Math worksheet focusing on multiplying and dividing fractions, with exercises for finding products and quotients.

Let's solve the problems step by step. The worksheet involves multiplication and division of fractions, mixed numbers, and whole numbers. Here are the solutions with explanations:

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Section 1: Multiply

#### Problem 1: \( 1 \times \frac{1}{6} \)
- Multiplying any number by 1 gives the same number.
- Therefore, \( 1 \times \frac{1}{6} = \frac{1}{6} \).

#### Problem 2: \( 9 \times \frac{7}{10} \)
- Multiply the whole number by the numerator of the fraction and keep the denominator the same.
- \( 9 \times \frac{7}{10} = \frac{9 \times 7}{10} = \frac{63}{10} \).

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Section 2: Find the product

#### Problem 1: \( \frac{6}{12} \times \frac{2}{10} \)
- Simplify each fraction first:
- \( \frac{6}{12} = \frac{1}{2} \)
- \( \frac{2}{10} = \frac{1}{5} \)
- Now multiply:
- \( \frac{1}{2} \times \frac{1}{5} = \frac{1 \times 1}{2 \times 5} = \frac{1}{10} \).

#### Problem 2: \( \frac{1}{16} \times \frac{7}{21} \)
- Simplify \( \frac{7}{21} \):
- \( \frac{7}{21} = \frac{1}{3} \)
- Now multiply:
- \( \frac{1}{16} \times \frac{1}{3} = \frac{1 \times 1}{16 \times 3} = \frac{1}{48} \).

#### Problem 3: \( \frac{8}{9} \times \frac{1}{2} \)
- Multiply the numerators and denominators:
- \( \frac{8}{9} \times \frac{1}{2} = \frac{8 \times 1}{9 \times 2} = \frac{8}{18} \)
- Simplify \( \frac{8}{18} \):
- \( \frac{8}{18} = \frac{4}{9} \).

#### Problem 4: \( \frac{11}{20} \times \frac{4}{14} \)
- Simplify \( \frac{4}{14} \):
- \( \frac{4}{14} = \frac{2}{7} \)
- Now multiply:
- \( \frac{11}{20} \times \frac{2}{7} = \frac{11 \times 2}{20 \times 7} = \frac{22}{140} \)
- Simplify \( \frac{22}{140} \):
- \( \frac{22}{140} = \frac{11}{70} \).

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Section 3: Find the product

#### Problem 1: \( \frac{14}{4} \times \frac{33}{10} \)
- Simplify \( \frac{14}{4} \):
- \( \frac{14}{4} = \frac{7}{2} \)
- Now multiply:
- \( \frac{7}{2} \times \frac{33}{10} = \frac{7 \times 33}{2 \times 10} = \frac{231}{20} \).

#### Problem 2: \( \frac{11}{3} \times \frac{26}{12} \)
- Simplify \( \frac{26}{12} \):
- \( \frac{26}{12} = \frac{13}{6} \)
- Now multiply:
- \( \frac{11}{3} \times \frac{13}{6} = \frac{11 \times 13}{3 \times 6} = \frac{143}{18} \).

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Section 4: Find the product

#### Problem 1: \( 3 \frac{2}{8} \times \frac{9}{10} \)
- Convert the mixed number to an improper fraction:
- \( 3 \frac{2}{8} = \frac{3 \times 8 + 2}{8} = \frac{24 + 2}{8} = \frac{26}{8} \)
- Simplify \( \frac{26}{8} \):
- \( \frac{26}{8} = \frac{13}{4} \)
- Now multiply:
- \( \frac{13}{4} \times \frac{9}{10} = \frac{13 \times 9}{4 \times 10} = \frac{117}{40} \).

#### Problem 2: \( 1 \frac{1}{3} \times \frac{3}{8} \)
- Convert the mixed number to an improper fraction:
- \( 1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3} \)
- Now multiply:
- \( \frac{4}{3} \times \frac{3}{8} = \frac{4 \times 3}{3 \times 8} = \frac{12}{24} \)
- Simplify \( \frac{12}{24} \):
- \( \frac{12}{24} = \frac{1}{2} \).

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Section 5: Find the quotient

#### Problem 1: \( \frac{1}{4} \div \frac{9}{10} \)
- To divide fractions, multiply by the reciprocal of the divisor:
- \( \frac{1}{4} \div \frac{9}{10} = \frac{1}{4} \times \frac{10}{9} = \frac{1 \times 10}{4 \times 9} = \frac{10}{36} \)
- Simplify \( \frac{10}{36} \):
- \( \frac{10}{36} = \frac{5}{18} \).

