Adding and Subtracting Rational Numbers Worksheet | Free ... - Free Printable

Problem: Solving the Addition and Subtraction of Rational Numbers

The task involves solving a series of problems involving addition and subtraction of rational numbers. Below, I will solve each problem step by step.

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Problem 1: \( 2 - (-73) \)

Solution:
- Subtracting a negative number is equivalent to adding its positive counterpart.
- \( 2 - (-73) = 2 + 73 = 75 \).

Answer: \( 75 \)

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Problem 2: \( 39 + (-20.4) \)

Solution:
- Adding a negative number is equivalent to subtracting its positive counterpart.
- \( 39 + (-20.4) = 39 - 20.4 = 18.6 \).

Answer: \( 18.6 \)

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Problem 3: \( 67.086 - (-20) \)

Solution:
- Subtracting a negative number is equivalent to adding its positive counterpart.
- \( 67.086 - (-20) = 67.086 + 20 = 87.086 \).

Answer: \( 87.086 \)

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Problem 4: \( 60 + (-19) \)

Solution:
- Adding a negative number is equivalent to subtracting its positive counterpart.
- \( 60 + (-19) = 60 - 19 = 41 \).

Answer: \( 41 \)

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Problem 5: \( 87 - 64.05 \)

Solution:
- Perform the subtraction directly.
- \( 87 - 64.05 = 22.95 \).

Answer: \( 22.95 \)

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Problem 6: \( 93 - (-31) \)

Solution:
- Subtracting a negative number is equivalent to adding its positive counterpart.
- \( 93 - (-31) = 93 + 31 = 124 \).

Answer: \( 124 \)

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Problem 7: \( 2 + 17.02 \)

Solution:
- Perform the addition directly.
- \( 2 + 17.02 = 19.02 \).

Answer: \( 19.02 \)

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Problem 8: \( 3.008 + (-46) \)

Solution:
- Adding a negative number is equivalent to subtracting its positive counterpart.
- \( 3.008 + (-46) = 3.008 - 46 = -42.992 \).

Answer: \( -42.992 \)

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Problem 9: \( 85.082 + 48.11 \)

Solution:
- Perform the addition directly.
- \( 85.082 + 48.11 = 133.192 \).

Answer: \( 133.192 \)

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Problem 10: \( 56.95 + 40 \)

Solution:
- Perform the addition directly.
- \( 56.95 + 40 = 96.95 \).

Answer: \( 96.95 \)

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Problem 11: \( 66 - 86.005 \)

Solution:
- Perform the subtraction directly.
- \( 66 - 86.005 = -19.005 \).

Answer: \( -19.005 \)

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Problem 12: \( 20 - (-4.09) \)

Solution:
- Subtracting a negative number is equivalent to adding its positive counterpart.
- \( 20 - (-4.09) = 20 + 4.09 = 24.09 \).

Answer: \( 24.09 \)

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Problem 13: \( 68 - 55 \)

Solution:
- Perform the subtraction directly.
- \( 68 - 55 = 13 \).

Answer: \( 13 \)

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Problem 14: \( 17 - (-58.12) \)

Solution:
- Subtracting a negative number is equivalent to adding its positive counterpart.
- \( 17 - (-58.12) = 17 + 58.12 = 75.12 \).

Answer: \( 75.12 \)

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Problem 15: \( 17.001 + 78 \)

Solution:
- Perform the addition directly.
- \( 17.001 + 78 = 95.001 \).

Answer: \( 95.001 \)

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Problem 16: \( 32 + (-72.1) \)

Solution:
- Adding a negative number is equivalent to subtracting its positive counterpart.
- \( 32 + (-72.1) = 32 - 72.1 = -40.1 \).

Answer: \( -40.1 \)

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Problem 17: \( 36.289 + (-83.73) \)

Solution:
- Adding a negative number is equivalent to subtracting its positive counterpart.
- \( 36.289 + (-83.73) = 36.289 - 83.73 = -47.441 \).

Answer: \( -47.441 \)

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Problem 18: \( 12.006 - (-49.29) \)

Solution:
- Subtracting a negative number is equivalent to adding its positive counterpart.
- \( 12.006 - (-49.29) = 12.006 + 49.29 = 61.296 \).

Answer: \( 61.296 \)

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Problem 19: \( 51.8 + (-92.004) \)

Solution:
- Adding a negative number is equivalent to subtracting its positive counterpart.
- \( 51.8 + (-92.004) = 51.8 - 92.004 = -40.204 \).

Answer: \( -40.204 \)

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Problem 20: \( 59.22 - 33.82 \)

Solution:
- Perform the subtraction directly.
- \( 59.22 - 33.82 = 25.4 \).

Answer: \( 25.4 \)

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Final Answers:

1. \( 75 \)
2. \( 18.6 \)
3. \( 87.086 \)
4. \( 41 \)
5. \( 22.95 \)
6. \( 124 \)
7. \( 19.02 \)
8. \( -42.992 \)
9. \( 133.192 \)
10. \( 96.95 \)
11. \( -19.005 \)
12. \( 24.09 \)
13. \( 13 \)
14. \( 75.12 \)
15. \( 95.001 \)
16. \( -40.1 \)
17. \( -47.441 \)
18. \( 61.296 \)
19. \( -40.204 \)
20. \( 25.4 \)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{l}
1. \, 75 \\
2. \, 18.6 \\
3. \, 87.086 \\
4. \, 41 \\
5. \, 22.95 \\
6. \, 124 \\
7. \, 19.02 \\
8. \, -42.992 \\
9. \, 133.192 \\
10. \, 96.95 \\
11. \, -19.005 \\
12. \, 24.09 \\
13. \, 13 \\
14. \, 75.12 \\
15. \, 95.001 \\
16. \, -40.1 \\
17. \, -47.441 \\
18. \, 61.296 \\
19. \, -40.204 \\
20. \, 25.4 \\
\end{array}
}
\]