Simplify \(\frac{31}{2}-\frac{21}{4}\) to \(\frac{41}{4}\).
\[\begin{aligned}&\frac{7}{6}\times \frac{41}{4}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{9}\\&7og(\frac{2}{3}-\frac{9}{6})+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{2}\end{aligned}\]
Simplify \(\frac{9}{6}\) to \(\frac{3}{2}\).
\[\begin{aligned}&\frac{7}{6}\times \frac{41}{4}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{9}\\&7og(\frac{2}{3}-\frac{3}{2})+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{2}\end{aligned}\]
Simplify \(\frac{2}{3}-\frac{3}{2}\) to \(-\frac{5}{6}\).
\[\begin{aligned}&\frac{7}{6}\times \frac{41}{4}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{9}\\&7og\times \frac{-5}{6}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{2}\end{aligned}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\begin{aligned}&\frac{7\times 41}{6\times 4}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{9}\\&7og\times \frac{-5}{6}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{2}\end{aligned}\]
Simplify \(7\times 41\) to \(287\).
\[\begin{aligned}&\frac{287}{6\times 4}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{9}\\&7og\times \frac{-5}{6}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{2}\end{aligned}\]
Simplify \(6\times 4\) to \(24\).
\[\begin{aligned}&\frac{287}{24}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{9}\\&7og\times \frac{-5}{6}+\frac{\frac{51}{8}}{\frac{3}{16}}-\frac{1}{2}\end{aligned}\]
Invert and multiply.
\[\begin{aligned}&\frac{287}{24}+\frac{51}{8}\times \frac{16}{3}-\frac{1}{9}\\&7og\times \frac{-5}{6}+\frac{51}{8}\times \frac{16}{3}-\frac{1}{2}\end{aligned}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\begin{aligned}&\frac{287}{24}+\frac{51\times 16}{8\times 3}-\frac{1}{9}\\&7og\times \frac{-5}{6}+\frac{51\times 16}{8\times 3}-\frac{1}{2}\end{aligned}\]
Simplify \(51\times 16\) to \(816\).
\[\begin{aligned}&\frac{287}{24}+\frac{816}{8\times 3}-\frac{1}{9}\\&7og\times \frac{-5}{6}+\frac{816}{8\times 3}-\frac{1}{2}\end{aligned}\]
Simplify \(8\times 3\) to \(24\).
\[\begin{aligned}&\frac{287}{24}+\frac{816}{24}-\frac{1}{9}\\&7og\times \frac{-5}{6}+\frac{816}{24}-\frac{1}{2}\end{aligned}\]
Simplify \(\frac{816}{24}\) to \(34\).
\[\begin{aligned}&\frac{287}{24}+34-\frac{1}{9}\\&7og\times \frac{-5}{6}+34-\frac{1}{2}\end{aligned}\]
287/24+34-1/9;7*o*g*-5/6+34-1/2
