# Calculate: -1 (2)/(3) * (-4+10) * (-(4)/(5)-3 (1)/(2))

## Expression: $-1 \frac{ 2 }{ 3 } \times \left( -4+10 \right) \times \left( -\frac{ 4 }{ 5 }-3 \frac{ 1 }{ 2 } \right)$

Convert the mixed number to an improper fraction

$-\frac{ 5 }{ 3 } \times \left( -4+10 \right) \times \left( -\frac{ 4 }{ 5 }-3 \frac{ 1 }{ 2 } \right)$

Calculate the sum

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

Convert the mixed number to an improper fraction

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

Calculate the difference

$-\frac{ 5 }{ 3 } \times 6 \times \left( -\frac{ 43 }{ 10 } \right)$

Multiplying two negatives equals a positive: $\left( - \right) \times \left( - \right)=\left( + \right)$

$\frac{ 5 }{ 3 } \times 6 \times \frac{ 43 }{ 10 }$

Cancel out the greatest common factor $3$

$5 \times 2 \times \frac{ 43 }{ 10 }$

Cancel out the greatest common factor $5$

$2 \times \frac{ 43 }{ 2 }$

Cancel out the greatest common factor $2$

$43$

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