Grade 6 fraction multiplication worksheet from K5 Learning.

Problem: Solve the mixed multiplication problems from the worksheet.

#### Worksheet Details
The worksheet is titled "Mixed Multiplication Problems" and is designed for Grade 6 students. It involves multiplying fractions, mixed numbers, and whole numbers. The task is to find the product of each given expression.

#### Solution Approach
1. Convert Mixed Numbers to Improper Fractions: If any of the numbers are mixed numbers (e.g., $ 4 \frac{3}{6} $), convert them to improper fractions.
2. Multiply Fractions: Multiply the numerators together and the denominators together.
3. Simplify the Result: Reduce the resulting fraction to its simplest form if possible.
4. Convert Back to Mixed Numbers: If the result is an improper fraction, convert it back to a mixed number.

Let's solve each problem step by step.

---

Problem 1: $ 6 \times 12 \frac{1}{2} $

- Convert $ 12 \frac{1}{2} $ to an improper fraction:
$$
12 \frac{1}{2} = \frac{12 \times 2 + 1}{2} = \frac{25}{2}
$$
- Multiply:
$$
6 \times \frac{25}{2} = \frac{6 \times 25}{2} = \frac{150}{2} = 75
$$
- Answer: $ 75 $

---

Problem 2: $ 4 \frac{3}{6} \times 11 \frac{7}{12} $

- Simplify $ 4 \frac{3}{6} $:
$$
4 \frac{3}{6} = 4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}
$$
- Simplify $ 11 \frac{7}{12} $:
$$
11 \frac{7}{12} = \frac{11 \times 12 + 7}{12} = \frac{139}{12}
$$
- Multiply:
$$
\frac{9}{2} \times \frac{139}{12} = \frac{9 \times 139}{2 \times 12} = \frac{1251}{24}
$$
- Simplify $ \frac{1251}{24} $:
$$
\frac{1251}{24} = 52 \frac{3}{8} \quad (\text{since } 1251 \div 24 = 52 \text{ remainder } 3)
$$
- Answer: $ 52 \frac{3}{8} $

---

Problem 3: $ 3 \frac{3}{8} \times 1 \frac{1}{3} $

- Convert $ 3 \frac{3}{8} $ to an improper fraction:
$$
3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{27}{8}
$$
- Convert $ 1 \frac{1}{3} $ to an improper fraction:
$$
1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}
$$
- Multiply:
$$
\frac{27}{8} \times \frac{4}{3} = \frac{27 \times 4}{8 \times 3} = \frac{108}{24}
$$
- Simplify $ \frac{108}{24} $:
$$
\frac{108}{24} = \frac{9}{2} = 4 \frac{1}{2}
$$
- Answer: $ 4 \frac{1}{2} $

---

Problem 4: $ \frac{7}{9} \times 6 \frac{2}{5} $

- Convert $ 6 \frac{2}{5} $ to an improper fraction:
$$
6 \frac{2}{5} = \frac{6 \times 5 + 2}{5} = \frac{32}{5}
$$
- Multiply:
$$
\frac{7}{9} \times \frac{32}{5} = \frac{7 \times 32}{9 \times 5} = \frac{224}{45}
$$
- Simplify $ \frac{224}{45} $:
$$
\frac{224}{45} = 4 \frac{44}{45}
$$
- Answer: $ 4 \frac{44}{45} $

---

Problem 5: $ \frac{4}{5} \times 6 \frac{1}{4} $

- Convert $ 6 \frac{1}{4} $ to an improper fraction:
$$
6 \frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{25}{4}
$$
- Multiply:
$$
\frac{4}{5} \times \frac{25}{4} = \frac{4 \times 25}{5 \times 4} = \frac{100}{20} = 5
$$
- Answer: $ 5 $

---

Problem 6: $ \frac{4}{10} \times 4 \frac{1}{3} $

- Simplify $ \frac{4}{10} $:
$$
\frac{4}{10} = \frac{2}{5}
$$
- Convert $ 4 \frac{1}{3} $ to an improper fraction:
$$
4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{13}{3}
$$
- Multiply:
$$
\frac{2}{5} \times \frac{13}{3} = \frac{2 \times 13}{5 \times 3} = \frac{26}{15}
$$
- Simplify $ \frac{26}{15} $:
$$
\frac{26}{15} = 1 \frac{11}{15}
$$
- Answer: $ 1 \frac{11}{15} $

---

Problem 7: $ \frac{4}{8} \times \frac{43}{7} $

- Simplify $ \frac{4}{8} $:
$$
\frac{4}{8} = \frac{1}{2}
$$
- Multiply:
$$
\frac{1}{2} \times \frac{43}{7} = \frac{1 \times 43}{2 \times 7} = \frac{43}{14}
$$
- Simplify $ \frac{43}{14} $:
$$
\frac{43}{14} = 3 \frac{1}{14}
$$
- Answer: $ 3 \frac{1}{14} $

