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

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

Evaluate

$$\frac{305}{72}\approx 4.236111111$$

Solution Steps

Convert 4 to fraction \frac{16}{4}.

$$4+\frac{1}{4+\frac{1}{\frac{16}{4}+\frac{1}{4}}}$$

Since \frac{16}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$4+\frac{1}{4+\frac{1}{\frac{16+1}{4}}}$$

Add 16 and 1 to get 17.

$$4+\frac{1}{4+\frac{1}{\frac{17}{4}}}$$

Divide 1 by \frac{17}{4} by multiplying 1 by the reciprocal of \frac{17}{4}.

$$4+\frac{1}{4+1\times \frac{4}{17}}$$

Multiply 1 and \frac{4}{17} to get \frac{4}{17}.

$$4+\frac{1}{4+\frac{4}{17}}$$

Convert 4 to fraction \frac{68}{17}.

$$4+\frac{1}{\frac{68}{17}+\frac{4}{17}}$$

Since \frac{68}{17} and \frac{4}{17} have the same denominator, add them by adding their numerators.

$$4+\frac{1}{\frac{68+4}{17}}$$

Add 68 and 4 to get 72.

$$4+\frac{1}{\frac{72}{17}}$$

Divide 1 by \frac{72}{17} by multiplying 1 by the reciprocal of \frac{72}{17}.

$$4+1\times \frac{17}{72}$$

Multiply 1 and \frac{17}{72} to get \frac{17}{72}.

$$4+\frac{17}{72}$$

Convert 4 to fraction \frac{288}{72}.

$$\frac{288}{72}+\frac{17}{72}$$

Since \frac{288}{72} and \frac{17}{72} have the same denominator, add them by adding their numerators.

$$\frac{288+17}{72}$$

Add 288 and 17 to get 305.

$$\frac{305}{72}$$

Factor

$$\frac{5 \cdot 61}{2 ^ {3} \cdot 3 ^ {2}} = 4\frac{17}{72} = 4.236111111111111$$