Integers Worksheets - Math Monks - Free Printable

Problem: Operations with Integers

The task is to perform various arithmetic operations with integers. Below, I will solve each problem step by step and provide the final answers.

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#### 1. \( 6 + (-1) \)
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 6 + (-1) = 6 - 1 = 5 \)

Answer: \( 5 \)

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#### 2. \( 6 \times (-2) \)
- Multiplying a positive number by a negative number results in a negative product.
- \( 6 \times (-2) = -12 \)

Answer: \( -12 \)

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#### 3. \( (-3) + (-2) \)
- Adding two negative numbers results in a negative sum.
- \( (-3) + (-2) = -3 - 2 = -5 \)

Answer: \( -5 \)

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#### 4. \( (-25) \div (-5) \)
- Dividing two negative numbers results in a positive quotient.
- \( (-25) \div (-5) = 25 \div 5 = 5 \)

Answer: \( 5 \)

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#### 5. \( 12 - (-63) \)
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 12 - (-63) = 12 + 63 = 75 \)

Answer: \( 75 \)

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#### 6. \( (-25) + (-77) \)
- Adding two negative numbers results in a negative sum.
- \( (-25) + (-77) = -25 - 77 = -102 \)

Answer: \( -102 \)

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#### 7. \( (-6) \div (-3) \)
- Dividing two negative numbers results in a positive quotient.
- \( (-6) \div (-3) = 6 \div 3 = 2 \)

Answer: \( 2 \)

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#### 8. \( 8 \times 3 \)
- Multiplying two positive numbers results in a positive product.
- \( 8 \times 3 = 24 \)

Answer: \( 24 \)

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#### 9. \( (-5) + (-1) \)
- Adding two negative numbers results in a negative sum.
- \( (-5) + (-1) = -5 - 1 = -6 \)

Answer: \( -6 \)

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#### 10. \( (-7) - 9 \)
- Subtracting a positive number from a negative number makes the result more negative.
- \( (-7) - 9 = -7 - 9 = -16 \)

Answer: \( -16 \)

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#### 11. \( (-49) \div (-7) \)
- Dividing two negative numbers results in a positive quotient.
- \( (-49) \div (-7) = 49 \div 7 = 7 \)

Answer: \( 7 \)

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#### 12. \( 24 \div (-3) \)
- Dividing a positive number by a negative number results in a negative quotient.
- \( 24 \div (-3) = -8 \)

Answer: \( -8 \)

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#### 13. \( (-6) + 6 \)
- Adding a number and its opposite results in zero.
- \( (-6) + 6 = 0 \)

Answer: \( 0 \)

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#### 14. \( (-9) \times (-5) \)
- Multiplying two negative numbers results in a positive product.
- \( (-9) \times (-5) = 45 \)

Answer: \( 45 \)

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#### 15. \( 7 - (-5) \)
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 7 - (-5) = 7 + 5 = 12 \)

Answer: \( 12 \)

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#### 16. \( (-4) \div (-2) \)
- Dividing two negative numbers results in a positive quotient.
- \( (-4) \div (-2) = 4 \div 2 = 2 \)

Answer: \( 2 \)

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#### 17. \( (-7) - (-7) \)
- Subtracting a number from itself results in zero.
- \( (-7) - (-7) = -7 + 7 = 0 \)

Answer: \( 0 \)

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#### 18. \( 9 - (-2) \)
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 9 - (-2) = 9 + 2 = 11 \)

Answer: \( 11 \)

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#### 19. \( 7 - (-9) \)
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 7 - (-9) = 7 + 9 = 16 \)

Answer: \( 16 \)

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#### 20. \( 1 + (-6) \)
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 1 + (-6) = 1 - 6 = -5 \)

Answer: \( -5 \)

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#### 21. \( 12 \div (-2) \)
- Dividing a positive number by a negative number results in a negative quotient.
- \( 12 \div (-2) = -6 \)

Answer: \( -6 \)

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#### 22. \( 4 \div (-4) \)
- Dividing a positive number by a negative number results in a negative quotient.
- \( 4 \div (-4) = -1 \)

Answer: \( -1 \)

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#### 23. \( 4 - 4 \)
- Subtracting a number from itself results in zero.
- \( 4 - 4 = 0 \)

Answer: \( 0 \)

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#### 24. \( 24 \div (-4) \)
- Dividing a positive number by a negative number results in a negative quotient.
- \( 24 \div (-4) = -6 \)

Answer: \( -6 \)

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#### 25. \( (-15) \div (-3) \)
- Dividing two negative numbers results in a positive quotient.
- \( (-15) \div (-3) = 15 \div 3 = 5 \)

Answer: \( 5 \)

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#### 26. \( (-6) + (-9) \)
- Adding two negative numbers results in a negative sum.
- \( (-6) + (-9) = -6 - 9 = -15 \)

Answer: \( -15 \)

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#### 27. \( (-32) \div 4 \)
- Dividing a negative number by a positive number results in a negative quotient.
- \( (-32) \div 4 = -8 \)

Answer: \( -8 \)

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#### 28. \( (-7) \times 7 \)
- Multiplying a negative number by a positive number results in a negative product.
- \( (-7) \times 7 = -49 \)

Answer: \( -49 \)

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#### 29. \( 8 \times (-7) \)
- Multiplying a positive number by a negative number results in a negative product.
- \( 8 \times (-7) = -56 \)

Answer: \( -56 \)

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#### 30. \( (-7) + (-9) \)
- Adding two negative numbers results in a negative sum.
- \( (-7) + (-9) = -7 - 9 = -16 \)

Answer: \( -16 \)

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#### 31. \( (-11) - 8 \)
- Subtracting a positive number from a negative number makes the result more negative.
- \( (-11) - 8 = -11 - 8 = -19 \)

Answer: \( -19 \)

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#### 32. \( 8 \div (-2) \)
- Dividing a positive number by a negative number results in a negative quotient.
- \( 8 \div (-2) = -4 \)

Answer: \( -4 \)

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#### 33. \( 21 - (-3) \)
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 21 - (-3) = 21 + 3 = 24 \)

Answer: \( 24 \)

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Final Answers:

\[
\boxed{
\begin{array}{lll}
1. & 5 & 2. & -12 & 3. & -5 \\
4. & 5 & 5. & 75 & 6. & -102 \\
7. & 2 & 8. & 24 & 9. & -6 \\
10. & -16 & 11. & 7 & 12. & -8 \\
13. & 0 & 14. & 45 & 15. & 12 \\
16. & 2 & 17. & 0 & 18. & 11 \\
19. & 16 & 20. & -5 & 21. & -6 \\
22. & -1 & 23. & 0 & 24. & -6 \\
25. & 5 & 26. & -15 & 27. & -8 \\
28. & -49 & 29. & -56 & 30. & -16 \\
31. & -19 & 32. & -4 & 33. & 24 \\
\end{array}
}
\]