Question

$$5 \frac{ 4444444 }{ \frac{ 4444444 }{ \frac{ 7777777 }{ 5.5.5.5 } } }$$

Answer

38888885/5.5.5.5

Solution


Invert and multiply.
\[5\times \frac{4444444}{4444444\times \frac{5.5.5.5}{7777777}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[5\times \frac{4444444}{\frac{4444444\times 5.5.5.5}{7777777}}\]
Invert and multiply.
\[5\times 4444444\times \frac{7777777}{4444444\times 5.5.5.5}\]
Cancel \(4444444\).
\[5\times \frac{7777777}{5.5.5.5}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{5\times 7777777}{5.5.5.5}\]
Simplify  \(5\times 7777777\)  to  \(38888885\).
\[\frac{38888885}{5.5.5.5}\]