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

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

Evaluate

$$\frac{29}{9}\approx 3.222222222$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

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

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 3 to get 2.

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

Divide 1 by \frac{2}{3} by multiplying 1 by the reciprocal of \frac{2}{3}.

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

Multiply 1 and \frac{3}{2} to get \frac{3}{2}.

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

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

$$3+\frac{1}{\frac{6}{2}+\frac{3}{2}}$$

Since \frac{6}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$3+\frac{1}{\frac{6+3}{2}}$$

Add 6 and 3 to get 9.

$$3+\frac{1}{\frac{9}{2}}$$

Divide 1 by \frac{9}{2} by multiplying 1 by the reciprocal of \frac{9}{2}.

$$3+1\times \frac{2}{9}$$

Multiply 1 and \frac{2}{9} to get \frac{2}{9}.

$$3+\frac{2}{9}$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{27}{9}+\frac{2}{9}$$

Since \frac{27}{9} and \frac{2}{9} have the same denominator, add them by adding their numerators.

$$\frac{27+2}{9}$$

Add 27 and 2 to get 29.

$$\frac{29}{9}$$

Factor

$$\frac{29}{3 ^ {2}} = 3\frac{2}{9} = 3.2222222222222223$$