Evaluate: -(1)/(8)+(1)/(8)/((5)/(6)-(3)/(4))-(1)/(5)/(2)/(13)

Expression: $-\frac{ 1 }{ 8 }+\frac{ 1 }{ 8 }\div\left( \frac{ 5 }{ 6 }-\frac{ 3 }{ 4 } \right)-\frac{ 1 }{ 5 }\div\frac{ 2 }{ 13 }$

Subtract the fractions

$-\frac{ 1 }{ 8 }+\frac{ 1 }{ 8 }\div\frac{ 1 }{ 12 }-\frac{ 1 }{ 5 }\div\frac{ 2 }{ 13 }$

To divide by a fraction, multiply by the reciprocal of that fraction

$-\frac{ 1 }{ 8 }+\frac{ 1 }{ 8 }\div\frac{ 1 }{ 12 }-\frac{ 1 }{ 5 } \times \frac{ 13 }{ 2 }$

To divide by a fraction, multiply by the reciprocal of that fraction

$-\frac{ 1 }{ 8 }+\frac{ 1 }{ 8 } \times 12-\frac{ 1 }{ 5 } \times \frac{ 13 }{ 2 }$

Multiply the fractions

$-\frac{ 1 }{ 8 }+\frac{ 1 }{ 8 } \times 12-\frac{ 13 }{ 10 }$

Cancel out the greatest common factor $4$

$-\frac{ 1 }{ 8 }+\frac{ 1 }{ 2 } \times 3-\frac{ 13 }{ 10 }$

Calculate the product

$-\frac{ 1 }{ 8 }+\frac{ 3 }{ 2 }-\frac{ 13 }{ 10 }$

Calculate the sum or difference

$\begin{align*}&\frac{ 3 }{ 40 } \\&0.075\end{align*}$