Solve 1+1/1/3+1{4+frac{1/5}}

$$1 + \frac { \frac { 1 } { 1 } } { 3 + \frac { 1 } { 4 + \frac { 1 } { 5 } } }$$

Evaluate

$$\frac{89}{68}\approx 1.308823529$$

Solution Steps

Divide 1 by 1 to get 1.

$$1+\frac{1}{3+\frac{1}{4+\frac{1}{5}}}$$

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

$$1+\frac{1}{3+\frac{1}{\frac{20}{5}+\frac{1}{5}}}$$

Since \frac{20}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$1+\frac{1}{3+\frac{1}{\frac{20+1}{5}}}$$

Add 20 and 1 to get 21.

$$1+\frac{1}{3+\frac{1}{\frac{21}{5}}}$$

Divide 1 by \frac{21}{5} by multiplying 1 by the reciprocal of \frac{21}{5}.

$$1+\frac{1}{3+1\times \frac{5}{21}}$$

Multiply 1 and \frac{5}{21} to get \frac{5}{21}.

$$1+\frac{1}{3+\frac{5}{21}}$$

Convert 3 to fraction \frac{63}{21}.

$$1+\frac{1}{\frac{63}{21}+\frac{5}{21}}$$

Since \frac{63}{21} and \frac{5}{21} have the same denominator, add them by adding their numerators.

$$1+\frac{1}{\frac{63+5}{21}}$$

Add 63 and 5 to get 68.

$$1+\frac{1}{\frac{68}{21}}$$

Divide 1 by \frac{68}{21} by multiplying 1 by the reciprocal of \frac{68}{21}.

$$1+1\times \frac{21}{68}$$

Multiply 1 and \frac{21}{68} to get \frac{21}{68}.

$$1+\frac{21}{68}$$

Convert 1 to fraction \frac{68}{68}.

$$\frac{68}{68}+\frac{21}{68}$$

Since \frac{68}{68} and \frac{21}{68} have the same denominator, add them by adding their numerators.

$$\frac{68+21}{68}$$

Add 68 and 21 to get 89.

$$\frac{89}{68}$$

Factor

$$\frac{89}{2 ^ {2} \cdot 17} = 1\frac{21}{68} = 1.3088235294117647$$