Grade 6 worksheet focused on multiplying fractions, providing 12 practice problems for students to solve.

To solve the problems in the "Multiplying Fractions" worksheet, we need to multiply the numerators together and the denominators together. Let's go through each problem step by step.

Section 1: First Set of Problems

#### Problem 1: $\frac{1}{2} \times \frac{1}{2}$
- Multiply the numerators: $1 \times 1 = 1$
- Multiply the denominators: $2 \times 2 = 4$
- Result: $\frac{1}{4}$

#### Problem 2: $\frac{3}{4} \times \frac{1}{5}$
- Multiply the numerators: $3 \times 1 = 3$
- Multiply the denominators: $4 \times 5 = 20$
- Result: $\frac{3}{20}$

#### Problem 3: $\frac{9}{10} \times \frac{5}{6}$
- Multiply the numerators: $9 \times 5 = 45$
- Multiply the denominators: $10 \times 6 = 60$
- Simplify: $\frac{45}{60} = \frac{3}{4}$ (divide numerator and denominator by 15)
- Result: $\frac{3}{4}$

#### Problem 4: $\frac{1}{5} \times \frac{10}{11}$
- Multiply the numerators: $1 \times 10 = 10$
- Multiply the denominators: $5 \times 11 = 55$
- Simplify: $\frac{10}{55} = \frac{2}{11}$ (divide numerator and denominator by 5)
- Result: $\frac{2}{11}$

#### Problem 5: $\frac{3}{7} \times \frac{1}{9}$
- Multiply the numerators: $3 \times 1 = 3$
- Multiply the denominators: $7 \times 9 = 63$
- Result: $\frac{3}{63} = \frac{1}{21}$ (simplify by dividing by 3)
- Result: $\frac{1}{21}$

#### Problem 6: $\frac{4}{9} \times \frac{3}{8}$
- Multiply the numerators: $4 \times 3 = 12$
- Multiply the denominators: $9 \times 8 = 72$
- Simplify: $\frac{12}{72} = \frac{1}{6}$ (divide numerator and denominator by 12)
- Result: $\frac{1}{6}$

#### Problem 7: $\frac{5}{6} \times \frac{10}{15}$
- Multiply the numerators: $5 \times 10 = 50$
- Multiply the denominators: $6 \times 15 = 90$
- Simplify: $\frac{50}{90} = \frac{5}{9}$ (divide numerator and denominator by 10)
- Result: $\frac{5}{9}$

#### Problem 8: $\frac{9}{10} \times \frac{8}{9}$
- Multiply the numerators: $9 \times 8 = 72$
- Multiply the denominators: $10 \times 9 = 90$
- Simplify: $\frac{72}{90} = \frac{4}{5}$ (divide numerator and denominator by 18)
- Result: $\frac{4}{5}$

#### Problem 9: $\frac{4}{9} \times \frac{1}{8}$
- Multiply the numerators: $4 \times 1 = 4$
- Multiply the denominators: $9 \times 8 = 72$
- Simplify: $\frac{4}{72} = \frac{1}{18}$ (divide numerator and denominator by 4)
- Result: $\frac{1}{18}$

#### Problem 10: $\frac{6}{7} \times \frac{4}{5}$
- Multiply the numerators: $6 \times 4 = 24$
- Multiply the denominators: $7 \times 5 = 35$
- Result: $\frac{24}{35}$

#### Problem 11: $\frac{14}{20} \times \frac{10}{12}$
- Multiply the numerators: $14 \times 10 = 140$
- Multiply the denominators: $20 \times 12 = 240$
- Simplify: $\frac{140}{240} = \frac{7}{12}$ (divide numerator and denominator by 20)
- Result: $\frac{7}{12}$

#### Problem 12: $\frac{5}{7} \times \frac{1}{2}$
- Multiply the numerators: $5 \times 1 = 5$
- Multiply the denominators: $7 \times 2 = 14$
- Result: $\frac{5}{14}$

Section 2: Second Set of Problems

#### Problem 1: $\frac{12}{15} \times \frac{5}{6}$
- Multiply the numerators: $12 \times 5 = 60$
- Multiply the denominators: $15 \times 6 = 90$
- Simplify: $\frac{60}{90} = \frac{2}{3}$ (divide numerator and denominator by 30)
- Result: $\frac{2}{3}$

#### Problem 2: $\frac{8}{9} \times \frac{9}{10}$
- Multiply the numerators: $8 \times 9 = 72$
- Multiply the denominators: $9 \times 10 = 90$
- Simplify: $\frac{72}{90} = \frac{4}{5}$ (divide numerator and denominator by 18)
- Result: $\frac{4}{5}$

