$\frac{ 5 }{ 4 }\div\left( -\frac{ 3 }{ 4 } \right)-\left( \frac{ 5 }{ 6 }-\frac{ 2 }{ 3 } \right)\div2 \times \frac{ 2 }{ 3 }$
Subtract the fractions$\frac{ 5 }{ 4 }\div\left( -\frac{ 3 }{ 4 } \right)-\frac{ 1 }{ 6 }\div2 \times \frac{ 2 }{ 3 }$
Dividing is equivalent to multiplying by the reciprocal$\frac{ 5 }{ 4 }\div\left( -\frac{ 3 }{ 4 } \right)-\frac{ 1 }{ 6 } \times \frac{ 1 }{ 2 } \times \frac{ 2 }{ 3 }$
Dividing a positive and a negative equals a negative: $\left( + \right)\div\left( - \right)=\left( - \right)$$-\frac{ 5 }{ 4 }\div\frac{ 3 }{ 4 }-\frac{ 1 }{ 6 } \times \frac{ 1 }{ 2 } \times \frac{ 2 }{ 3 }$
To divide by a fraction, multiply by the reciprocal of that fraction$-\frac{ 5 }{ 4 } \times \frac{ 4 }{ 3 }-\frac{ 1 }{ 6 } \times \frac{ 1 }{ 2 } \times \frac{ 2 }{ 3 }$
Cancel out the greatest common factor $2$$-\frac{ 5 }{ 4 } \times \frac{ 4 }{ 3 }-\frac{ 1 }{ 6 } \times \frac{ 1 }{ 3 }$
Cancel out the greatest common factor $4$$-5 \times \frac{ 1 }{ 3 }-\frac{ 1 }{ 6 } \times \frac{ 1 }{ 3 }$
Multiply the fractions$-5 \times \frac{ 1 }{ 3 }-\frac{ 1 }{ 18 }$
Calculate the product$-\frac{ 5 }{ 3 }-\frac{ 1 }{ 18 }$
Calculate the difference$\begin{align*}&-\frac{ 31 }{ 18 } \\&\begin{array} { l }-1 \frac{ 13 }{ 18 },& -1.7\overset{ \cdot }{ 2 } \end{array}\end{align*}$