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

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

Evaluate

$$\frac{9}{11}\approx 0.818181818$$

Solution Steps

Add 4 and 4 to get 8.

$$\frac{4}{4+\frac{4}{4+\frac{4}{8}}}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{4}{4+\frac{4}{4+\frac{1}{2}}}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{4}{4+\frac{4}{\frac{8}{2}+\frac{1}{2}}}$$

Since \frac{8}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{4}{4+\frac{4}{\frac{8+1}{2}}}$$

Add 8 and 1 to get 9.

$$\frac{4}{4+\frac{4}{\frac{9}{2}}}$$

Divide 4 by \frac{9}{2} by multiplying 4 by the reciprocal of \frac{9}{2}.

$$\frac{4}{4+4\times \frac{2}{9}}$$

Express 4\times \frac{2}{9} as a single fraction.

$$\frac{4}{4+\frac{4\times 2}{9}}$$

Multiply 4 and 2 to get 8.

$$\frac{4}{4+\frac{8}{9}}$$

Convert 4 to fraction \frac{36}{9}.

$$\frac{4}{\frac{36}{9}+\frac{8}{9}}$$

Since \frac{36}{9} and \frac{8}{9} have the same denominator, add them by adding their numerators.

$$\frac{4}{\frac{36+8}{9}}$$

Add 36 and 8 to get 44.

$$\frac{4}{\frac{44}{9}}$$

Divide 4 by \frac{44}{9} by multiplying 4 by the reciprocal of \frac{44}{9}.

$$4\times \frac{9}{44}$$

Express 4\times \frac{9}{44} as a single fraction.

$$\frac{4\times 9}{44}$$

Multiply 4 and 9 to get 36.

$$\frac{36}{44}$$

Reduce the fraction \frac{36}{44} to lowest terms by extracting and canceling out 4.

$$\frac{9}{11}$$

Factor

$$\frac{3 ^ {2}}{11} = 0.8181818181818182$$