#### Problem 3: $\frac{1}{2} \times \frac{3}{4}$
- Multiply the numerators: $1 \times 3 = 3$
- Multiply the denominators: $2 \times 4 = 8$
- Result: $\frac{3}{8}$

#### Problem 4: $\frac{7}{8} \times \frac{2}{5}$
- Multiply the numerators: $7 \times 2 = 14$
- Multiply the denominators: $8 \times 5 = 40$
- Simplify: $\frac{14}{40} = \frac{7}{20}$ (divide numerator and denominator by 2)
- Result: $\frac{7}{20}$

#### Problem 5: $\frac{6}{7} \times \frac{1}{7}$
- Multiply the numerators: $6 \times 1 = 6$
- Multiply the denominators: $7 \times 7 = 49$
- Result: $\frac{6}{49}$

#### Problem 6: $\frac{8}{10} \times \frac{5}{7}$
- Multiply the numerators: $8 \times 5 = 40$
- Multiply the denominators: $10 \times 7 = 70$
- Simplify: $\frac{40}{70} = \frac{4}{7}$ (divide numerator and denominator by 10)
- Result: $\frac{4}{7}$

#### Problem 7: $\frac{1}{10} \times \frac{1}{5}$
- Multiply the numerators: $1 \times 1 = 1$
- Multiply the denominators: $10 \times 5 = 50$
- Result: $\frac{1}{50}$

#### Problem 8: $\frac{7}{8} \times \frac{2}{5}$
- Multiply the numerators: $7 \times 2 = 14$
- Multiply the denominators: $8 \times 5 = 40$
- Simplify: $\frac{14}{40} = \frac{7}{20}$ (divide numerator and denominator by 2)
- Result: $\frac{7}{20}$

#### Problem 9: $\frac{8}{11} \times \frac{3}{4}$
- Multiply the numerators: $8 \times 3 = 24$
- Multiply the denominators: $11 \times 4 = 44$
- Simplify: $\frac{24}{44} = \frac{6}{11}$ (divide numerator and denominator by 4)
- Result: $\frac{6}{11}$

#### Problem 10: $\frac{5}{9} \times \frac{3}{4}$
- Multiply the numerators: $5 \times 3 = 15$
- Multiply the denominators: $9 \times 4 = 36$
- Simplify: $\frac{15}{36} = \frac{5}{12}$ (divide numerator and denominator by 3)
- Result: $\frac{5}{12}$

#### Problem 11: $\frac{3}{4} \times \frac{3}{4}$
- Multiply the numerators: $3 \times 3 = 9$
- Multiply the denominators: $4 \times 4 = 16$
- Result: $\frac{9}{16}$

#### Problem 12: $\frac{4}{5} \times \frac{8}{10}$
- Multiply the numerators: $4 \times 8 = 32$
- Multiply the denominators: $5 \times 10 = 50$
- Simplify: $\frac{32}{50} = \frac{16}{25}$ (divide numerator and denominator by 2)
- Result: $\frac{16}{25}$

Final Answers:

First Set:
1. $\frac{1}{4}$
2. $\frac{3}{20}$
3. $\frac{3}{4}$
4. $\frac{2}{11}$
5. $\frac{1}{21}$
6. $\frac{1}{6}$
7. $\frac{5}{9}$
8. $\frac{4}{5}$
9. $\frac{1}{18}$
10. $\frac{24}{35}$
11. $\frac{7}{12}$
12. $\frac{5}{14}$

Second Set:
1. $\frac{2}{3}$
2. $\frac{4}{5}$
3. $\frac{3}{8}$
4. $\frac{7}{20}$
5. $\frac{6}{49}$
6. $\frac{4}{7}$
7. $\frac{1}{50}$
8. $\frac{7}{20}$
9. $\frac{6}{11}$
10. $\frac{5}{12}$
11. $\frac{9}{16}$
12. $\frac{16}{25}$

Boxed Final Answer:

\[
\boxed{
\begin{array}{ccc}
\text{First Set:} & & \\
1. \frac{1}{4} & 5. \frac{1}{21} & 9. \frac{1}{18} \\
2. \frac{3}{20} & 6. \frac{1}{6} & 10. \frac{24}{35} \\
3. \frac{3}{4} & 7. \frac{5}{9} & 11. \frac{7}{12} \\
4. \frac{2}{11} & 8. \frac{4}{5} & 12. \frac{5}{14} \\
\\
\text{Second Set:} & & \\
1. \frac{2}{3} & 5. \frac{6}{49} & 9. \frac{6}{11} \\
2. \frac{4}{5} & 6. \frac{4}{7} & 10. \frac{5}{12} \\
3. \frac{3}{8} & 7. \frac{1}{50} & 11. \frac{9}{16} \\
4. \frac{7}{20} & 8. \frac{7}{20} & 12. \frac{16}{25} \\
\end{array}
}
\]