Solve 1/4+2:1/2/frac{5-frac{5{4}}{4}}*(0,4-4)^-2=

$$\frac { \frac { 1 } { 4 } + 2 : \frac { 1 } { 2 } } { \frac { 5 - \frac { 5 } { 4 } } { 4 } } \cdot ( 0,4 - 4 ) ^ { - 2 } =$$

Evaluate

$$\frac{85}{243}\approx 0,349794239$$

Solution Steps

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

$$\frac{\frac{1}{4}+2\times 2}{\frac{5-\frac{5}{4}}{4}}\left(0,4-4\right)^{-2}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{1}{4}+4}{\frac{5-\frac{5}{4}}{4}}\left(0,4-4\right)^{-2}$$

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

$$\frac{\frac{17}{4}}{\frac{5-\frac{5}{4}}{4}}\left(0,4-4\right)^{-2}$$

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

$$\frac{\frac{17}{4}}{\frac{\frac{15}{4}}{4}}\left(0,4-4\right)^{-2}$$

Express \frac{\frac{15}{4}}{4} as a single fraction.

$$\frac{\frac{17}{4}}{\frac{15}{4\times 4}}\left(0,4-4\right)^{-2}$$

Multiply 4 and 4 to get 16.

$$\frac{\frac{17}{4}}{\frac{15}{16}}\left(0,4-4\right)^{-2}$$

Divide \frac{17}{4} by \frac{15}{16} by multiplying \frac{17}{4} by the reciprocal of \frac{15}{16}.

$$\frac{17}{4}\times \frac{16}{15}\left(0,4-4\right)^{-2}$$

Multiply \frac{17}{4} and \frac{16}{15} to get \frac{68}{15}.

$$\frac{68}{15}\left(0,4-4\right)^{-2}$$

Subtract 4 from 0,4 to get -3,6.

$$\frac{68}{15}\left(-3,6\right)^{-2}$$

Calculate -3,6 to the power of -2 and get \frac{25}{324}.

$$\frac{68}{15}\times \frac{25}{324}$$

Multiply \frac{68}{15} and \frac{25}{324} to get \frac{85}{243}.

$$\frac{85}{243}$$

Factor

$$\frac{5 \cdot 17}{3 ^ {5}} = 0.3497942386831276$$