$0.5-\frac{ 7.5 }{ 100 }+5 \frac{ 6 }{ 7 }$
Convert the mixed number to an improper fraction$0.5-\frac{ 7.5 }{ 100 }+\frac{ 41 }{ 7 }$
Divide the numbers$0.5-0.075+\frac{ 41 }{ 7 }$
Subtract the numbers$0.425+\frac{ 41 }{ 7 }$
Convert the decimal into a fraction$\frac{ 17 }{ 40 }+\frac{ 41 }{ 7 }$
Add the fractions$\begin{align*}&\frac{ 1759 }{ 280 } \\&\begin{array} { l }6 \frac{ 79 }{ 280 },& 6.282\overset{ \cdot }{ 1 } 4285\overset{ \cdot }{ 7 } \end{array}\end{align*}$