Solve for: 5.2+2.1/(4.5-4 (1)/(7))

Expression: $5.2+2.1\div\left( 4.5-4 \frac{ 1 }{ 7 } \right)$

Convert the decimal into a fraction

$\frac{ 26 }{ 5 }+2.1\div\left( 4.5-4 \frac{ 1 }{ 7 } \right)$

Convert the decimal into a fraction

$\frac{ 26 }{ 5 }+\frac{ 21 }{ 10 }\div\left( 4.5-4 \frac{ 1 }{ 7 } \right)$

Convert the decimal into a fraction

$\frac{ 26 }{ 5 }+\frac{ 21 }{ 10 }\div\left( \frac{ 9 }{ 2 }-4 \frac{ 1 }{ 7 } \right)$

Convert the mixed number to an improper fraction

$\frac{ 26 }{ 5 }+\frac{ 21 }{ 10 }\div\left( \frac{ 9 }{ 2 }-\frac{ 29 }{ 7 } \right)$

Subtract the fractions

$\frac{ 26 }{ 5 }+\frac{ 21 }{ 10 }\div\frac{ 5 }{ 14 }$

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

$\frac{ 26 }{ 5 }+\frac{ 21 }{ 10 } \times \frac{ 14 }{ 5 }$

Cancel out the greatest common factor $2$

$\frac{ 26 }{ 5 }+\frac{ 21 }{ 5 } \times \frac{ 7 }{ 5 }$

Multiply the fractions

$\frac{ 26 }{ 5 }+\frac{ 147 }{ 25 }$

Add the fractions

$\begin{align*}&\frac{ 277 }{ 25 } \\&\begin{array} { l }11 \frac{ 2 }{ 25 },& 11.08\end{array}\end{align*}$