Answer key for adding and subtracting integers worksheet.

The task involves solving a series of problems that involve adding and subtracting integers. Below, I will explain the solution for each problem step by step.

General Rules for Adding and Subtracting Integers:

1. Adding Integers:
- If both numbers are positive, add them normally.
- If both numbers are negative, add their absolute values and keep the negative sign.
- If one number is positive and the other is negative, subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.

2. Subtracting Integers:
- Subtracting a negative integer is the same as adding its positive counterpart.
- Subtracting a positive integer is the same as adding its negative counterpart.

---

Solutions to Each Problem:

#### Problems 1–10:
1. 7 + (-3) + 9
- First, add \( 7 + (-3) = 4 \).
- Then, add \( 4 + 9 = 13 \).
- Answer: \( 13 \)

2. 4 + (-7) + (-2)
- First, add \( 4 + (-7) = -3 \).
- Then, add \( -3 + (-2) = -5 \).
- Answer: \( -5 \)

3. -3 + 4 + 7
- First, add \( -3 + 4 = 1 \).
- Then, add \( 1 + 7 = 8 \).
- Answer: \( 8 \)

4. -6 + (-7) + (-8)
- Add all negative numbers: \( -6 + (-7) + (-8) = -21 \).
- Answer: \( -21 \)

5. 9 + (-4) + (-6)
- First, add \( 9 + (-4) = 5 \).
- Then, add \( 5 + (-6) = -1 \).
- Answer: \( -1 \)

6. 7 + 9 + (-4)
- First, add \( 7 + 9 = 16 \).
- Then, add \( 16 + (-4) = 12 \).
- Answer: \( 12 \)

7. -9 + (-3) + (-4)
- Add all negative numbers: \( -9 + (-3) + (-4) = -16 \).
- Answer: \( -16 \)

8. -7 + (-8) + 9
- First, add \( -7 + (-8) = -15 \).
- Then, add \( -15 + 9 = -6 \).
- Answer: \( -6 \)

9. -3 + (-7) + (-6)
- Add all negative numbers: \( -3 + (-7) + (-6) = -16 \).
- Answer: \( -16 \)

10. 7 + 9 + (-6)
- First, add \( 7 + 9 = 16 \).
- Then, add \( 16 + (-6) = 10 \).
- Answer: \( 10 \)

#### Problems 11–20:
11. -6 + (-9) + 4
- First, add \( -6 + (-9) = -15 \).
- Then, add \( -15 + 4 = -11 \).
- Answer: \( -11 \)

12. 8 + (-8) + 7
- First, add \( 8 + (-8) = 0 \).
- Then, add \( 0 + 7 = 7 \).
- Answer: \( 7 \)

13. -5 + (-3) + 9
- First, add \( -5 + (-3) = -8 \).
- Then, add \( -8 + 9 = 1 \).
- Answer: \( 1 \)

14. -4 + (-6) + 4
- First, add \( -4 + (-6) = -10 \).
- Then, add \( -10 + 4 = -6 \).
- Answer: \( -6 \)

15. 9 + 11 + (-13)
- First, add \( 9 + 11 = 20 \).
- Then, add \( 20 + (-13) = 7 \).
- Answer: \( 7 \)

16. 15 + (-17) + (-20)
- First, add \( 15 + (-17) = -2 \).
- Then, add \( -2 + (-20) = -22 \).
- Answer: \( -22 \)

17. 30 + (-27) + 4
- First, add \( 30 + (-27) = 3 \).
- Then, add \( 3 + 4 = 7 \).
- Answer: \( 7 \)

18. -29 + (-31) + (-32)
- Add all negative numbers: \( -29 + (-31) + (-32) = -92 \).
- Answer: \( -92 \)

19. 40 + (-51) + 16
- First, add \( 40 + (-51) = -11 \).
- Then, add \( -11 + 16 = 5 \).
- Answer: \( 5 \)

20. -46 + (-51) + 41
- First, add \( -46 + (-51) = -97 \).
- Then, add \( -97 + 41 = -56 \).
- Answer: \( -56 \)

#### Problems 21–22:
21. -9 + (-50) + (-3)
- Add all negative numbers: \( -9 + (-50) + (-3) = -62 \).
- Answer: \( -62 \)

22. 10 + (-10) + (-13)
- First, add \( 10 + (-10) = 0 \).
- Then, add \( 0 + (-13) = -13 \).
- Answer: \( -13 \)

23. 7 + 9 + (-13)
- First, add \( 7 + 9 = 16 \).
- Then, add \( 16 + (-13) = 3 \).
- Answer: \( 3 \)

24. 10 + 18 + (-4)
- First, add \( 10 + 18 = 28 \).
- Then, add \( 28 + (-4) = 24 \).
- Answer: \( 24 \)

---

Final Answer:

\[
\boxed{13, -5, 8, -21, -1, 12, -16, -6, -16, 10, -11, 7, 1, -6, 7, -22, 7, -92, 5, -56, -62, -13, 3, 24}
\]