Solve 3+2/3+3{4+frac{2/3}}

$$3+ \frac{ 2 }{ 3+ \frac{ 3 }{ 4+ \frac{ 2 }{ 3 } } }$$

Evaluate

$$\frac{181}{51}\approx 3.549019608$$

Solution Steps

Convert 4 to fraction \frac{12}{3}.

$$3+\frac{2}{3+\frac{3}{\frac{12}{3}+\frac{2}{3}}}$$

Since \frac{12}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$3+\frac{2}{3+\frac{3}{\frac{12+2}{3}}}$$

Add 12 and 2 to get 14.

$$3+\frac{2}{3+\frac{3}{\frac{14}{3}}}$$

Divide 3 by \frac{14}{3} by multiplying 3 by the reciprocal of \frac{14}{3}.

$$3+\frac{2}{3+3\times \frac{3}{14}}$$

Express 3\times \frac{3}{14} as a single fraction.

$$3+\frac{2}{3+\frac{3\times 3}{14}}$$

Multiply 3 and 3 to get 9.

$$3+\frac{2}{3+\frac{9}{14}}$$

Convert 3 to fraction \frac{42}{14}.

$$3+\frac{2}{\frac{42}{14}+\frac{9}{14}}$$

Since \frac{42}{14} and \frac{9}{14} have the same denominator, add them by adding their numerators.

$$3+\frac{2}{\frac{42+9}{14}}$$

Add 42 and 9 to get 51.

$$3+\frac{2}{\frac{51}{14}}$$

Divide 2 by \frac{51}{14} by multiplying 2 by the reciprocal of \frac{51}{14}.

$$3+2\times \frac{14}{51}$$

Express 2\times \frac{14}{51} as a single fraction.

$$3+\frac{2\times 14}{51}$$

Multiply 2 and 14 to get 28.

$$3+\frac{28}{51}$$

Convert 3 to fraction \frac{153}{51}.

$$\frac{153}{51}+\frac{28}{51}$$

Since \frac{153}{51} and \frac{28}{51} have the same denominator, add them by adding their numerators.

$$\frac{153+28}{51}$$

Add 153 and 28 to get 181.

$$\frac{181}{51}$$

Factor

$$\frac{181}{3 \cdot 17} = 3\frac{28}{51} = 3.549019607843137$$