Worksheet for practicing addition and subtraction of integers with 22 problems.

Problem: Solving Integer Addition and Subtraction

The task involves solving a series of integer addition and subtraction problems. We will solve each problem step by step, explaining the process for clarity.

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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 number is the same as adding its positive counterpart.
- Subtracting a positive number is the same as adding its negative counterpart.

3. Order of Operations:
- Perform operations from left to right unless parentheses dictate otherwise.

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Solutions:

#### Problem 1: \( 8 + (-23) - (-5) \)
- Simplify step by step:
\[
8 + (-23) - (-5) = 8 - 23 + 5
\]
- First, \( 8 - 23 = -15 \)
- Then, \( -15 + 5 = -10 \)
- Answer: \(-10\)

#### Problem 2: \( (-43) + 13 - (-9) \)
- Simplify step by step:
\[
(-43) + 13 - (-9) = -43 + 13 + 9
\]
- First, \( -43 + 13 = -30 \)
- Then, \( -30 + 9 = -21 \)
- Answer: \(-21\)

#### Problem 3: \( (-47) + (-12) \)
- Add two negative numbers:
\[
(-47) + (-12) = -(47 + 12) = -59
\]
- Answer: \(-59\)

#### Problem 4: \( (-15) + (-13) + (-25) \)
- Add three negative numbers:
\[
(-15) + (-13) + (-25) = -(15 + 13 + 25) = -53
\]
- Answer: \(-53\)

#### Problem 5: \( (-35) + (-24) \)
- Add two negative numbers:
\[
(-35) + (-24) = -(35 + 24) = -59
\]
- Answer: \(-59\)

#### Problem 6: \( 24 + (-10) - (-27) \)
- Simplify step by step:
\[
24 + (-10) - (-27) = 24 - 10 + 27
\]
- First, \( 24 - 10 = 14 \)
- Then, \( 14 + 27 = 41 \)
- Answer: \(41\)

#### Problem 7: \( (-7) + (-15) - (-7) \)
- Simplify step by step:
\[
(-7) + (-15) - (-7) = -7 - 15 + 7
\]
- First, \( -7 - 15 = -22 \)
- Then, \( -22 + 7 = -15 \)
- Answer: \(-15\)

#### Problem 8: \( 21 + (-16) + (-22) \)
- Simplify step by step:
\[
21 + (-16) + (-22) = 21 - 16 - 22
\]
- First, \( 21 - 16 = 5 \)
- Then, \( 5 - 22 = -17 \)
- Answer: \(-17\)

#### Problem 9: \( (-2) + 7 + (-30) \)
- Simplify step by step:
\[
(-2) + 7 + (-30) = -2 + 7 - 30
\]
- First, \( -2 + 7 = 5 \)
- Then, \( 5 - 30 = -25 \)
- Answer: \(-25\)

#### Problem 10: \( 33 + (-11) \)
- Simplify:
\[
33 + (-11) = 33 - 11 = 22
\]
- Answer: \(22\)

#### Problem 11: \( 7 + (-27) + (-26) \)
- Simplify step by step:
\[
7 + (-27) + (-26) = 7 - 27 - 26
\]
- First, \( 7 - 27 = -20 \)
- Then, \( -20 - 26 = -46 \)
- Answer: \(-46\)

#### Problem 12: \( (-46) + (-23) \)
- Add two negative numbers:
\[
(-46) + (-23) = -(46 + 23) = -69
\]
- Answer: \(-69\)

#### Problem 13: \( 39 + 18 + (-14) \)
- Simplify step by step:
\[
39 + 18 + (-14) = 39 + 18 - 14
\]
- First, \( 39 + 18 = 57 \)
- Then, \( 57 - 14 = 43 \)
- Answer: \(43\)

#### Problem 14: \( 10 + 6 + (-18) \)
- Simplify step by step:
\[
10 + 6 + (-18) = 10 + 6 - 18
\]
- First, \( 10 + 6 = 16 \)
- Then, \( 16 - 18 = -2 \)
- Answer: \(-2\)

#### Problem 15: \( 49 + 19 + (-14) \)
- Simplify step by step:
\[
49 + 19 + (-14) = 49 + 19 - 14
\]
- First, \( 49 + 19 = 68 \)
- Then, \( 68 - 14 = 54 \)
- Answer: \(54\)

#### Problem 16: \( (-1) + (-15) \)
- Add two negative numbers:
\[
(-1) + (-15) = -(1 + 15) = -16
\]
- Answer: \(-16\)

#### Problem 17: \( 20 + 24 + (-28) \)
- Simplify step by step:
\[
20 + 24 + (-28) = 20 + 24 - 28
\]
- First, \( 20 + 24 = 44 \)
- Then, \( 44 - 28 = 16 \)
- Answer: \(16\)

#### Problem 18: \( (-33) + 24 - (-14) \)
- Simplify step by step:
\[
(-33) + 24 - (-14) = -33 + 24 + 14
\]
- First, \( -33 + 24 = -9 \)
- Then, \( -9 + 14 = 5 \)
- Answer: \(5\)

#### Problem 19: \( (-49) + (-6) + (-16) \)
- Add three negative numbers:
\[
(-49) + (-6) + (-16) = -(49 + 6 + 16) = -71
\]
- Answer: \(-71\)

#### Problem 20: \( 39 + (-8) - (-12) \)
- Simplify step by step:
\[
39 + (-8) - (-12) = 39 - 8 + 12
\]
- First, \( 39 - 8 = 31 \)
- Then, \( 31 + 12 = 43 \)
- Answer: \(43\)

#### Problem 21: \( 28 + (-27) - (-27) \)
- Simplify step by step:
\[
28 + (-27) - (-27) = 28 - 27 + 27
\]
- First, \( 28 - 27 = 1 \)
- Then, \( 1 + 27 = 28 \)
- Answer: \(28\)

#### Problem 22: \( 18 + (-8) + (-13) \)
- Simplify step by step:
\[
18 + (-8) + (-13) = 18 - 8 - 13
\]
- First, \( 18 - 8 = 10 \)
- Then, \( 10 - 13 = -3 \)
- Answer: \(-3\)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & -10 \\
2. & -21 \\
3. & -59 \\
4. & -53 \\
5. & -59 \\
6. & 41 \\
7. & -15 \\
8. & -17 \\
9. & -25 \\
10. & 22 \\
11. & -46 \\
12. & -69 \\
13. & 43 \\
14. & -2 \\
15. & 54 \\
16. & -16 \\
17. & 16 \\
18. & 5 \\
19. & -71 \\
20. & 43 \\
21. & 28 \\
22. & -3 \\
\end{array}
}
\]