Solve 1+1/1+1{3+frac{1/2}}

$$1+ \frac{ 1 }{ 1+ \frac{ 1 }{ 3+ \frac{ 1 }{ 2 } } }$$

Evaluate

$$\frac{16}{9}\approx 1.777777778$$

Solution Steps

Convert 3 to fraction \frac{6}{2}.

$$1+\frac{1}{1+\frac{1}{\frac{6}{2}+\frac{1}{2}}}$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$1+\frac{1}{1+\frac{1}{\frac{6+1}{2}}}$$

Add 6 and 1 to get 7.

$$1+\frac{1}{1+\frac{1}{\frac{7}{2}}}$$

Divide 1 by \frac{7}{2} by multiplying 1 by the reciprocal of \frac{7}{2}.

$$1+\frac{1}{1+1\times \frac{2}{7}}$$

Multiply 1 and \frac{2}{7} to get \frac{2}{7}.

$$1+\frac{1}{1+\frac{2}{7}}$$

Convert 1 to fraction \frac{7}{7}.

$$1+\frac{1}{\frac{7}{7}+\frac{2}{7}}$$

Since \frac{7}{7} and \frac{2}{7} have the same denominator, add them by adding their numerators.

$$1+\frac{1}{\frac{7+2}{7}}$$

Add 7 and 2 to get 9.

$$1+\frac{1}{\frac{9}{7}}$$

Divide 1 by \frac{9}{7} by multiplying 1 by the reciprocal of \frac{9}{7}.

$$1+1\times \frac{7}{9}$$

Multiply 1 and \frac{7}{9} to get \frac{7}{9}.

$$1+\frac{7}{9}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{9}{9}+\frac{7}{9}$$

Since \frac{9}{9} and \frac{7}{9} have the same denominator, add them by adding their numerators.

$$\frac{9+7}{9}$$

Add 9 and 7 to get 16.

$$\frac{16}{9}$$

Factor

$$\frac{2 ^ {4}}{3 ^ {2}} = 1\frac{7}{9} = 1.7777777777777777$$