Fraction multiplication worksheet for students to practice multiplying fractions with the same denominators.

Problem Description:

The task involves multiplying fractions with the same denominators and then simplifying the results to their lowest terms. The worksheet provides 12 problems, each requiring multiplication of two fractions.

Solution Approach:

1. Multiply the Numerators: Multiply the numerators of the two fractions.
2. Multiply the Denominators: Multiply the denominators of the two fractions.
3. Simplify the Result: Reduce the resulting fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Step-by-Step Solutions:

#### Problem 1: $\frac{1}{3} \times \frac{2}{3}$
- Multiply the numerators: $1 \times 2 = 2$
- Multiply the denominators: $3 \times 3 = 9$
- Result: $\frac{2}{9}$
- Simplify: $\frac{2}{9}$ is already in its lowest terms.
- Answer: $\frac{2}{9}$

#### Problem 2: $\frac{7}{6} \times \frac{2}{6}$
- Multiply the numerators: $7 \times 2 = 14$
- Multiply the denominators: $6 \times 6 = 36$
- Result: $\frac{14}{36}$
- Simplify: The GCD of 14 and 36 is 2. Divide both by 2: $\frac{14 \div 2}{36 \div 2} = \frac{7}{18}$
- Answer: $\frac{7}{18}$

#### Problem 3: $\frac{2}{3} \times \frac{2}{3}$
- Multiply the numerators: $2 \times 2 = 4$
- Multiply the denominators: $3 \times 3 = 9$
- Result: $\frac{4}{9}$
- Simplify: $\frac{4}{9}$ is already in its lowest terms.
- Answer: $\frac{4}{9}$

#### Problem 4: $\frac{2}{5} \times \frac{3}{5}$
- Multiply the numerators: $2 \times 3 = 6$
- Multiply the denominators: $5 \times 5 = 25$
- Result: $\frac{6}{25}$
- Simplify: $\frac{6}{25}$ is already in its lowest terms.
- Answer: $\frac{6}{25}$

#### Problem 5: $\frac{3}{5} \times \frac{4}{5}$
- Multiply the numerators: $3 \times 4 = 12$
- Multiply the denominators: $5 \times 5 = 25$
- Result: $\frac{12}{25}$
- Simplify: $\frac{12}{25}$ is already in its lowest terms.
- Answer: $\frac{12}{25}$

#### Problem 6: $\frac{1}{5} \times \frac{1}{5}$
- Multiply the numerators: $1 \times 1 = 1$
- Multiply the denominators: $5 \times 5 = 25$
- Result: $\frac{1}{25}$
- Simplify: $\frac{1}{25}$ is already in its lowest terms.
- Answer: $\frac{1}{25}$

#### Problem 7: $\frac{1}{4} \times \frac{1}{4}$
- Multiply the numerators: $1 \times 1 = 1$
- Multiply the denominators: $4 \times 4 = 16$
- Result: $\frac{1}{16}$
- Simplify: $\frac{1}{16}$ is already in its lowest terms.
- Answer: $\frac{1}{16}$

#### Problem 8: $\frac{6}{6} \times \frac{6}{6}$
- Multiply the numerators: $6 \times 6 = 36$
- Multiply the denominators: $6 \times 6 = 36$
- Result: $\frac{36}{36}$
- Simplify: $\frac{36}{36} = 1$
- Answer: $1$

#### Problem 9: $\frac{5}{6} \times \frac{3}{6}$
- Multiply the numerators: $5 \times 3 = 15$
- Multiply the denominators: $6 \times 6 = 36$
- Result: $\frac{15}{36}$
- Simplify: The GCD of 15 and 36 is 3. Divide both by 3: $\frac{15 \div 3}{36 \div 3} = \frac{5}{12}$
- Answer: $\frac{5}{12}$

#### Problem 10: $\frac{3}{8} \times \frac{5}{8}$
- Multiply the numerators: $3 \times 5 = 15$
- Multiply the denominators: $8 \times 8 = 64$
- Result: $\frac{15}{64}$
- Simplify: $\frac{15}{64}$ is already in its lowest terms.
- Answer: $\frac{15}{64}$

#### Problem 11: $\frac{7}{6} \times \frac{3}{6}$
- Multiply the numerators: $7 \times 3 = 21$
- Multiply the denominators: $6 \times 6 = 36$
- Result: $\frac{21}{36}$
- Simplify: The GCD of 21 and 36 is 3. Divide both by 3: $\frac{21 \div 3}{36 \div 3} = \frac{7}{12}$
- Answer: $\frac{7}{12}$

#### Problem 12: $\frac{2}{4} \times \frac{3}{4}$
- Multiply the numerators: $2 \times 3 = 6$
- Multiply the denominators: $4 \times 4 = 16$
- Result: $\frac{6}{16}$
- Simplify: The GCD of 6 and 16 is 2. Divide both by 2: $\frac{6 \div 2}{16 \div 2} = \frac{3}{8}$
- Answer: $\frac{3}{8}$

#### Problem 13: $\frac{2}{6} \times \frac{4}{6}$
- Multiply the numerators: $2 \times 4 = 8$
- Multiply the denominators: $6 \times 6 = 36$
- Result: $\frac{8}{36}$
- Simplify: The GCD of 8 and 36 is 4. Divide both by 4: $\frac{8 \div 4}{36 \div 4} = \frac{2}{9}$
- Answer: $\frac{2}{9}$

Final Answers:

1. $\frac{2}{9}$
2. $\frac{7}{18}$
3. $\frac{4}{9}$
4. $\frac{6}{25}$
5. $\frac{12}{25}$
6. $\frac{1}{25}$
7. $\frac{1}{16}$
8. $1$
9. $\frac{5}{12}$
10. $\frac{15}{64}$
11. $\frac{7}{12}$
12. $\frac{3}{8}$
13. $\frac{2}{9}$

Boxed Final Answer:

$$
\boxed{\frac{2}{9}, \frac{7}{18}, \frac{4}{9}, \frac{6}{25}, \frac{12}{25}, \frac{1}{25}, \frac{1}{16}, 1, \frac{5}{12}, \frac{15}{64}, \frac{7}{12}, \frac{3}{8}, \frac{2}{9}}
$$