Question

multiply: (change improper fractions to mixed numbers. reduce.)
(1) $\frac{1}{4} \times \frac{3}{5} =$
(2) $\frac{1}{3} \times \frac{3}{4} =$
(3) $\frac{12}{11} \times \frac{3}{28} =$
(4) $\frac{5}{9} \times \frac{9}{20} =$
(5) $\frac{7}{16} \times \frac{10}{21} =$
(6) $\frac{8}{9} \times \frac{27}{20} =$
(7) $\frac{12}{1} \times \frac{5}{4} \times \frac{1}{3} =$
(8) $\frac{3}{7} \times \frac{12}{5} \times \frac{7}{18} =$
(9) $\frac{5}{8} \times \frac{11}{15} \times \frac{3}{2} =$
(10) $12 \times \frac{5}{16} =$
(11) $\frac{7}{36} \times 8 =$
(12) $\frac{9}{25} \times 3\frac{1}{3} =$
(13) $2\frac{1}{10} \times 8\frac{1}{3} \times \frac{2}{7} =$
(14) $3\frac{1}{5} \times 2\frac{1}{2} \times 1\frac{1}{12} =$

Explanation:

Step1: Simplify (13) mixed numbers

Convert to improper fractions:
$2\frac{1}{10}=\frac{21}{10}$, $8\frac{1}{3}=\frac{25}{3}$
Expression: $2\frac{1}{10} \times 8\frac{1}{3} \times \frac{2}{7} = \frac{21}{10} \times \frac{25}{3} \times \frac{2}{7}$

Step2: Cross-reduce (13) fractions

Cancel common factors:
$\frac{21}{10} \times \frac{25}{3} \times \frac{2}{7} = \frac{\cancel{21}^3}{\cancel{10}^1} \times \frac{\cancel{25}^5}{\cancel{3}^1} \times \frac{\cancel{2}^1}{\cancel{7}^1}$
Expression: $3 \times 5 \times \frac{1}{1} = 15$

Step3: Simplify (14) mixed numbers

Convert to improper fractions:
$3\frac{1}{5}=\frac{16}{5}$, $2\frac{1}{2}=\frac{5}{2}$, $1\frac{1}{12}=\frac{13}{12}$
Expression: $3\frac{1}{5} \times 2\frac{1}{2} \times 1\frac{1}{12} = \frac{16}{5} \times \frac{5}{2} \times \frac{13}{12}$

Step4: Cross-reduce (14) fractions

Cancel common factors:
$\frac{16}{5} \times \frac{5}{2} \times \frac{13}{12} = \frac{\cancel{16}^4}{\cancel{5}^1} \times \frac{\cancel{5}^1}{\cancel{2}^1} \times \frac{13}{\cancel{12}^3}$
Expression: $\frac{4 \times 13}{3} = \frac{52}{3}$

Step5: Convert (14) to mixed number

Divide numerator by denominator:
$\frac{52}{3} = 17\frac{1}{3}$

Answer:

(13) $15$
(14) $17\frac{1}{3}$

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Verified Answers for Completed Problems:

(1) $\frac{3}{20}$
(2) $\frac{1}{4}$
(3) $\frac{9}{22}$
(4) $\frac{1}{4}$
(5) $\frac{5}{24}$
(6) $1\frac{4}{5}$
(7) $5$
(8) $\frac{2}{5}$
(9) $\frac{11}{16}$
(10) $3\frac{3}{4}$
(11) $1\frac{5}{9}$
(12) $1\frac{1}{5}$