Adding and Subtracting Negative Numbers - Free Printable

Problem Explanation and Solution

The worksheet focuses on adding and subtracting negative numbers. Let's solve each section step by step.

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#### Section A: Use the number line above to help you answer these questions.

We will solve each problem using basic arithmetic rules for adding and subtracting integers.

1. (-1) + 7 =
- Start at -1 on the number line and move 7 units to the right.
- Result: 6

2. (-1) - 7 =
- Start at -1 on the number line and move 7 units to the left.
- Result: -8

3. 6 + (-3) =
- Start at 6 on the number line and move 3 units to the left.
- Result: 3

4. 6 - (-3) =
- Subtracting a negative is the same as adding a positive.
- Start at 6 on the number line and move 3 units to the right.
- Result: 9

5. (-4) + (-5) =
- Adding two negatives results in a larger negative.
- Start at -4 on the number line and move 5 units to the left.
- Result: -9

6. (-4) - (-5) =
- Subtracting a negative is the same as adding a positive.
- Start at -4 on the number line and move 5 units to the right.
- Result: 1

7. 3 + (-3) =
- Adding a number and its opposite results in zero.
- Result: 0

8. 3 - (-3) =
- Subtracting a negative is the same as adding a positive.
- Start at 3 on the number line and move 3 units to the right.
- Result: 6

9. (-2) + (-3) =
- Adding two negatives results in a larger negative.
- Start at -2 on the number line and move 3 units to the left.
- Result: -5

10. (-2) - (-3) =
- Subtracting a negative is the same as adding a positive.
- Start at -2 on the number line and move 3 units to the right.
- Result: 1

11. 7 + (-5) =
- Start at 7 on the number line and move 5 units to the left.
- Result: 2

12. (-3) - 6 =
- Start at -3 on the number line and move 6 units to the left.
- Result: -9

13. 4 + (-8) =
- Start at 4 on the number line and move 8 units to the left.
- Result: -4

14. (-1) - (-10) =
- Subtracting a negative is the same as adding a positive.
- Start at -1 on the number line and move 10 units to the right.
- Result: 9

15. 7 + (-9) =
- Start at 7 on the number line and move 9 units to the left.
- Result: -2

16. (-1) - 8 =
- Start at -1 on the number line and move 8 units to the left.
- Result: -9

17. (-5) + (-3) =
- Adding two negatives results in a larger negative.
- Start at -5 on the number line and move 3 units to the left.
- Result: -8

18. (-6) - (-7) =
- Subtracting a negative is the same as adding a positive.
- Start at -6 on the number line and move 7 units to the right.
- Result: 1

19. 8 + (-9) =
- Start at 8 on the number line and move 9 units to the left.
- Result: -1

20. 4 - (-6) =
- Subtracting a negative is the same as adding a positive.
- Start at 4 on the number line and move 6 units to the right.
- Result: 10

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#### Section B: Use two numbers from the list below to answer each of the questions.

The list of numbers is: -5, 3, -8, -1, -4, 7, -2

1. ____ + ____ = -2
- Possible pairs: (-5 + 3), (7 + -9), etc.
- Solution: -5 + 3 = -2

2. ____ - ____ = 1
- Possible pairs: (3 - 2), (7 - 6), etc.
- Solution: 3 - 2 = 1

3. ____ + ____ = -6
- Possible pairs: (-8 + -4), (-5 + -1), etc.
- Solution: -8 + -4 = -6

4. ____ - ____ = -6
- Possible pairs: (-5 - 1), (-8 - -2), etc.
- Solution: -5 - 1 = -6

5. ____ + ____ = -3
- Possible pairs: (-5 + 2), (-4 + -1), etc.
- Solution: -4 + -1 = -3

6. ____ - ____ = -4
- Possible pairs: (-5 - 1), (-8 - -4), etc.
- Solution: -5 - 1 = -4

7. Find 4 different ways to make this work:
- ____ + ____ = -1
- Possible pairs: (-5 + 4), (-4 + -1), (-3 + -2), etc.
- Solutions: -5 + 4 = -1, -4 + -1 = -1, -3 + -2 = -1, -2 + -3 = -1
- ____ - ____ = -1
- Possible pairs: (-5 - -4), (-4 - -3), etc.
- Solutions: -5 - -4 = -1, -4 - -3 = -1, -3 - -2 = -1, -2 - -1 = -1

8. Choose three numbers from the list to make this correct:
- ____ + ____ - ____ = -10
- Possible combinations: (-8 + -4 - 2), (-5 + -5 - 0), etc.
- Solution: -8 + -4 - 2 = -10

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Final Answers:

#### Section A:
1. 6
2. -8
3. 3
4. 9
5. -9
6. 1
7. 0
8. 6
9. -5
10. 1
11. 2
12. -9
13. -4
14. 9
15. -2
16. -9
17. -8
18. 1
19. -1
20. 10

#### Section B:
1. -5 + 3 = -2
2. 3 - 2 = 1
3. -8 + -4 = -6
4. -5 - 1 = -6
5. -4 + -1 = -3
6. -5 - 1 = -4
7.
- -5 + 4 = -1
- -4 + -1 = -1
- -3 + -2 = -1
- -2 + -3 = -1
- -5 - -4 = -1
- -4 - -3 = -1
- -3 - -2 = -1
- -2 - -1 = -1
8. -8 + -4 - 2 = -10

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Final Answer Boxed:
\[
\boxed{
\begin{array}{l}
\text{Section A:} \\
1. 6, 2. -8, 3. 3, 4. 9, 5. -9, 6. 1, 7. 0, 8. 6, 9. -5, 10. 1, \\
11. 2, 12. -9, 13. -4, 14. 9, 15. -2, 16. -9, 17. -8, 18. 1, 19. -1, 20. 10. \\
\text{Section B:} \\
1. -5 + 3 = -2, \\
2. 3 - 2 = 1, \\
3. -8 + -4 = -6, \\
4. -5 - 1 = -6, \\
5. -4 + -1 = -3, \\
6. -5 - 1 = -4, \\
7. \text{Examples: } -5 + 4 = -1, -4 + -1 = -1, -3 + -2 = -1, -2 + -3 = -1, \\
8. -8 + -4 - 2 = -10.
\end{array}
}
\]