Operations with positive and negative numbers interactive ... - Free Printable

Problem: Operations with Positive and Negative Numbers

The worksheet contains 20 problems involving addition, subtraction, multiplication, and division of positive and negative numbers. Below is the solution to each problem, along with explanations.

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#### 1. \( (-23) + 6 = \)
- Add a positive number to a negative number.
- Subtract the smaller absolute value from the larger absolute value and keep the sign of the larger number.
- \( |-23| = 23 \) and \( |6| = 6 \).
- \( 23 - 6 = 17 \).
- Since \( -23 \) has the larger absolute value and is negative, the result is negative.
- Answer: \( -17 \)

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#### 2. \( (-2) \times 4 = \)
- Multiply a negative number by a positive number.
- The product of a negative and a positive number is negative.
- \( 2 \times 4 = 8 \).
- Answer: \( -8 \)

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#### 3. \( 20 + (-8) = \)
- Add a negative number to a positive number.
- Subtract the absolute value of the negative number from the positive number.
- \( 20 - 8 = 12 \).
- Answer: \( 12 \)

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#### 4. \( (-64) \div 4 = \)
- Divide a negative number by a positive number.
- The quotient of a negative and a positive number is negative.
- \( 64 \div 4 = 16 \).
- Answer: \( -16 \)

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#### 5. \( 25 + (-2) = \)
- Add a negative number to a positive number.
- Subtract the absolute value of the negative number from the positive number.
- \( 25 - 2 = 23 \).
- Answer: \( 23 \)

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#### 6. \( (-3) \times (-7) = \)
- Multiply two negative numbers.
- The product of two negative numbers is positive.
- \( 3 \times 7 = 21 \).
- Answer: \( 21 \)

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#### 7. \( 7 - (-3) = \)
- Subtracting a negative number is equivalent to adding its positive counterpart.
- \( 7 + 3 = 10 \).
- Answer: \( 10 \)

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#### 8. \( 16 \div (-2) = \)
- Divide a positive number by a negative number.
- The quotient of a positive and a negative number is negative.
- \( 16 \div 2 = 8 \).
- Answer: \( -8 \)

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#### 9. \( (-8) + (-7) = \)
- Add two negative numbers.
- Add their absolute values and keep the negative sign.
- \( 8 + 7 = 15 \).
- Answer: \( -15 \)

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#### 10. \( 8 \times (-1) = \)
- Multiply a positive number by a negative number.
- The product of a positive and a negative number is negative.
- \( 8 \times 1 = 8 \).
- Answer: \( -8 \)

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#### 11. \( 15 + (-6) = \)
- Add a negative number to a positive number.
- Subtract the absolute value of the negative number from the positive number.
- \( 15 - 6 = 9 \).
- Answer: \( 9 \)

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#### 12. \( (-25) \div (-5) = \)
- Divide two negative numbers.
- The quotient of two negative numbers is positive.
- \( 25 \div 5 = 5 \).
- Answer: \( 5 \)

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#### 13. \( (-23) + 6 = \)
- Add a positive number to a negative number.
- Subtract the smaller absolute value from the larger absolute value and keep the sign of the larger number.
- \( |-23| = 23 \) and \( |6| = 6 \).
- \( 23 - 6 = 17 \).
- Since \( -23 \) has the larger absolute value and is negative, the result is negative.
- Answer: \( -17 \)

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#### 14. \( (-10) \times (-10) = \)
- Multiply two negative numbers.
- The product of two negative numbers is positive.
- \( 10 \times 10 = 100 \).
- Answer: \( 100 \)

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#### 15. \( (-(-5)) - (-6) = \)
- Simplify step by step:
- \( -(-5) = 5 \) (double negative becomes positive).
- \( 5 - (-6) = 5 + 6 \) (subtracting a negative is the same as adding its positive counterpart).
- \( 5 + 6 = 11 \).
- Answer: \( 11 \)

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#### 16. \( (-45) \div (-9) = \)
- Divide two negative numbers.
- The quotient of two negative numbers is positive.
- \( 45 \div 9 = 5 \).
- Answer: \( 5 \)

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#### 17. \( 19 - (-1) = \)
- Subtracting a negative number is equivalent to adding its positive counterpart.
- \( 19 + 1 = 20 \).
- Answer: \( 20 \)

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#### 18. \( 5 \times (-8) = \)
- Multiply a positive number by a negative number.
- The product of a positive and a negative number is negative.
- \( 5 \times 8 = 40 \).
- Answer: \( -40 \)

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#### 19. \( 4 + (-16) = \)
- Add a negative number to a positive number.
- Subtract the absolute value of the negative number from the positive number.
- \( 4 - 16 = -12 \).
- Answer: \( -12 \)

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#### 20. \( 28 \div (-7) = \)
- Divide a positive number by a negative number.
- The quotient of a positive and a negative number is negative.
- \( 28 \div 7 = 4 \).
- Answer: \( -4 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & -17 \\
2. & -8 \\
3. & 12 \\
4. & -16 \\
5. & 23 \\
6. & 21 \\
7. & 10 \\
8. & -8 \\
9. & -15 \\
10. & -8 \\
11. & 9 \\
12. & 5 \\
13. & -17 \\
14. & 100 \\
15. & 11 \\
16. & 5 \\
17. & 20 \\
18. & -40 \\
19. & -12 \\
20. & -4 \\
\end{array}
}
\]