Practice worksheet for dividing rational numbers, featuring 24 problems to simplify.

It looks like you've uploaded a worksheet titled "Dividing Rational Numbers" with several problems involving division of fractions, decimals, and integers. Since I can't view images directly, I’ll guide you through how to solve these types of problems step-by-step, and then walk through a few examples based on the typical format of such worksheets.

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🔧 How to Divide Rational Numbers

Rational numbers include fractions, decimals, and integers. When dividing rational numbers:

1. Convert mixed numbers to improper fractions (if needed).
2. Change division into multiplication by flipping the second number (the divisor) — this is called the reciprocal.
3. Multiply the numerators and multiply the denominators.
4. Simplify the result if possible.
5. Check the sign:
- Positive ÷ Positive = Positive
- Negative ÷ Negative = Positive
- Positive ÷ Negative = Negative
- Negative ÷ Positive = Negative

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Let’s go through some sample problems that are likely on your worksheet (based on common patterns):

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✔ Example 1:

Problem: $ \frac{3}{4} \div \frac{2}{5} $

Step 1: Flip the second fraction:
$ \frac{3}{4} \times \frac{5}{2} $

Step 2: Multiply:
$ \frac{3 \times 5}{4 \times 2} = \frac{15}{8} $

Step 3: Simplify or convert to mixed number:
$ \frac{15}{8} = 1\frac{7}{8} $

✔ Answer: $ 1\frac{7}{8} $

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✔ Example 2:

Problem: $ -\frac{2}{3} \div \frac{4}{9} $

Step 1: Flip the second fraction:
$ -\frac{2}{3} \times \frac{9}{4} $

Step 2: Multiply:
$ \frac{-2 \times 9}{3 \times 4} = \frac{-18}{12} $

Step 3: Simplify:
$ \frac{-18}{12} = -\frac{3}{2} = -1\frac{1}{2} $

✔ Answer: $ -1\frac{1}{2} $

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✔ Example 3:

Problem: $ 6 \div \left(-\frac{3}{4}\right) $

Step 1: Convert 6 to a fraction: $ \frac{6}{1} $

Step 2: Flip the divisor:
$ \frac{6}{1} \times \left(-\frac{4}{3}\right) $

Step 3: Multiply:
$ \frac{6 \times (-4)}{1 \times 3} = \frac{-24}{3} = -8 $

✔ Answer: $ -8 $

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✔ Example 4:

Problem: $ -\frac{5}{6} \div (-\frac{1}{2}) $

Step 1: Flip the second fraction:
$ -\frac{5}{6} \times (-\frac{2}{1}) $

Step 2: Multiply:
$ \frac{-5 \times -2}{6 \times 1} = \frac{10}{6} = \frac{5}{3} = 1\frac{2}{3} $

✔ Answer: $ 1\frac{2}{3} $

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✔ Example 5:

Problem: $ 0.8 \div (-0.2) $

Step 1: Convert decimals to fractions:
$ 0.8 = \frac{8}{10} = \frac{4}{5} $,
$ -0.2 = -\frac{2}{10} = -\frac{1}{5} $

Step 2: Divide:
$ \frac{4}{5} \div \left(-\frac{1}{5}\right) = \frac{4}{5} \times (-5) = -4 $

✔ Answer: $ -4 $

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📌 General Tips:

- Always simplify before multiplying (cancel common factors).
- Watch out for signs — two negatives make a positive!
- If you're dividing by a decimal, convert both to fractions first.

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If you can provide the specific problems from the image (e.g., list them), I can solve each one exactly as they appear.

Otherwise, use the method above for any division problem involving rational numbers.

Let me know which problems you'd like help with!