Solve 1/4+frac{2/frac{1{2}}}{5-5/4/-frac{4{3}}}left(4div10-4right)^-2

$$\frac{ \frac{ 1 }{ 4 } + \frac{ 2 }{ \frac{ 1 }{ 2 } } }{ \frac{ 5- \frac{ 5 }{ 4 } }{ - \frac{ 4 }{ 3 } } } { \left(4 \div 10-4 \right) }^{ -2 }$$

Evaluate

$$-\frac{85}{729}\approx -0.11659808$$

Solution Steps

Divide 2 by \frac{1}{2} by multiplying 2 by the reciprocal of \frac{1}{2}.

$$\frac{\frac{1}{4}+2\times 2}{\frac{5-\frac{5}{4}}{-\frac{4}{3}}}\left(\frac{4}{10}-4\right)^{-2}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{1}{4}+4}{\frac{5-\frac{5}{4}}{-\frac{4}{3}}}\left(\frac{4}{10}-4\right)^{-2}$$

Add \frac{1}{4} and 4 to get \frac{17}{4}.

$$\frac{\frac{17}{4}}{\frac{5-\frac{5}{4}}{-\frac{4}{3}}}\left(\frac{4}{10}-4\right)^{-2}$$

Subtract \frac{5}{4} from 5 to get \frac{15}{4}.

$$\frac{\frac{17}{4}}{\frac{\frac{15}{4}}{-\frac{4}{3}}}\left(\frac{4}{10}-4\right)^{-2}$$

Divide \frac{15}{4} by -\frac{4}{3} by multiplying \frac{15}{4} by the reciprocal of -\frac{4}{3}.

$$\frac{\frac{17}{4}}{\frac{15}{4}\left(-\frac{3}{4}\right)}\left(\frac{4}{10}-4\right)^{-2}$$

Multiply \frac{15}{4} and -\frac{3}{4} to get -\frac{45}{16}.

$$\frac{\frac{17}{4}}{-\frac{45}{16}}\left(\frac{4}{10}-4\right)^{-2}$$

Divide \frac{17}{4} by -\frac{45}{16} by multiplying \frac{17}{4} by the reciprocal of -\frac{45}{16}.

$$\frac{17}{4}\left(-\frac{16}{45}\right)\left(\frac{4}{10}-4\right)^{-2}$$

Multiply \frac{17}{4} and -\frac{16}{45} to get -\frac{68}{45}.

$$-\frac{68}{45}\left(\frac{4}{10}-4\right)^{-2}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{68}{45}\left(\frac{2}{5}-4\right)^{-2}$$

Subtract 4 from \frac{2}{5} to get -\frac{18}{5}.

$$-\frac{68}{45}\left(-\frac{18}{5}\right)^{-2}$$

Calculate -\frac{18}{5} to the power of -2 and get \frac{25}{324}.

$$-\frac{68}{45}\times \frac{25}{324}$$

Multiply -\frac{68}{45} and \frac{25}{324} to get -\frac{85}{729}.

$$-\frac{85}{729}$$

Factor

$$-\frac{85}{729} = -0.11659807956104253$$