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

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

Evaluate

$$\frac{5}{9}\approx 0.555555556$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

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

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

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

Add 4 and 1 to get 5.

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

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

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

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

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

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

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

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

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

Add 4 and 5 to get 9.

$$\frac{1}{\frac{9}{5}}$$

Divide 1 by \frac{9}{5} by multiplying 1 by the reciprocal of \frac{9}{5}.

$$1\times \frac{5}{9}$$

Multiply 1 and \frac{5}{9} to get \frac{5}{9}.

$$\frac{5}{9}$$

Factor

$$\frac{5}{3 ^ {2}} = 0.5555555555555556$$