Solve 5/5+5{5+frac{5/5+5}}

$$\frac{ 5 }{ 5+ \frac{ 5 }{ 5+ \frac{ 5 }{ 5+5 } } }$$

Evaluate

$$\frac{11}{13}\approx 0.846153846$$

Solution Steps

Add 5 and 5 to get 10.

$$\frac{5}{5+\frac{5}{5+\frac{5}{10}}}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{5}{5+\frac{5}{5+\frac{1}{2}}}$$

Convert 5 to fraction \frac{10}{2}.

$$\frac{5}{5+\frac{5}{\frac{10}{2}+\frac{1}{2}}}$$

Since \frac{10}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{5}{5+\frac{5}{\frac{10+1}{2}}}$$

Add 10 and 1 to get 11.

$$\frac{5}{5+\frac{5}{\frac{11}{2}}}$$

Divide 5 by \frac{11}{2} by multiplying 5 by the reciprocal of \frac{11}{2}.

$$\frac{5}{5+5\times \frac{2}{11}}$$

Express 5\times \frac{2}{11} as a single fraction.

$$\frac{5}{5+\frac{5\times 2}{11}}$$

Multiply 5 and 2 to get 10.

$$\frac{5}{5+\frac{10}{11}}$$

Convert 5 to fraction \frac{55}{11}.

$$\frac{5}{\frac{55}{11}+\frac{10}{11}}$$

Since \frac{55}{11} and \frac{10}{11} have the same denominator, add them by adding their numerators.

$$\frac{5}{\frac{55+10}{11}}$$

Add 55 and 10 to get 65.

$$\frac{5}{\frac{65}{11}}$$

Divide 5 by \frac{65}{11} by multiplying 5 by the reciprocal of \frac{65}{11}.

$$5\times \frac{11}{65}$$

Express 5\times \frac{11}{65} as a single fraction.

$$\frac{5\times 11}{65}$$

Multiply 5 and 11 to get 55.

$$\frac{55}{65}$$

Reduce the fraction \frac{55}{65} to lowest terms by extracting and canceling out 5.

$$\frac{11}{13}$$

Factor

$$\frac{11}{13} = 0.8461538461538461$$