Practice adding and subtracting positive and negative integers with this 40-problem worksheet designed for classroom or homework use.

Problem Description:

The task involves solving a series of arithmetic problems involving addition and subtraction of integers. The problems are presented in a table format with 40 questions divided into two columns.

Solution Approach:

To solve these problems, we need to apply the basic rules of integer arithmetic:
1. Addition of Integers:
- Adding two positive integers results in a positive sum.
- Adding two negative integers results in a negative sum.
- Adding a positive and a negative integer involves subtracting their absolute values and keeping the sign of the larger absolute value.

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

We will solve each problem step by step.

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Detailed Solutions:

#### Column 1: Problems 1–20

1. -7 + (-4) =
- Adding two negative integers: \(-7 + (-4) = -(7 + 4) = -11\)
- Answer: \(-11\)

2. 6 + (-3) =
- Adding a positive and a negative integer: \(6 + (-3) = 6 - 3 = 3\)
- Answer: \(3\)

3. -8 + (-3) =
- Adding two negative integers: \(-8 + (-3) = -(8 + 3) = -11\)
- Answer: \(-11\)

4. 2 + (-9) =
- Adding a positive and a negative integer: \(2 + (-9) = 2 - 9 = -7\)
- Answer: \(-7\)

5. -7 + (-5) =
- Adding two negative integers: \(-7 + (-5) = -(7 + 5) = -12\)
- Answer: \(-12\)

6. -3 − 9 =
- Subtracting a positive integer: \(-3 - 9 = -3 + (-9) = -(3 + 9) = -12\)
- Answer: \(-12\)

7. -5 − (-3) =
- Subtracting a negative integer: \(-5 - (-3) = -5 + 3 = -2\)
- Answer: \(-2\)

8. -4 + 9 =
- Adding a positive and a negative integer: \(-4 + 9 = 9 - 4 = 5\)
- Answer: \(5\)

9. -3 + (-3) =
- Adding two negative integers: \(-3 + (-3) = -(3 + 3) = -6\)
- Answer: \(-6\)

10. 2 + (-3) =
- Adding a positive and a negative integer: \(2 + (-3) = 2 - 3 = -1\)
- Answer: \(-1\)

11. 2 − 6 =
- Subtracting a positive integer: \(2 - 6 = -(6 - 2) = -4\)
- Answer: \(-4\)

12. -4 − 2 =
- Subtracting a positive integer: \(-4 - 2 = -4 + (-2) = -(4 + 2) = -6\)
- Answer: \(-6\)

13. 6 − (-6) =
- Subtracting a negative integer: \(6 - (-6) = 6 + 6 = 12\)
- Answer: \(12\)

14. -7 + (-6) =
- Adding two negative integers: \(-7 + (-6) = -(7 + 6) = -13\)
- Answer: \(-13\)

15. -2 − 2 =
- Subtracting a positive integer: \(-2 - 2 = -2 + (-2) = -(2 + 2) = -4\)
- Answer: \(-4\)

16. 4 − (-5) =
- Subtracting a negative integer: \(4 - (-5) = 4 + 5 = 9\)
- Answer: \(9\)

17. -5 − 5 =
- Subtracting a positive integer: \(-5 - 5 = -5 + (-5) = -(5 + 5) = -10\)
- Answer: \(-10\)

18. -8 − 2 =
- Subtracting a positive integer: \(-8 - 2 = -8 + (-2) = -(8 + 2) = -10\)
- Answer: \(-10\)

19. -9 − (-8) =
- Subtracting a negative integer: \(-9 - (-8) = -9 + 8 = -1\)
- Answer: \(-1\)

20. 5 + 10 =
- Adding two positive integers: \(5 + 10 = 15\)
- Answer: \(15\)

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#### Column 2: Problems 21–40

21. 10 − (-2) =
- Subtracting a negative integer: \(10 - (-2) = 10 + 2 = 12\)
- Answer: \(12\)

22. 4 + (-10) =
- Adding a positive and a negative integer: \(4 + (-10) = 4 - 10 = -6\)
- Answer: \(-6\)

23. -8 + 5 =
- Adding a positive and a negative integer: \(-8 + 5 = -(8 - 5) = -3\)
- Answer: \(-3\)

24. 7 + 7 =
- Adding two positive integers: \(7 + 7 = 14\)
- Answer: \(14\)

25. 9 + (-7) =
- Adding a positive and a negative integer: \(9 + (-7) = 9 - 7 = 2\)
- Answer: \(2\)

26. 10 − (-9) =
- Subtracting a negative integer: \(10 - (-9) = 10 + 9 = 19\)
- Answer: \(19\)

27. 4 − 8 =
- Subtracting a positive integer: \(4 - 8 = -(8 - 4) = -4\)
- Answer: \(-4\)

28. -10 + (-8) =
- Adding two negative integers: \(-10 + (-8) = -(10 + 8) = -18\)
- Answer: \(-18\)

29. 10 − 6 =
- Subtracting a positive integer: \(10 - 6 = 4\)
- Answer: \(4\)

30. 10 − (-3) =
- Subtracting a negative integer: \(10 - (-3) = 10 + 3 = 13\)
- Answer: \(13\)

31. 10 + (-10) =
- Adding a positive and a negative integer: \(10 + (-10) = 0\)
- Answer: \(0\)

32. -6 + 9 =
- Adding a positive and a negative integer: \(-6 + 9 = 9 - 6 = 3\)
- Answer: \(3\)

33. -9 − (-5) =
- Subtracting a negative integer: \(-9 - (-5) = -9 + 5 = -4\)
- Answer: \(-4\)

34. 6 + 8 =
- Adding two positive integers: \(6 + 8 = 14\)
- Answer: \(14\)

35. 4 − (-6) =
- Subtracting a negative integer: \(4 - (-6) = 4 + 6 = 10\)
- Answer: \(10\)

36. 4 − (-3) =
- Subtracting a negative integer: \(4 - (-3) = 4 + 3 = 7\)
- Answer: \(7\)

37. 7 − (-8) =
- Subtracting a negative integer: \(7 - (-8) = 7 + 8 = 15\)
- Answer: \(15\)

38. 5 + 2 =
- Adding two positive integers: \(5 + 2 = 7\)
- Answer: \(7\)

39. 10 + (-7) =
- Adding a positive and a negative integer: \(10 + (-7) = 10 - 7 = 3\)
- Answer: \(3\)

40. 7 − (-3) =
- Subtracting a negative integer: \(7 - (-3) = 7 + 3 = 10\)
- Answer: \(10\)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. -11 & 21. 12 \\
2. 3 & 22. -6 \\
3. -11 & 23. -3 \\
4. -7 & 24. 14 \\
5. -12 & 25. 2 \\
6. -12 & 26. 19 \\
7. -2 & 27. -4 \\
8. 5 & 28. -18 \\
9. -6 & 29. 4 \\
10. -1 & 30. 13 \\
11. -4 & 31. 0 \\
12. -6 & 32. 3 \\
13. 12 & 33. -4 \\
14. -13 & 34. 14 \\
15. -4 & 35. 10 \\
16. 9 & 36. 7 \\
17. -10 & 37. 15 \\
18. -10 & 38. 7 \\
19. -1 & 39. 3 \\
20. 15 & 40. 10 \\
\end{array}
}
\]