---

Problem 8: $ \frac{4}{12} \times \frac{19}{3} $

- Simplify $ \frac{4}{12} $:
$$
\frac{4}{12} = \frac{1}{3}
$$
- Multiply:
$$
\frac{1}{3} \times \frac{19}{3} = \frac{1 \times 19}{3 \times 3} = \frac{19}{9}
$$
- Simplify $ \frac{19}{9} $:
$$
\frac{19}{9} = 2 \frac{1}{9}
$$
- Answer: $ 2 \frac{1}{9} $

---

Problem 9: $ \frac{2}{5} \times \frac{19}{4} $

- Multiply:
$$
\frac{2}{5} \times \frac{19}{4} = \frac{2 \times 19}{5 \times 4} = \frac{38}{20}
$$
- Simplify $ \frac{38}{20} $:
$$
\frac{38}{20} = \frac{19}{10} = 1 \frac{9}{10}
$$
- Answer: $ 1 \frac{9}{10} $

---

Problem 10: $ \frac{1}{4} \times 9 $

- Multiply:
$$
\frac{1}{4} \times 9 = \frac{1 \times 9}{4} = \frac{9}{4}
$$
- Simplify $ \frac{9}{4} $:
$$
\frac{9}{4} = 2 \frac{1}{4}
$$
- Answer: $ 2 \frac{1}{4} $

---

Problem 11: $ \frac{5}{11} \times 6 $

- Multiply:
$$
\frac{5}{11} \times 6 = \frac{5 \times 6}{11} = \frac{30}{11}
$$
- Simplify $ \frac{30}{11} $:
$$
\frac{30}{11} = 2 \frac{8}{11}
$$
- Answer: $ 2 \frac{8}{11} $

---

Problem 12: $ \frac{6}{5} \times 11 $

- Multiply:
$$
\frac{6}{5} \times 11 = \frac{6 \times 11}{5} = \frac{66}{5}
$$
- Simplify $ \frac{66}{5} $:
$$
\frac{66}{5} = 13 \frac{1}{5}
$$
- Answer: $ 13 \frac{1}{5} $

---

Problem 13: $ 7 \frac{8}{11} \times 6 $

- Convert $ 7 \frac{8}{11} $ to an improper fraction:
$$
7 \frac{8}{11} = \frac{7 \times 11 + 8}{11} = \frac{85}{11}
$$
- Multiply:
$$
\frac{85}{11} \times 6 = \frac{85 \times 6}{11} = \frac{510}{11}
$$
- Simplify $ \frac{510}{11} $:
$$
\frac{510}{11} = 46 \frac{4}{11}
$$
- Answer: $ 46 \frac{4}{11} $

---

Problem 14: $ 2 \frac{1}{2} \times 8 $

- Convert $ 2 \frac{1}{2} $ to an improper fraction:
$$
2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}
$$
- Multiply:
$$
\frac{5}{2} \times 8 = \frac{5 \times 8}{2} = \frac{40}{2} = 20
$$
- Answer: $ 20 $

---

Problem 15: $ 7 \frac{3}{6} \times 5 $

- Simplify $ 7 \frac{3}{6} $:
$$
7 \frac{3}{6} = 7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{15}{2}
$$
- Multiply:
$$
\frac{15}{2} \times 5 = \frac{15 \times 5}{2} = \frac{75}{2}
$$
- Simplify $ \frac{75}{2} $:
$$
\frac{75}{2} = 37 \frac{1}{2}
$$
- Answer: $ 37 \frac{1}{2} $

---

Problem 16: $ 6 \times 2 $

- Multiply:
$$
6 \times 2 = 12
$$
- Answer: $ 12 $

---

Problem 17: $ 15 \times 2 $

- Multiply:
$$
15 \times 2 = 30
$$
- Answer: $ 30 $

---

Problem 18: $ 9 \times 14 $

- Multiply:
$$
9 \times 14 = 126
$$
- Answer: $ 126 $

---

Final Answers

$$
\boxed{
\begin{aligned}
1. & \ 75 \\
2. & \ 52 \frac{3}{8} \\
3. & \ 4 \frac{1}{2} \\
4. & \ 4 \frac{44}{45} \\
5. & \ 5 \\
6. & \ 1 \frac{11}{15} \\
7. & \ 3 \frac{1}{14} \\
8. & \ 2 \frac{1}{9} \\
9. & \ 1 \frac{9}{10} \\
10. & \ 2 \frac{1}{4} \\
11. & \ 2 \frac{8}{11} \\
12. & \ 13 \frac{1}{5} \\
13. & \ 46 \frac{4}{11} \\
14. & \ 20 \\
15. & \ 37 \frac{1}{2} \\
16. & \ 12 \\
17. & \ 30 \\
18. & \ 126 \\
\end{aligned}
}
$$