Worksheet for practicing multiplication and division of fractions.

Problem: Solving the given problems involving multiplying and dividing fractions.

#### Step-by-Step Solutions:

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1. \( \frac{1}{2} \times \frac{5}{4} \)

To multiply fractions, multiply the numerators together and the denominators together:
\[
\frac{1}{2} \times \frac{5}{4} = \frac{1 \times 5}{2 \times 4} = \frac{5}{8}
\]

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

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2. \( \frac{1}{6} \div \frac{8}{11} \)

To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
\[
\frac{1}{6} \div \frac{8}{11} = \frac{1}{6} \times \frac{11}{8} = \frac{1 \times 11}{6 \times 8} = \frac{11}{48}
\]

Answer: \( \boxed{\frac{11}{48}} \)

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3. \( \frac{1}{3} \div \frac{13}{9} \)

Again, to divide fractions, multiply the first fraction by the reciprocal of the second fraction:
\[
\frac{1}{3} \div \frac{13}{9} = \frac{1}{3} \times \frac{9}{13} = \frac{1 \times 9}{3 \times 13} = \frac{9}{39}
\]
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3:
\[
\frac{9}{39} = \frac{9 \div 3}{39 \div 3} = \frac{3}{13}
\]

Answer: \( \boxed{\frac{3}{13}} \)

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4. \( \frac{13}{4} \div \frac{1}{2} \)

Multiply the first fraction by the reciprocal of the second fraction:
\[
\frac{13}{4} \div \frac{1}{2} = \frac{13}{4} \times \frac{2}{1} = \frac{13 \times 2}{4 \times 1} = \frac{26}{4}
\]
Simplify the fraction by dividing the numerator and denominator by their GCD, which is 2:
\[
\frac{26}{4} = \frac{26 \div 2}{4 \div 2} = \frac{13}{2}
\]

Answer: \( \boxed{\frac{13}{2}} \)

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5. \( \frac{17}{6} \div \frac{3}{5} \)

Multiply the first fraction by the reciprocal of the second fraction:
\[
\frac{17}{6} \div \frac{3}{5} = \frac{17}{6} \times \frac{5}{3} = \frac{17 \times 5}{6 \times 3} = \frac{85}{18}
\]

Answer: \( \boxed{\frac{85}{18}} \)

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6. \( \frac{1}{4} \times \frac{5}{3} \)

Multiply the numerators and denominators:
\[
\frac{1}{4} \times \frac{5}{3} = \frac{1 \times 5}{4 \times 3} = \frac{5}{12}
\]

Answer: \( \boxed{\frac{5}{12}} \)

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7. \( \frac{11}{2} \div \frac{1}{2} \)

Multiply the first fraction by the reciprocal of the second fraction:
\[
\frac{11}{2} \div \frac{1}{2} = \frac{11}{2} \times \frac{2}{1} = \frac{11 \times 2}{2 \times 1} = \frac{22}{2}
\]
Simplify the fraction:
\[
\frac{22}{2} = 11
\]

Answer: \( \boxed{11} \)

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8. \( \frac{4}{3} \div \frac{11}{12} \)

Multiply the first fraction by the reciprocal of the second fraction:
\[
\frac{4}{3} \div \frac{11}{12} = \frac{4}{3} \times \frac{12}{11} = \frac{4 \times 12}{3 \times 11} = \frac{48}{33}
\]
Simplify the fraction by dividing the numerator and denominator by their GCD, which is 3:
\[
\frac{48}{33} = \frac{48 \div 3}{33 \div 3} = \frac{16}{11}
\]

Answer: \( \boxed{\frac{16}{11}} \)

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9. \( \frac{1}{3} \times \frac{20}{9} \)

Multiply the numerators and denominators:
\[
\frac{1}{3} \times \frac{20}{9} = \frac{1 \times 20}{3 \times 9} = \frac{20}{27}
\]

Answer: \( \boxed{\frac{20}{27}} \)

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10. \( \frac{13}{7} \times \frac{14}{11} \)

Multiply the numerators and denominators:
\[
\frac{13}{7} \times \frac{14}{11} = \frac{13 \times 14}{7 \times 11} = \frac{182}{77}
\]
Simplify the fraction by dividing the numerator and denominator by their GCD, which is 7:
\[
\frac{182}{77} = \frac{182 \div 7}{77 \div 7} = \frac{26}{11}
\]

Answer: \( \boxed{\frac{26}{11}} \)

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Final Answers:

1. \( \boxed{\frac{5}{8}} \)
2. \( \boxed{\frac{11}{48}} \)
3. \( \boxed{\frac{3}{13}} \)
4. \( \boxed{\frac{13}{2}} \)
5. \( \boxed{\frac{85}{18}} \)
6. \( \boxed{\frac{5}{12}} \)
7. \( \boxed{11} \)
8. \( \boxed{\frac{16}{11}} \)
9. \( \boxed{\frac{20}{27}} \)
10. \( \boxed{\frac{26}{11}} \)