Fraction division worksheet focusing on problems with common denominators, ideal for math practice.

Problem Overview:

The task involves dividing fractions using the method of common denominators. Dividing fractions can be simplified by multiplying the first fraction by the reciprocal of the second fraction. However, the worksheet specifies using common denominators, which is an alternative approach.

Steps to Solve:

1. Understand the Division of Fractions:
- When dividing two fractions, say \( \frac{a}{b} \div \frac{c}{d} \), it is equivalent to \( \frac{a}{b} \times \frac{d}{c} \).
- Alternatively, if we use common denominators, we compare the numerators after ensuring both fractions have the same denominator.

2. Using Common Denominators:
- Convert both fractions to have the same denominator.
- Then, divide the numerators of the resulting fractions.

3. Simplify the Results:
- After performing the division, simplify the resulting fraction if possible.

Solution to Each Problem:

#### 1. \( \frac{6}{9} \div \frac{5}{9} \)
- Both fractions already have a common denominator (9).
- Divide the numerators: \( 6 \div 5 = \frac{6}{5} \).
- Simplify: \( \frac{6}{5} \).

Answer: \( \frac{6}{5} \)

#### 2. \( \frac{1}{4} \div \frac{3}{4} \)
- Both fractions already have a common denominator (4).
- Divide the numerators: \( 1 \div 3 = \frac{1}{3} \).
- Simplify: \( \frac{1}{3} \).

Answer: \( \frac{1}{3} \)

#### 3. \( \frac{2}{4} \div \frac{3}{4} \)
- Both fractions already have a common denominator (4).
- Divide the numerators: \( 2 \div 3 = \frac{2}{3} \).
- Simplify: \( \frac{2}{3} \).

Answer: \( \frac{2}{3} \)

#### 4. \( \frac{5}{8} \div \frac{3}{8} \)
- Both fractions already have a common denominator (8).
- Divide the numerators: \( 5 \div 3 = \frac{5}{3} \).
- Simplify: \( \frac{5}{3} \).

Answer: \( \frac{5}{3} \)

#### 5. \( \frac{1}{2} \div \frac{1}{2} \)
- Both fractions already have a common denominator (2).
- Divide the numerators: \( 1 \div 1 = 1 \).
- Simplify: \( 1 \).

Answer: \( 1 \)

#### 6. \( \frac{6}{8} \div \frac{2}{8} \)
- Both fractions already have a common denominator (8).
- Divide the numerators: \( 6 \div 2 = 3 \).
- Simplify: \( 3 \).

Answer: \( 3 \)

#### 7. \( \frac{8}{9} \div \frac{5}{9} \)
- Both fractions already have a common denominator (9).
- Divide the numerators: \( 8 \div 5 = \frac{8}{5} \).
- Simplify: \( \frac{8}{5} \).

Answer: \( \frac{8}{5} \)

#### 8. \( \frac{2}{4} \div \frac{1}{4} \)
- Both fractions already have a common denominator (4).
- Divide the numerators: \( 2 \div 1 = 2 \).
- Simplify: \( 2 \).

Answer: \( 2 \)

#### 9. \( \frac{6}{8} \div \frac{7}{8} \)
- Both fractions already have a common denominator (8).
- Divide the numerators: \( 6 \div 7 = \frac{6}{7} \).
- Simplify: \( \frac{6}{7} \).

Answer: \( \frac{6}{7} \)

#### 10. \( \frac{1}{3} \div \frac{1}{3} \)
- Both fractions already have a common denominator (3).
- Divide the numerators: \( 1 \div 1 = 1 \).
- Simplify: \( 1 \).

Answer: \( 1 \)

#### 11. \( \frac{3}{6} \div \frac{1}{6} \)
- Both fractions already have a common denominator (6).
- Divide the numerators: \( 3 \div 1 = 3 \).
- Simplify: \( 3 \).

Answer: \( 3 \)

#### 12. \( \frac{1}{6} \div \frac{5}{6} \)
- Both fractions already have a common denominator (6).
- Divide the numerators: \( 1 \div 5 = \frac{1}{5} \).
- Simplify: \( \frac{1}{5} \).

Answer: \( \frac{1}{5} \)

#### 13. \( \frac{2}{5} \div \frac{1}{5} \)
- Both fractions already have a common denominator (5).
- Divide the numerators: \( 2 \div 1 = 2 \).
- Simplify: \( 2 \).

Answer: \( 2 \)

#### 14. \( \frac{2}{5} \div \frac{2}{5} \)
- Both fractions already have a common denominator (5).
- Divide the numerators: \( 2 \div 2 = 1 \).
- Simplify: \( 1 \).

Answer: \( 1 \)

#### 15. \( \frac{3}{8} \div \frac{4}{8} \)
- Both fractions already have a common denominator (8).
- Divide the numerators: \( 3 \div 4 = \frac{3}{4} \).
- Simplify: \( \frac{3}{4} \).

Answer: \( \frac{3}{4} \)

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ \frac{6}{5} \\
2. & \ \frac{1}{3} \\
3. & \ \frac{2}{3} \\
4. & \ \frac{5}{3} \\
5. & \ 1 \\
6. & \ 3 \\
7. & \ \frac{8}{5} \\
8. & \ 2 \\
9. & \ \frac{6}{7} \\
10. & \ 1 \\
11. & \ 3 \\
12. & \ \frac{1}{5} \\
13. & \ 2 \\
14. & \ 1 \\
15. & \ \frac{3}{4}
\end{aligned}
}
\]