Math Problem Solver

\[\frac{\frac{0.2}{0.5}}{0.2} + \frac{0.16}{0.8} \cdot 0.2 - 0.2 \cdot 0.3 = \frac{99}{50} = 1.98\]

\[\begin{aligned}\frac{\frac{0.2}{0.5}}{0.2} + \frac{0.16}{0.8} \cdot 0.2 - 0.2 \cdot 0.3& = \frac{2}{10} \cdot \frac{1}{\frac{5}{10}} \cdot \frac{1}{\frac{2}{10}} + \frac{16}{100} \cdot \frac{1}{\frac{8}{10}} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = \frac{2}{10} \cdot \frac{1}{\frac{1}{2}} \cdot \frac{1}{\frac{2}{10}} + \frac{16}{100} \cdot \frac{1}{\frac{8}{10}} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = \frac{2}{10} \cdot 2 \cdot \frac{1}{\frac{2}{10}} + \frac{16}{100} \cdot \frac{1}{\frac{8}{10}} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = \frac{2}{10} \cdot 2 \cdot \frac{1}{\frac{1}{5}} + \frac{16}{100} \cdot \frac{1}{\frac{8}{10}} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = \frac{2}{10} \cdot 10 + \frac{16}{100} \cdot \frac{1}{\frac{8}{10}} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = \frac{10}{5} + \frac{16}{100} \cdot \frac{1}{\frac{8}{10}} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = 2 + \frac{16}{100} \cdot \frac{1}{\frac{8}{10}} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = 2 + \frac{16}{100} \cdot \frac{1}{\frac{4}{5}} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = 2 + \frac{16}{100} \cdot \frac{5}{4} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = 2 + \frac{4}{25} \cdot \frac{5}{4} \cdot \frac{2}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = 2 + \frac{2}{5} \cdot \frac{1}{10} - \frac{2}{10} \cdot \frac{3}{10}\\& = 2 + \frac{1}{25} - \frac{2}{10} \cdot \frac{3}{10}\\& = 2 + \frac{1}{25} - \frac{3}{5} \cdot \frac{1}{10}\\& = 2 + \frac{1}{25} - \frac{3}{50}\\& = \frac{51}{25} - \frac{3}{50}\\& = \frac{99}{50}\end{aligned}\]