Multiplying+Dividing Rational Numbers - Kuta Software - Free Printable

Problem: Solving the Quotients for Multiplying and Dividing Positives and Negatives

The task involves finding the quotients of various fractions and division problems. The key rules to remember are:

1. Division of Positive Numbers: The quotient is positive.
2. Division of Negative Numbers: The quotient is positive.
3. Division of a Positive by a Negative (or vice versa): The quotient is negative.

Let's solve each problem step by step.

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Problem 1: \( \frac{10}{5} \)

- Step: Divide 10 by 5.
- Calculation: \( 10 \div 5 = 2 \)
- Answer: \( 2 \)

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Problem 2: \( \frac{-24}{12} \)

- Step: Divide -24 by 12.
- Calculation: \( -24 \div 12 = -2 \)
- Answer: \( -2 \)

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Problem 3: \( \frac{-20}{-2} \)

- Step: Divide -20 by -2.
- Calculation: \( -20 \div -2 = 10 \)
- Answer: \( 10 \)

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Problem 4: \( \frac{-300}{-20} \)

- Step: Divide -300 by -20.
- Calculation: \( -300 \div -20 = 15 \)
- Answer: \( 15 \)

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Problem 5: \( \frac{65}{5} \)

- Step: Divide 65 by 5.
- Calculation: \( 65 \div 5 = 13 \)
- Answer: \( 13 \)

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Problem 6: \( \frac{-66}{-6} \)

- Step: Divide -66 by -6.
- Calculation: \( -66 \div -6 = 11 \)
- Answer: \( 11 \)

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Problem 7: \( \frac{75}{-15} \)

- Step: Divide 75 by -15.
- Calculation: \( 75 \div -15 = -5 \)
- Answer: \( -5 \)

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Problem 8: \( \frac{-56}{-14} \)

- Step: Divide -56 by -14.
- Calculation: \( -56 \div -14 = 4 \)
- Answer: \( 4 \)

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Problem 9: \( \frac{102}{-17} \)

- Step: Divide 102 by -17.
- Calculation: \( 102 \div -17 = -6 \)
- Answer: \( -6 \)

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Problem 10: \( \frac{-72}{-4} \)

- Step: Divide -72 by -4.
- Calculation: \( -72 \div -4 = 18 \)
- Answer: \( 18 \)

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Problem 11: \( 153 \div 17 \)

- Step: Divide 153 by 17.
- Calculation: \( 153 \div 17 = 9 \)
- Answer: \( 9 \)

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Problem 12: \( 12 \div -3 \)

- Step: Divide 12 by -3.
- Calculation: \( 12 \div -3 = -4 \)
- Answer: \( -4 \)

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Problem 13: \( 48 \div 6 \)

- Step: Divide 48 by 6.
- Calculation: \( 48 \div 6 = 8 \)
- Answer: \( 8 \)

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Problem 14: \( -120 \div -20 \)

- Step: Divide -120 by -20.
- Calculation: \( -120 \div -20 = 6 \)
- Answer: \( 6 \)

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Problem 15: \( 306 \div 18 \)

- Step: Divide 306 by 18.
- Calculation: \( 306 \div 18 = 17 \)
- Answer: \( 17 \)

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Problem 16: \( -65 \div 13 \)

- Step: Divide -65 by 13.
- Calculation: \( -65 \div 13 = -5 \)
- Answer: \( -5 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 2 \\
2) & -2 \\
3) & 10 \\
4) & 15 \\
5) & 13 \\
6) & 11 \\
7) & -5 \\
8) & 4 \\
9) & -6 \\
10) & 18 \\
11) & 9 \\
12) & -4 \\
13) & 8 \\
14) & 6 \\
15) & 17 \\
16) & -5 \\
\end{array}
}
\]