Math Problem Solver

\[\frac{\frac{2 \cdot \left(.8 + .3\right)}{2} \cdot \left(1.4 + 1.11 \cdot .125\right)}{2} = \frac{13541}{16000} = 0.8463125\]

\[\begin{aligned}\frac{\frac{2 \cdot \left(.8 + .3\right)}{2} \cdot \left(1.4 + 1.11 \cdot .125\right)}{2}& = 2 \cdot \left(\frac{8}{10} + \frac{3}{10}\right) \cdot \frac{1}{2} \cdot \left(1 + \frac{4}{10} + \left(1 + \frac{11}{100}\right) \cdot \frac{125}{1000}\right) \cdot \frac{1}{2}\\& = 2 \cdot \left(\frac{4}{5} + \frac{3}{10}\right) \cdot \frac{1}{2} \cdot \left(1 + \frac{4}{10} + \left(1 + \frac{11}{100}\right) \cdot \frac{125}{1000}\right) \cdot \frac{1}{2}\\& = 2 \cdot \frac{11}{10} \cdot \frac{1}{2} \cdot \left(1 + \frac{4}{10} + \left(1 + \frac{11}{100}\right) \cdot \frac{125}{1000}\right) \cdot \frac{1}{2}\\& = 2 \cdot \frac{11}{10} \cdot \frac{1}{2} \cdot \left(1 + \frac{2}{5} + \left(1 + \frac{11}{100}\right) \cdot \frac{125}{1000}\right) \cdot \frac{1}{2}\\& = 2 \cdot \frac{11}{10} \cdot \frac{1}{2} \cdot \left(1 + \frac{2}{5} + \frac{111}{100} \cdot \frac{125}{1000}\right) \cdot \frac{1}{2}\\& = 2 \cdot \frac{11}{10} \cdot \frac{1}{2} \cdot \left(1 + \frac{2}{5} + \frac{555}{4} \cdot \frac{1}{1000}\right) \cdot \frac{1}{2}\\& = 2 \cdot \frac{11}{10} \cdot \frac{1}{2} \cdot \left(1 + \frac{2}{5} + \frac{111}{800}\right) \cdot \frac{1}{2}\\& = 2 \cdot \frac{11}{10} \cdot \frac{1}{2} \cdot \left(\frac{7}{5} + \frac{111}{800}\right) \cdot \frac{1}{2}\\& = 2 \cdot \frac{11}{10} \cdot \frac{1}{2} \cdot \frac{1231}{800} \cdot \frac{1}{2}\\& = 2 \cdot \frac{11}{10} \cdot \frac{1}{2} \cdot \frac{1231}{1600}\\& = \frac{11}{5} \cdot \frac{1}{2} \cdot \frac{1231}{1600}\\& = \frac{11}{10} \cdot \frac{1231}{1600}\\& = \frac{13541}{16000}\end{aligned}\]