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Perform the following multiplications. Convert improper fractions to mixed numbers.
$1\frac{1}{8}\cdot 4\frac{2}{3}$
Convert each mixed number to an improper fraction.
$1\frac{1}{8}=\frac{8\cdot 1+1}{8}=\frac{9}{8}$
$4\frac{2}{3}=\frac{4\cdot 3+2}{3}=\frac{\text{14}}{3}$
$\frac{\stackrel{3}{\overline{)9}}}{\underset{4}{\overline{)8}}}\cdot \frac{\stackrel{7}{\overline{)14}}}{\underset{1}{\overline{)3}}}=\frac{3\cdot 7}{4\cdot 1}=\frac{\text{21}}{4}=5\frac{1}{4}$
$\text{16}\cdot 8\frac{1}{5}$
Convert $8\frac{1}{5}$ to an improper fraction.
$8\frac{1}{5}=\frac{5\cdot 8+1}{5}=\frac{\text{41}}{5}$
$\frac{16}{1}\cdot \frac{41}{5}$ .
There are no common factors to divide out.
$\frac{\text{16}}{1}\cdot \frac{\text{41}}{5}=\frac{\text{16}\cdot \text{41}}{1\cdot 5}=\frac{\text{656}}{5}=\text{131}\frac{1}{5}$
$9\frac{1}{6}\cdot \text{12}\frac{3}{5}$
Convert to improper fractions.
$9\frac{1}{6}=\frac{6\cdot 9+1}{6}=\frac{\text{55}}{6}$
$\text{12}\frac{3}{5}=\frac{5\cdot \text{12}+3}{5}=\frac{\text{63}}{5}$
$\frac{\stackrel{\text{11}}{\overline{)55}}}{\underset{2}{\overline{)6}}}\cdot \frac{\stackrel{\text{21}}{\overline{)63}}}{\underset{1}{\overline{)5}}}=\frac{\text{11}\cdot \text{21}}{2\cdot 1}=\frac{\text{231}}{2}=\text{115}\frac{1}{2}$
$\begin{array}{ccc}\hfill \frac{11}{8}\cdot 4\frac{1}{2}\cdot 3\frac{1}{8}& =& \frac{11}{8}\cdot \frac{\stackrel{3}{\overline{)9}}}{\underset{1}{\overline{)2}}}\cdot \frac{\stackrel{5}{\overline{)10}}}{\underset{1}{\overline{)3}}}\hfill \\ & =& \frac{11\cdot 3\cdot 5}{8\cdot 1\cdot 1}=\frac{165}{8}=20\frac{5}{8}\hfill \end{array}$
Perform the following multiplications. Convert improper fractions to mixed numbers.
$2\frac{2}{3}\cdot 2\frac{1}{4}$
6
$6\frac{2}{3}\cdot 3\frac{3}{\text{10}}$
22
$7\frac{1}{8}\cdot \text{12}$
$\text{85}\frac{1}{2}$
$2\frac{2}{5}\cdot 3\frac{3}{4}\cdot 3\frac{1}{3}$
30
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