Evaluate: ((7)/(12)/(-14))-(3)/(8) * (5)/(3)

Expression: $\left( \frac{ 7 }{ 12 }\div\left( -14 \right) \right)-\frac{ 3 }{ 8 } \times \frac{ 5 }{ 3 }$

Dividing a positive and a negative equals a negative: $\left( + \right)\div\left( - \right)=\left( - \right)$

$\left( -\frac{ 7 }{ 12 }\div14 \right)-\frac{ 3 }{ 8 } \times \frac{ 5 }{ 3 }$

Dividing is equivalent to multiplying by the reciprocal

$\left( -\frac{ 7 }{ 12 } \times \frac{ 1 }{ 14 } \right)-\frac{ 3 }{ 8 } \times \frac{ 5 }{ 3 }$

Cancel out the greatest common factor $3$

$\left( -\frac{ 7 }{ 12 } \times \frac{ 1 }{ 14 } \right)-\frac{ 1 }{ 8 } \times 5$

Cancel out the greatest common factor $7$

$\left( -\frac{ 1 }{ 12 } \times \frac{ 1 }{ 2 } \right)-\frac{ 1 }{ 8 } \times 5$

Calculate the product

$\left( -\frac{ 1 }{ 12 } \times \frac{ 1 }{ 2 } \right)-\frac{ 5 }{ 8 }$

Multiply the fractions

$\left( -\frac{ 1 }{ 24 } \right)-\frac{ 5 }{ 8 }$

Remove unnecessary parentheses

$-\frac{ 1 }{ 24 }-\frac{ 5 }{ 8 }$

Calculate the difference

$\begin{align*}&-\frac{ 2 }{ 3 } \\&-0.\overset{ \cdot }{ 6 } \end{align*}$