Evaluate: (11.2)/(16)=(n)/(4.8)

Expression: $\frac{ 11.2 }{ 16 }=\frac{ n }{ 4.8 }$

Divide the numbers

$0.7=\frac{ n }{ 4.8 }$

Convert the decimal into a fraction

$0.7=\frac{ n }{ \frac{ 24 }{ 5 } }$

Simplify the complex fraction

$0.7=\frac{ 5n }{ 24 }$

Multiply both sides of the equation by $\frac{ 24 }{ 5 }$

$\frac{ 24 }{ 5 } \times 0.7=n$

Convert the decimal into a fraction

$\frac{ 24 }{ 5 } \times \frac{ 7 }{ 10 }=n$

Cancel out the greatest common factor $2$

$\frac{ 12 }{ 5 } \times \frac{ 7 }{ 5 }=n$

Multiply the fractions

$\frac{ 84 }{ 25 }=n$

Swap the sides of the equation

$\begin{align*}&n=\frac{ 84 }{ 25 } \\&\begin{array} { l }n=3 \frac{ 9 }{ 25 },& n=3.36\end{array}\end{align*}$