Solve 5+1/5+1{1-frac{1/5}}=

$$5 + \frac { 1 } { 5 + \frac { 1 } { 1 - \frac { 1 } { 5 } } } =$$

Evaluate

$$\frac{129}{25}=5.16$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

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

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 5 to get 4.

$$5+\frac{1}{5+\frac{1}{\frac{4}{5}}}$$

Divide 1 by \frac{4}{5} by multiplying 1 by the reciprocal of \frac{4}{5}.

$$5+\frac{1}{5+1\times \frac{5}{4}}$$

Multiply 1 and \frac{5}{4} to get \frac{5}{4}.

$$5+\frac{1}{5+\frac{5}{4}}$$

Convert 5 to fraction \frac{20}{4}.

$$5+\frac{1}{\frac{20}{4}+\frac{5}{4}}$$

Since \frac{20}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$5+\frac{1}{\frac{20+5}{4}}$$

Add 20 and 5 to get 25.

$$5+\frac{1}{\frac{25}{4}}$$

Divide 1 by \frac{25}{4} by multiplying 1 by the reciprocal of \frac{25}{4}.

$$5+1\times \frac{4}{25}$$

Multiply 1 and \frac{4}{25} to get \frac{4}{25}.

$$5+\frac{4}{25}$$

Convert 5 to fraction \frac{125}{25}.

$$\frac{125}{25}+\frac{4}{25}$$

Since \frac{125}{25} and \frac{4}{25} have the same denominator, add them by adding their numerators.

$$\frac{125+4}{25}$$

Add 125 and 4 to get 129.

$$\frac{129}{25}$$

Factor

$$\frac{3 \cdot 43}{5 ^ {2}} = 5\frac{4}{25} = 5.16$$