Adding and Subtracting Negative Numbers - Free Printable

Problem Overview:

The task involves solving addition and subtraction problems involving both positive and negative numbers. The number line provided at the top of the worksheet can be used as a visual aid to help solve these problems.

Key Concepts:

1. Adding Positive Numbers: Move to the right on the number line.
2. Adding Negative Numbers: Move to the left on the number line.
3. Subtracting Positive Numbers: Move to the left on the number line.
4. Subtracting Negative Numbers: Move to the right on the number line (since subtracting a negative is equivalent to adding a positive).

Solution Approach:

We will solve each problem step by step, using the rules above and the number line for visualization.

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Solutions:

#### Section 1: Problems 1–20

1. 5 + (-3) =
- Start at 5, move 3 units to the left.
- Result: \( 5 - 3 = 2 \)
- Answer: 2

2. 5 − (-3) =
- Subtracting a negative is the same as adding a positive.
- Start at 5, move 3 units to the right.
- Result: \( 5 + 3 = 8 \)
- Answer: 8

3. 2 + (-4) =
- Start at 2, move 4 units to the left.
- Result: \( 2 - 4 = -2 \)
- Answer: -2

4. 2 − (-4) =
- Subtracting a negative is the same as adding a positive.
- Start at 2, move 4 units to the right.
- Result: \( 2 + 4 = 6 \)
- Answer: 6

5. (-5) + 3 =
- Start at -5, move 3 units to the right.
- Result: \( -5 + 3 = -2 \)
- Answer: -2

6. (-5) − 3 =
- Start at -5, move 3 units to the left.
- Result: \( -5 - 3 = -8 \)
- Answer: -8

7. (-3) + 6 =
- Start at -3, move 6 units to the right.
- Result: \( -3 + 6 = 3 \)
- Answer: 3

8. (-3) − 6 =
- Start at -3, move 6 units to the left.
- Result: \( -3 - 6 = -9 \)
- Answer: -9

9. 2 + (-5) =
- Start at 2, move 5 units to the left.
- Result: \( 2 - 5 = -3 \)
- Answer: -3

10. 2 − (-5) =
- Subtracting a negative is the same as adding a positive.
- Start at 2, move 5 units to the right.
- Result: \( 2 + 5 = 7 \)
- Answer: 7

11. 7 + (-1) =
- Start at 7, move 1 unit to the left.
- Result: \( 7 - 1 = 6 \)
- Answer: 6

12. 7 − (-1) =
- Subtracting a negative is the same as adding a positive.
- Start at 7, move 1 unit to the right.
- Result: \( 7 + 1 = 8 \)
- Answer: 8

13. 1 + (-6) =
- Start at 1, move 6 units to the left.
- Result: \( 1 - 6 = -5 \)
- Answer: -5

14. 1 − (-6) =
- Subtracting a negative is the same as adding a positive.
- Start at 1, move 6 units to the right.
- Result: \( 1 + 6 = 7 \)
- Answer: 7

15. (-4) + (-5) =
- Start at -4, move 5 units to the left.
- Result: \( -4 - 5 = -9 \)
- Answer: -9

16. (-4) − (-5) =
- Subtracting a negative is the same as adding a positive.
- Start at -4, move 5 units to the right.
- Result: \( -4 + 5 = 1 \)
- Answer: 1

17. (-3) + (-7) =
- Start at -3, move 7 units to the left.
- Result: \( -3 - 7 = -10 \)
- Answer: -10

18. (-3) − (-7) =
- Subtracting a negative is the same as adding a positive.
- Start at -3, move 7 units to the right.
- Result: \( -3 + 7 = 4 \)
- Answer: 4

19. 4 + (-6) =
- Start at 4, move 6 units to the left.
- Result: \( 4 - 6 = -2 \)
- Answer: -2

20. 4 − (-6) =
- Subtracting a negative is the same as adding a positive.
- Start at 4, move 6 units to the right.
- Result: \( 4 + 6 = 10 \)
- Answer: 10

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#### Section 2: Problems 21–40

21. 3 + (-4) =
- Start at 3, move 4 units to the left.
- Result: \( 3 - 4 = -1 \)
- Answer: -1

22. (-4) − 5 =
- Start at -4, move 5 units to the left.
- Result: \( -4 - 5 = -9 \)
- Answer: -9

23. (-6) + 5 =
- Start at -6, move 5 units to the right.
- Result: \( -6 + 5 = -1 \)
- Answer: -1

24. 2 − (-6) =
- Subtracting a negative is the same as adding a positive.
- Start at 2, move 6 units to the right.
- Result: \( 2 + 6 = 8 \)
- Answer: 8

25. 3 + (-5) =
- Start at 3, move 5 units to the left.
- Result: \( 3 - 5 = -2 \)
- Answer: -2

26. 5 − (-3) =
- Subtracting a negative is the same as adding a positive.
- Start at 5, move 3 units to the right.
- Result: \( 5 + 3 = 8 \)
- Answer: 8

27. 8 + (-7) =
- Start at 8, move 7 units to the left.
- Result: \( 8 - 7 = 1 \)
- Answer: 1

28. (-3) − (-4) =
- Subtracting a negative is the same as adding a positive.
- Start at -3, move 4 units to the right.
- Result: \( -3 + 4 = 1 \)
- Answer: 1

29. 7 + (-10) =
- Start at 7, move 10 units to the left.
- Result: \( 7 - 10 = -3 \)
- Answer: -3

30. (-1) − 7 =
- Start at -1, move 7 units to the left.
- Result: \( -1 - 7 = -8 \)
- Answer: -8

31. (-6) + 11 =
- Start at -6, move 11 units to the right.
- Result: \( -6 + 11 = 5 \)
- Answer: 5

32. (-8) − (-10) =
- Subtracting a negative is the same as adding a positive.
- Start at -8, move 10 units to the right.
- Result: \( -8 + 10 = 2 \)
- Answer: 2

33. (-10) + 7 =
- Start at -10, move 7 units to the right.
- Result: \( -10 + 7 = -3 \)
- Answer: -3

34. 8 − 12 =
- Start at 8, move 12 units to the left.
- Result: \( 8 - 12 = -4 \)
- Answer: -4

35. 4 + (-11) =
- Start at 4, move 11 units to the left.
- Result: \( 4 - 11 = -7 \)
- Answer: -7

36. (-6) − 3 =
- Start at -6, move 3 units to the left.
- Result: \( -6 - 3 = -9 \)
- Answer: -9

37. (-5) + (-4) =
- Start at -5, move 4 units to the left.
- Result: \( -5 - 4 = -9 \)
- Answer: -9

38. (-2) − (-10) =
- Subtracting a negative is the same as adding a positive.
- Start at -2, move 10 units to the right.
- Result: \( -2 + 10 = 8 \)
- Answer: 8

39. (-8) + 15 =
- Start at -8, move 15 units to the right.
- Result: \( -8 + 15 = 7 \)
- Answer: 7

40. (-7) − (-12) =
- Subtracting a negative is the same as adding a positive.
- Start at -7, move 12 units to the right.
- Result: \( -7 + 12 = 5 \)
- Answer: 5

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Final Answer:

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