Question

$$\frac{ 33333 }{ \frac{ 44444 }{ \frac{ 77777 }{ 99999 } } }$$

Answer

7/12

Solution


Simplify  \(\frac{77777}{99999}\)  to  \(\frac{7}{9}\).
\[\frac{33333}{\frac{44444}{\frac{7}{9}}}\]
Invert and multiply.
\[\frac{33333}{44444\times \frac{9}{7}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{33333}{\frac{44444\times 9}{7}}\]
Simplify  \(44444\times 9\)  to  \(399996\).
\[\frac{33333}{\frac{399996}{7}}\]
Invert and multiply.
\[33333\times \frac{7}{399996}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{33333\times 7}{399996}\]
Simplify  \(33333\times 7\)  to  \(233331\).
\[\frac{233331}{399996}\]
Simplify.
\[\frac{7}{12}\]

Decimal Form: 0.583333