3/5÷ (2/5− 0.25) + (1.5 ÷3/4) ÷ (3/10−4/5)

asked by guest
on Nov 23, 2024 at 7:44 am



You asked:

Evaluate the expression: \(\frac{\frac{3}{5}}{\frac{2}{5} - 0.25} + \frac{\frac{\frac{1.5}{3}}{4}}{\frac{3}{10} - \frac{4}{5}}\)

MathBot Answer:

\[\frac{\frac{3}{5}}{\frac{2}{5} - 0.25} + \frac{\frac{\frac{1.5}{3}}{4}}{\frac{3}{10} - \frac{4}{5}} = \frac{15}{4} = 3.75\]

\[\begin{aligned}\frac{\frac{3}{5}}{\frac{2}{5} - 0.25} + \frac{\frac{\frac{1.5}{3}}{4}}{\frac{3}{10} - \frac{4}{5}}& = \frac{3}{5} \cdot \frac{1}{\frac{2}{5} - \frac{25}{100}} + \left(1 + \frac{5}{10}\right) \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{\frac{3}{10} - \frac{4}{5}}\\& = \frac{3}{5} \cdot \frac{1}{\frac{2}{5} - \frac{1}{4}} + \left(1 + \frac{5}{10}\right) \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{\frac{3}{10} - \frac{4}{5}}\\& = \frac{3}{5} \cdot \frac{1}{\frac{3}{20}} + \left(1 + \frac{5}{10}\right) \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{\frac{3}{10} - \frac{4}{5}}\\& = 4 + \left(1 + \frac{5}{10}\right) \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{\frac{3}{10} - \frac{4}{5}}\\& = 4 + \left(1 + \frac{1}{2}\right) \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{\frac{3}{10} - \frac{4}{5}}\\& = 4 + \frac{3}{2} \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{\frac{3}{10} - \frac{4}{5}}\\& = 4 + \frac{3}{2} \cdot \frac{1}{3} \cdot \frac{1}{4} \cdot \frac{1}{- \frac{1}{2}}\\& = 4 + \frac{3}{2} \cdot \frac{1}{3} \cdot - \frac{1}{2}\\& = 4 + \frac{1}{2} \cdot - \frac{1}{2}\\& = 4 - \frac{1}{4}\\& = \frac{15}{4}\end{aligned}\]

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