Solve for: (2)/(3) * (4/(5)/(9))+((7)/(8)-(5)/(6)-(1)/(3))

Expression: $\frac{ 2 }{ 3 } \times \left( 4\div\frac{ 5 }{ 9 } \right)+\left( \frac{ 7 }{ 8 }-\frac{ 5 }{ 6 }-\frac{ 1 }{ 3 } \right)$

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

$\frac{ 2 }{ 3 } \times \left( 4 \times \frac{ 9 }{ 5 } \right)+\left( \frac{ 7 }{ 8 }-\frac{ 5 }{ 6 }-\frac{ 1 }{ 3 } \right)$

Calculate the difference

$\frac{ 2 }{ 3 } \times \left( 4 \times \frac{ 9 }{ 5 } \right)+\left( -\frac{ 7 }{ 24 } \right)$

Calculate the product

$\frac{ 2 }{ 3 } \times \frac{ 36 }{ 5 }+\left( -\frac{ 7 }{ 24 } \right)$

When there is a $+$ in front of an expression in parentheses, the expression remains the same

$\frac{ 2 }{ 3 } \times \frac{ 36 }{ 5 }-\frac{ 7 }{ 24 }$

Cancel out the greatest common factor $3$

$2 \times \frac{ 12 }{ 5 }-\frac{ 7 }{ 24 }$

Calculate the product

$\frac{ 24 }{ 5 }-\frac{ 7 }{ 24 }$

Subtract the fractions

\begin{align*}&\frac{ 541 }{ 120 } \\&\begin{array} { l }4 \frac{ 61 }{ 120 },& 4.508\overset{ \cdot }{ 3 } \end{array}\end{align*}

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