Practice worksheet for dividing rational numbers, featuring 24 problems to simplify fractions with positive and negative values.

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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📝 Example Problems (Based on Common Worksheet Format)

Let’s assume your worksheet includes problems like:

#### 1. $ \frac{3}{4} \div \frac{2}{5} $

Step 1: Change division to multiplication by the reciprocal:
$$
\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2}
$$

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

Step 3: Simplify (already simplified), convert to mixed number:
$$
= 1 \frac{7}{8}
$$

✔ Answer: $ 1 \frac{7}{8} $

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#### 2. $ -\frac{5}{6} \div \frac{1}{3} $

Step 1: Flip the second fraction:
$$
-\frac{5}{6} \div \frac{1}{3} = -\frac{5}{6} \times \frac{3}{1}
$$

Step 2: Multiply:
$$
= -\frac{15}{6} = -\frac{5}{2}
$$

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

✔ Answer: $ -2 \frac{1}{2} $

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#### 3. $ 4 \div \frac{2}{3} $

Step 1: Convert 4 to a fraction: $ \frac{4}{1} $
$$
\frac{4}{1} \div \frac{2}{3} = \frac{4}{1} \times \frac{3}{2} = \frac{12}{2} = 6
$$

✔ Answer: $ 6 $

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#### 4. $ -\frac{3}{8} \div (-\frac{1}{4}) $

Step 1: Flip the second fraction:
$$
-\frac{3}{8} \div (-\frac{1}{4}) = -\frac{3}{8} \times (-\frac{4}{1})
$$

Step 2: Multiply:
$$
= \frac{12}{8} = \frac{3}{2} = 1 \frac{1}{2}
$$

✔ Answer: $ 1 \frac{1}{2} $

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#### 5. $ 0.6 \div 0.2 $

Step 1: Convert to fractions:
$$
0.6 = \frac{6}{10}, \quad 0.2 = \frac{2}{10}
$$
So:
$$
\frac{6}{10} \div \frac{2}{10} = \frac{6}{10} \times \frac{10}{2} = \frac{60}{20} = 3
$$

✔ Answer: $ 3 $

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✔ General Tips:

- Always simplify before multiplying when possible.
- Use sign rules carefully.
- For decimals, converting to fractions often makes division easier.

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Alternatively, if you’d like, you can type out the problems here, and I’ll walk you through each one!