#### Problem 2: \( \frac{5}{9} \div \frac{1}{2} \)
- Multiply by the reciprocal of the divisor:
- \( \frac{5}{9} \div \frac{1}{2} = \frac{5}{9} \times \frac{2}{1} = \frac{5 \times 2}{9 \times 1} = \frac{10}{9} \).

#### Problem 3: \( 9 \frac{1}{2} \div \frac{1}{2} \)
- Convert the mixed number to an improper fraction:
- \( 9 \frac{1}{2} = \frac{9 \times 2 + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2} \)
- Multiply by the reciprocal of the divisor:
- \( \frac{19}{2} \div \frac{1}{2} = \frac{19}{2} \times \frac{2}{1} = \frac{19 \times 2}{2 \times 1} = \frac{38}{2} = 19 \).

#### Problem 4: \( 9 \frac{6}{10} \div \frac{4}{10} \)
- Convert the mixed number to an improper fraction:
- \( 9 \frac{6}{10} = \frac{9 \times 10 + 6}{10} = \frac{90 + 6}{10} = \frac{96}{10} \)
- Simplify \( \frac{96}{10} \):
- \( \frac{96}{10} = \frac{48}{5} \)
- Multiply by the reciprocal of the divisor:
- \( \frac{48}{5} \div \frac{4}{10} = \frac{48}{5} \times \frac{10}{4} = \frac{48 \times 10}{5 \times 4} = \frac{480}{20} = 24 \).

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Section 6: Divide

#### Problem 1: \( 1 \div \frac{3}{10} \)
- Multiply by the reciprocal of the divisor:
- \( 1 \div \frac{3}{10} = 1 \times \frac{10}{3} = \frac{10}{3} \).

#### Problem 2: \( 6 \div \frac{1}{2} \)
- Multiply by the reciprocal of the divisor:
- \( 6 \div \frac{1}{2} = 6 \times \frac{2}{1} = \frac{6 \times 2}{1} = 12 \).

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Section 7: Find the quotient

#### Problem 1: \( 9 \frac{2}{5} \div 1 \frac{1}{3} \)
- Convert both mixed numbers to improper fractions:
- \( 9 \frac{2}{5} = \frac{9 \times 5 + 2}{5} = \frac{45 + 2}{5} = \frac{47}{5} \)
- \( 1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3} \)
- Multiply by the reciprocal of the divisor:
- \( \frac{47}{5} \div \frac{4}{3} = \frac{47}{5} \times \frac{3}{4} = \frac{47 \times 3}{5 \times 4} = \frac{141}{20} \).

#### Problem 2: \( 6 \frac{1}{12} \div 4 \frac{2}{5} \)
- Convert both mixed numbers to improper fractions:
- \( 6 \frac{1}{12} = \frac{6 \times 12 + 1}{12} = \frac{72 + 1}{12} = \frac{73}{12} \)
- \( 4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5} \)
- Multiply by the reciprocal of the divisor:
- \( \frac{73}{12} \div \frac{22}{5} = \frac{73}{12} \times \frac{5}{22} = \frac{73 \times 5}{12 \times 22} = \frac{365}{264} \).

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Final Answers

1. \( \frac{1}{6} \)
2. \( \frac{63}{10} \)
3. \( \frac{1}{10} \)
4. \( \frac{1}{48} \)
5. \( \frac{4}{9} \)
6. \( \frac{11}{70} \)
7. \( \frac{231}{20} \)
8. \( \frac{143}{18} \)
9. \( \frac{117}{40} \)
10. \( \frac{1}{2} \)
11. \( \frac{5}{18} \)
12. \( \frac{10}{9} \)
13. \( 19 \)
14. \( 24 \)
15. \( \frac{10}{3} \)
16. \( 12 \)
17. \( \frac{141}{20} \)
18. \( \frac{365}{264} \)

\[
\boxed{\frac{1}{6}, \frac{63}{10}, \frac{1}{10}, \frac{1}{48}, \frac{4}{9}, \frac{11}{70}, \frac{231}{20}, \frac{143}{18}, \frac{117}{40}, \frac{1}{2}, \frac{5}{18}, \frac{10}{9}, 19, 24, \frac{10}{3}, 12, \frac{141}{20}, \frac{365}{264}}
\]