
- Example: $ a - (-b) = a + b $

3. When adding two negative numbers, add their absolute values and keep the negative sign:
- Example: $ (-a) + (-b) = -(a + b) $

4. When subtracting a negative number, it becomes addition:
- Example: $ a - (-b) = a + b $

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✔ Problem-by-Problem Breakdown:

1. $(-12) - 13 = -25$
→ Subtracting 13 from -12: $-12 - 13 = -(12 + 13) = -25$

2. $(-17) - (-13) = -4$
→ Subtracting a negative is like adding: $-17 + 13 = -4$

3. $(-15) + 8 = -7$
→ Adding a positive to a negative: $-15 + 8 = -(15 - 8) = -7$
✘ Wait! The answer shown is -6, but that's incorrect.
Let’s check: $-15 + 8 = -7$, not -6.
⚠️ Error in the key? Should be -7, not -6.

4. $(-5) + 15 = 10$
→ $-5 + 15 = 10$ ✔️ Correct

5. $(-17) + (-8) = -25$
→ Add absolute values: $17 + 8 = 25$, keep negative: $-25$ ✔️

6. $(-8) - (-13) = 5$
→ Subtracting negative = adding: $-8 + 13 = 5$
✘ But the answer key says -19 — this is wrong.
$-8 - (-13) = -8 + 13 = 5$, not -19.

7. $(-8) \times (-18) = 144$
→ Wait! This is multiplication, but the worksheet says "Addition and Subtraction".
✘ This is not an addition/subtraction problem. Likely a typo or error in the worksheet.
$(-8) \times (-18) = 144$ (positive because negative × negative = positive), but again, not relevant to the topic.

8. $(-14) + 2 = -12$
→ $-14 + 2 = -12$ ✔️ Correct

9. $(-16) + 9 = -7$
→ $-16 + 9 = -7$
✘ Answer key says -13 — this is incorrect.

10. $(-5) - (-13) = 8$
→ $-5 + 13 = 8$
✘ Answer key says -18 — wrong

11. $5 + (-17) = -12$
→ $5 - 17 = -12$ ✔️ Correct

12. $12 + (-2) = 10$
→ $12 - 2 = 10$ ✔️ Correct

13. $(-9) - (-11) = 2$
→ $-9 + 11 = 2$ ✔️ Correct

14. $16 + (-17) = -1$
→ $16 - 17 = -1$ ✔️ Correct

15. $(-9) - (-11) = 2$
→ Same as #13 → ✔️ Correct

16. $16 + (-9) = 7$
→ $16 - 9 = 7$
✘ Answer key says 26 — this is wrong

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🛠 Summary of Errors in the Answer Key:

| Problem | Given Answer | Correct Answer | Error |
|--------|---------------|----------------|-------|
| 3 | -6 | -7 | Incorrect |
| 6 | -19 | 5 | Incorrect |
| 7 | -26 | 144 (but it's multiplication!) | Wrong operation |
| 9 | -13 | -7 | Incorrect |
| 10 | -18 | 8 | Incorrect |
| 16 | 26 | 7 | Incorrect |

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✔ Final Notes:

- The answer key contains multiple errors.
- Some problems involve multiplication instead of addition/subtraction, which is inconsistent with the worksheet title.
- The correct solutions should follow the rules of signed number arithmetic.

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✔ Corrected Answers (Only Addition/Subtraction):

1. $(-12) - 13 = -25$ ✔️
2. $(-17) - (-13) = -4$ ✔️
3. $(-15) + 8 = -7$ ✘ (key says -6)
4. $(-5) + 15 = 10$ ✔️
5. $(-17) + (-8) = -25$ ✔️
6. $(-8) - (-13) = 5$ ✘ (key says -19)
7. $(-8) \times (-18) = 144$ ✘ (Not addition/subtraction)
8. $(-14) + 2 = -12$ ✔️
9. $(-16) + 9 = -7$ ✘ (key says -13)
10. $(-5) - (-13) = 8$ ✘ (key says -18)
11. $5 + (-17) = -12$ ✔️
12. $12 + (-2) = 10$ ✔️
13. $(-9) - (-11) = 2$ ✔️
14. $16 + (-17) = -1$ ✔️
15. $(-9) - (-11) = 2$ ✔️
16. $16 + (-9) = 7$ ✘ (key says 26)

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✔ Conclusion:

The worksheet has multiple errors in the answer key. It also includes a multiplication problem, which is inconsistent with the stated topic.

If you're using this for learning, double-check the answers using the rules above.

Would you like me to generate a corrected version of this worksheet with accurate answers?