Fraction Multiplication Reciprocal
1. Multiply the fractions and mixed numbers:
21. Calculate $\frac{2}{3} \times 3 \times \frac{1}{8}$.
Simplify: $3$ as $\frac{3}{1}$.
Multiply numerators: $2 \times 3 \times 1 = 6$.
Multiply denominators: $3 \times 1 \times 8 = 24$.
Result: $\frac{6}{24} = \frac{1}{4}$ after simplification.
22. Calculate $\frac{1}{2} \times 4 \times \frac{4}{5}$.
4 as $\frac{4}{1}$.
Multiply numerators: $1 \times 4 \times 4 = 16$.
Multiply denominators: $2 \times 1 \times 5 = 10$.
Result: $\frac{16}{10} = \frac{8}{5} = 1 \frac{3}{5}$.
23. Calculate $1 \frac{1}{7} \times 2 \frac{1}{2} \times 1 \frac{7}{8}$.
Convert to improper fractions:
$1 \frac{1}{7} = \frac{8}{7}$,
$2 \frac{1}{2} = \frac{5}{2}$,
$1 \frac{7}{8} = \frac{15}{8}$.
Multiply numerators: $8 \times 5 \times 15 = 600$.
Multiply denominators: $7 \times 2 \times 8 = 112$.
Result: $\frac{600}{112} = \frac{75}{14} = 5 \frac{5}{14}$.
24. Calculate $7 \times 3 \frac{2}{3} \times 1 \frac{1}{4}$.
Convert mixed numbers:
$3 \frac{2}{3} = \frac{11}{3}$,
$1 \frac{1}{4} = \frac{5}{4}$.
Express 7 as $\frac{7}{1}$.
Multiply numerators: $7 \times 11 \times 5 = 385$.
Multiply denominators: $1 \times 3 \times 4 = 12$.
Result: $\frac{385}{12} = 32 \frac{1}{12}$.
2. Write the reciprocals:
25. Reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$.
26. Reciprocal of $\frac{3}{2}$ is $\frac{2}{3}$.
27. Reciprocal of $\frac{2}{7}$ is $\frac{7}{2}$.
28. Reciprocal of $2 \frac{1}{6} = \frac{13}{6}$ is $\frac{6}{13}$.
29. Reciprocal of $3 \frac{2}{7} = \frac{23}{7}$ is $\frac{7}{23}$.
30. Reciprocal of $4 \frac{1}{4} = \frac{17}{4}$ is $\frac{4}{17}$.