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

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

Evaluate

$$\frac{10}{23}\approx 0.434782609$$

Solution Steps

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

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

Since \frac{9}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add 9 and 1 to get 10.

$$\frac{1}{2+\frac{1}{\frac{10}{3}}}$$

Divide 1 by \frac{10}{3} by multiplying 1 by the reciprocal of \frac{10}{3}.

$$\frac{1}{2+1\times \frac{3}{10}}$$

Multiply 1 and \frac{3}{10} to get \frac{3}{10}.

$$\frac{1}{2+\frac{3}{10}}$$

Convert 2 to fraction \frac{20}{10}.

$$\frac{1}{\frac{20}{10}+\frac{3}{10}}$$

Since \frac{20}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{20+3}{10}}$$

Add 20 and 3 to get 23.

$$\frac{1}{\frac{23}{10}}$$

Divide 1 by \frac{23}{10} by multiplying 1 by the reciprocal of \frac{23}{10}.

$$1\times \frac{10}{23}$$

Multiply 1 and \frac{10}{23} to get \frac{10}{23}.

$$\frac{10}{23}$$

Factor

$$\frac{2 \cdot 5}{23} = 0.43478260869565216$$