Solve 3/5+5{5+frac{5/5+5}}

$$\frac { 3 } { 5 + \frac { 5 } { 5 + \frac { 5 } { 5 + 5 } } }$$

Evaluate

$$\frac{33}{65}\approx 0.507692308$$

Solution Steps

Add 5 and 5 to get 10.

$$\frac{3}{5+\frac{5}{5+\frac{5}{10}}}$$

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

$$\frac{3}{5+\frac{5}{5+\frac{1}{2}}}$$

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

$$\frac{3}{5+\frac{5}{\frac{10}{2}+\frac{1}{2}}}$$

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

$$\frac{3}{5+\frac{5}{\frac{10+1}{2}}}$$

Add 10 and 1 to get 11.

$$\frac{3}{5+\frac{5}{\frac{11}{2}}}$$

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

$$\frac{3}{5+5\times \frac{2}{11}}$$

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

$$\frac{3}{5+\frac{5\times 2}{11}}$$

Multiply 5 and 2 to get 10.

$$\frac{3}{5+\frac{10}{11}}$$

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

$$\frac{3}{\frac{55}{11}+\frac{10}{11}}$$

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

$$\frac{3}{\frac{55+10}{11}}$$

Add 55 and 10 to get 65.

$$\frac{3}{\frac{65}{11}}$$

Divide 3 by \frac{65}{11} by multiplying 3 by the reciprocal of \frac{65}{11}.

$$3\times \frac{11}{65}$$

Express 3\times \frac{11}{65} as a single fraction.

$$\frac{3\times 11}{65}$$

Multiply 3 and 11 to get 33.

$$\frac{33}{65}$$

Factor

$$\frac{3 \cdot 11}{5 \cdot 13} = 0.5076923076923077$$