(2/3-0.75)/ $\sqrt{1/16}$ + (4/15)/(-8/25)* $\sqrt{64/25}$ + 6* $\sqrt{25/144}$

asked by guest
on Jan 26, 2025 at 7:44 am



You asked:

Evaluate the expression: \(\frac{\frac{2}{3} - 0.75}{\sqrt{\frac{1}{16}}} + \frac{\frac{4}{15}}{\frac{-8}{25}} \sqrt{\frac{64}{25}} + 6 \sqrt{\frac{25}{144}}\)

MathBot Answer:

\[\frac{\frac{2}{3} - 0.75}{\sqrt{\frac{1}{16}}} + \frac{\frac{4}{15}}{\frac{-8}{25}} \sqrt{\frac{64}{25}} + 6 \sqrt{\frac{25}{144}} = \frac{5}{6} = 0.8\overline{3}\]

\[\begin{aligned}\frac{\frac{2}{3} - 0.75}{\sqrt{\frac{1}{16}}} + \frac{\frac{4}{15}}{\frac{-8}{25}} \sqrt{\frac{64}{25}} + 6 \sqrt{\frac{25}{144}}& = \left(\frac{2}{3} - \frac{75}{100}\right) \cdot \frac{1}{\sqrt{\frac{1}{16}}} + \frac{4}{15} \cdot \frac{1}{- \frac{8}{25}} \cdot \sqrt{\frac{64}{25}} + 6 \cdot \sqrt{\frac{25}{144}}\\& = \left(\frac{2}{3} - \frac{3}{4}\right) \cdot \frac{1}{\sqrt{\frac{1}{16}}} + \frac{4}{15} \cdot \frac{1}{- \frac{8}{25}} \cdot \sqrt{\frac{64}{25}} + 6 \cdot \sqrt{\frac{25}{144}}\\& = - \frac{1}{12} \cdot \frac{1}{\sqrt{\frac{1}{16}}} + \frac{4}{15} \cdot \frac{1}{- \frac{8}{25}} \cdot \sqrt{\frac{64}{25}} + 6 \cdot \sqrt{\frac{25}{144}}\\& = - \frac{1}{12} \cdot \frac{1}{\frac{1}{4}} + \frac{4}{15} \cdot \frac{1}{- \frac{8}{25}} \cdot \sqrt{\frac{64}{25}} + 6 \cdot \sqrt{\frac{25}{144}}\\& = - \frac{1}{3} + \frac{4}{15} \cdot \frac{1}{- \frac{8}{25}} \cdot \sqrt{\frac{64}{25}} + 6 \cdot \sqrt{\frac{25}{144}}\\& = - \frac{1}{3} + \frac{4}{15} \cdot - \frac{25}{8} \cdot \sqrt{\frac{64}{25}} + 6 \cdot \sqrt{\frac{25}{144}}\\& = - \frac{1}{3} + \frac{4}{15} \cdot - \frac{25}{8} \cdot \frac{8}{5} + 6 \cdot \sqrt{\frac{25}{144}}\\& = - \frac{1}{3} - \frac{4}{3} + 6 \cdot \sqrt{\frac{25}{144}}\\& = - \frac{1}{3} - \frac{4}{3} + 6 \cdot \frac{5}{12}\\& = - \frac{1}{3} - \frac{4}{3} + \frac{5}{2}\\& = - \frac{5}{3} + \frac{5}{2}\\& = \frac{5}{6}\end{aligned}\]

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