Solve 3+[8-5div{4-2div(2+8/13)}]

$$3 + [ 8 - 5 \div \{ 4 - 2 \div ( 2 + \frac { 8 } { 13 } ) \} ]$$

Evaluate

$$\frac{104}{11}\approx 9.454545455$$

Solution Steps

Add 3 and 8 to get 11.

$$11-\frac{5}{4-\frac{2}{2+\frac{8}{13}}}$$

Convert 2 to fraction \frac{26}{13}.

$$11-\frac{5}{4-\frac{2}{\frac{26}{13}+\frac{8}{13}}}$$

Since \frac{26}{13} and \frac{8}{13} have the same denominator, add them by adding their numerators.

$$11-\frac{5}{4-\frac{2}{\frac{26+8}{13}}}$$

Add 26 and 8 to get 34.

$$11-\frac{5}{4-\frac{2}{\frac{34}{13}}}$$

Divide 2 by \frac{34}{13} by multiplying 2 by the reciprocal of \frac{34}{13}.

$$11-\frac{5}{4-2\times \frac{13}{34}}$$

Express 2\times \frac{13}{34} as a single fraction.

$$11-\frac{5}{4-\frac{2\times 13}{34}}$$

Multiply 2 and 13 to get 26.

$$11-\frac{5}{4-\frac{26}{34}}$$

Reduce the fraction \frac{26}{34} to lowest terms by extracting and canceling out 2.

$$11-\frac{5}{4-\frac{13}{17}}$$

Convert 4 to fraction \frac{68}{17}.

$$11-\frac{5}{\frac{68}{17}-\frac{13}{17}}$$

Since \frac{68}{17} and \frac{13}{17} have the same denominator, subtract them by subtracting their numerators.

$$11-\frac{5}{\frac{68-13}{17}}$$

Subtract 13 from 68 to get 55.

$$11-\frac{5}{\frac{55}{17}}$$

Divide 5 by \frac{55}{17} by multiplying 5 by the reciprocal of \frac{55}{17}.

$$11-5\times \frac{17}{55}$$

Express 5\times \frac{17}{55} as a single fraction.

$$11-\frac{5\times 17}{55}$$

Multiply 5 and 17 to get 85.

$$11-\frac{85}{55}$$

Reduce the fraction \frac{85}{55} to lowest terms by extracting and canceling out 5.

$$11-\frac{17}{11}$$

Convert 11 to fraction \frac{121}{11}.

$$\frac{121}{11}-\frac{17}{11}$$

Since \frac{121}{11} and \frac{17}{11} have the same denominator, subtract them by subtracting their numerators.

$$\frac{121-17}{11}$$

Subtract 17 from 121 to get 104.

$$\frac{104}{11}$$

Factor

$$\frac{2 ^ {3} \cdot 13}{11} = 9\frac{5}{11} = 9.454545454545455$$