Simplify \(\frac{3}{15}\) to \(\frac{1}{5}\).
\[\begin{aligned}&\frac{5}{6}\times \frac{6}{10}\times \frac{51}{44}\\&\frac{1}{2}of\times \frac{\frac{2}{5}}{\frac{1}{5}}\times \frac{7}{15}\times \frac{6}{7}(\frac{11}{2}\times \frac{1}{2})\end{aligned}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\begin{aligned}&\frac{5}{6}\times \frac{6}{10}\times \frac{51}{44}\\&\frac{1}{2}of\times \frac{\frac{2}{5}}{\frac{1}{5}}\times \frac{7}{15}\times \frac{6}{7}\times \frac{11\times 1}{2\times 2}\end{aligned}\]
Simplify \(11\times 1\) to \(11\).
\[\begin{aligned}&\frac{5}{6}\times \frac{6}{10}\times \frac{51}{44}\\&\frac{1}{2}of\times \frac{\frac{2}{5}}{\frac{1}{5}}\times \frac{7}{15}\times \frac{6}{7}\times \frac{11}{2\times 2}\end{aligned}\]
Simplify \(2\times 2\) to \(4\).
\[\begin{aligned}&\frac{5}{6}\times \frac{6}{10}\times \frac{51}{44}\\&\frac{1}{2}of\times \frac{\frac{2}{5}}{\frac{1}{5}}\times \frac{7}{15}\times \frac{6}{7}\times \frac{11}{4}\end{aligned}\]
Simplify \(\frac{6}{10}\) to \(\frac{3}{5}\).
\[\begin{aligned}&\frac{5}{6}\times \frac{3}{5}\times \frac{51}{44}\\&\frac{1}{2}of\times \frac{\frac{2}{5}}{\frac{1}{5}}\times \frac{7}{15}\times \frac{6}{7}\times \frac{11}{4}\end{aligned}\]
Invert and multiply.
\[\begin{aligned}&\frac{5}{6}\times \frac{3}{5}\times \frac{51}{44}\\&\frac{1}{2}of(\frac{2}{5}\times 5)\times \frac{7}{15}\times \frac{6}{7}\times \frac{11}{4}\end{aligned}\]
Cancel \(5\).
\[\begin{aligned}&\frac{5}{6}\times \frac{3}{5}\times \frac{51}{44}\\&\frac{1}{2}of\times 2\times \frac{7}{15}\times \frac{6}{7}\times \frac{11}{4}\end{aligned}\]
5/6*3/5*51/44;1/2*o*f*2*7/15*6/7*11/4
