Adding Integers worksheet with problems involving positive and negative numbers, designed for math education.

Problem Description:

The task involves calculating the sums of pairs of integers. The worksheet provides a series of addition problems involving positive and negative integers. We need to solve each problem step by step.

Solution Approach:

1. Understand Integer Addition Rules:
- Adding two positive integers: Add their absolute values, and the result is positive.
- Adding two negative integers: Add their absolute values, and the result is negative.
- Adding a positive and a negative integer: Subtract the smaller absolute value from the larger one, and the sign of the result is the same as the number with the larger absolute value.

2. Solve Each Problem:
We will calculate each sum systematically using the rules above.

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Step-by-Step Calculations:

#### First Row:
1. \( (+10) + (+8) = 10 + 8 = 18 \)
2. \( (-4) + (-4) = -4 - 4 = -8 \)
3. \( (-9) + (+6) = -9 + 6 = -3 \)

#### Second Row:
4. \( (-12) + (+10) = -12 + 10 = -2 \)
5. \( (+6) + (+10) = 6 + 10 = 16 \)
6. \( (-9) + (+9) = -9 + 9 = 0 \)

#### Third Row:
7. \( (+10) + (+9) = 10 + 9 = 19 \)
8. \( (-3) + (+6) = -3 + 6 = 3 \)
9. \( (+7) + (-6) = 7 - 6 = 1 \)

#### Fourth Row:
10. \( (-9) + (+11) = -9 + 11 = 2 \)
11. \( (-11) + (+12) = -11 + 12 = 1 \)
12. \( (-1) + (+8) = -1 + 8 = 7 \)

#### Fifth Row:
13. \( (+12) + (-8) = 12 - 8 = 4 \)
14. \( (+7) + (-3) = 7 - 3 = 4 \)
15. \( (-4) + (+12) = -4 + 12 = 8 \)

#### Sixth Row:
16. \( (+11) + (+10) = 11 + 10 = 21 \)
17. \( (-7) + (+1) = -7 + 1 = -6 \)
18. \( (+5) + (-1) = 5 - 1 = 4 \)

#### Seventh Row:
19. \( (-9) + (-10) = -9 - 10 = -19 \)
20. \( (-10) + (-1) = -10 - 1 = -11 \)
21. \( (+11) + (-3) = 11 - 3 = 8 \)

#### Eighth Row:
22. \( (+12) + (+12) = 12 + 12 = 24 \)
23. \( (-4) + (-9) = -4 - 9 = -13 \)
24. \( (+8) + (+12) = 8 + 12 = 20 \)

#### Ninth Row:
25. \( (-10) + (+12) = -10 + 12 = 2 \)
26. \( (-5) + (+4) = -5 + 4 = -1 \)
27. \( (+9) + (-12) = 9 - 12 = -3 \)

#### Tenth Row:
28. \( (+8) + (-9) = 8 - 9 = -1 \)
29. \( (-11) + (+5) = -11 + 5 = -6 \)
30. \( (-7) + (+10) = -7 + 10 = 3 \)

#### Eleventh Row:
31. \( (+12) + (+11) = 12 + 11 = 23 \)
32. \( (+2) + (+4) = 2 + 4 = 6 \)
33. \( (-8) + (-7) = -8 - 7 = -15 \)

#### Twelfth Row:
34. \( (+8) + (-8) = 8 - 8 = 0 \)
35. \( (-2) + (+1) = -2 + 1 = -1 \)
36. \( (-11) + (+8) = -11 + 8 = -3 \)

#### Thirteenth Row:
37. \( (+10) + (+10) = 10 + 10 = 20 \)
38. \( (+12) + (-5) = 12 - 5 = 7 \)
39. \( (+12) + (+1) = 12 + 1 = 13 \)

#### Fourteenth Row:
40. \( (+10) + (+3) = 10 + 3 = 13 \)
41. \( (-11) + (+2) = -11 + 2 = -9 \)
42. \( (+3) + (+5) = 3 + 5 = 8 \)

#### Fifteenth Row:
43. \( (-6) + (+5) = -6 + 5 = -1 \)
44. \( (-4) + (+5) = -4 + 5 = 1 \)
45. \( (-6) + (+7) = -6 + 7 = 1 \)

#### Sixteenth Row:
46. \( (+1) + (+2) = 1 + 2 = 3 \)
47. \( (+6) + (+6) = 6 + 6 = 12 \)
48. \( (+8) + (+11) = 8 + 11 = 19 \)

#### Seventeenth Row:
49. \( (-3) + (+11) = -3 + 11 = 8 \)
50. \( (-2) + (+7) = -2 + 7 = 5 \)
51. \( (-2) + (+8) = -2 + 8 = 6 \)

#### Eighteenth Row:
52. \( (-11) + (-6) = -11 - 6 = -17 \)
53. \( (+7) + (+11) = 7 + 11 = 18 \)
54. \( (+11) + (+7) = 11 + 7 = 18 \)

#### Nineteenth Row:
55. \( (+3) + (+8) = 3 + 8 = 11 \)
56. \( (-5) + (+7) = -5 + 7 = 2 \)
57. \( (+11) + (+11) = 11 + 11 = 22 \)

#### Twentieth Row:
58. \( (+5) + (+8) = 5 + 8 = 13 \)
59. \( (-11) + (-9) = -11 - 9 = -20 \)
60. \( (-4) + (+11) = -4 + 11 = 7 \)

#### Twenty-first Row:
61. \( (-6) + (+4) = -6 + 4 = -2 \)
62. \( (-9) + (-3) = -9 - 3 = -12 \)
63. \( (+6) + (-12) = 6 - 12 = -6 \)

#### Twenty-second Row:
64. \( (+10) + (+11) = 10 + 11 = 21 \)
65. \( (+1) + (-10) = 1 - 10 = -9 \)
66. \( (-5) + (+10) = -5 + 10 = 5 \)

#### Twenty-third Row:
67. \( (-12) + (-9) = -12 - 9 = -21 \)
68. \( (+4) + (+1) = 4 + 1 = 5 \)
69. \( (-8) + (+6) = -8 + 6 = -2 \)

#### Twenty-fourth Row:
70. \( (-7) + (-12) = -7 - 12 = -19 \)
71. \( (-3) + (+4) = -3 + 4 = 1 \)
72. \( (-1) + (+11) = -1 + 11 = 10 \)

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Final Answer:

\[
\boxed{
\begin{array}{ccc}
18 & -8 & -3 \\
-2 & 16 & 0 \\
19 & 3 & 1 \\
2 & 1 & 7 \\
4 & 4 & 8 \\
21 & -6 & 4 \\
-19 & -11 & 8 \\
24 & -13 & 20 \\
2 & -1 & -3 \\
-1 & -6 & 3 \\
23 & 6 & -15 \\
0 & -1 & -3 \\
20 & 7 & 13 \\
13 & -9 & 8 \\
-1 & 1 & 1 \\
3 & 12 & 19 \\
8 & 5 & 6 \\
-17 & 18 & 18 \\
11 & 2 & 22 \\
13 & -20 & 7 \\
-2 & -12 & -6 \\
21 & -9 & 5 \\
-21 & 5 & -2 \\
-19 & 1 & 10 \\
\end{array}
}
\]