Solve 3+2/3+1{1+frac{1/4}}

$$3 + \frac { 2 } { 3 + \frac { 1 } { 1 + \frac { 1 } { 4 } } }$$

Evaluate

$$\frac{67}{19}\approx 3.526315789$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$3+\frac{2}{3+\frac{1}{\frac{4}{4}+\frac{1}{4}}}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$3+\frac{2}{3+\frac{1}{\frac{4+1}{4}}}$$

Add 4 and 1 to get 5.

$$3+\frac{2}{3+\frac{1}{\frac{5}{4}}}$$

Divide 1 by \frac{5}{4} by multiplying 1 by the reciprocal of \frac{5}{4}.

$$3+\frac{2}{3+1\times \frac{4}{5}}$$

Multiply 1 and \frac{4}{5} to get \frac{4}{5}.

$$3+\frac{2}{3+\frac{4}{5}}$$

Convert 3 to fraction \frac{15}{5}.

$$3+\frac{2}{\frac{15}{5}+\frac{4}{5}}$$

Since \frac{15}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$3+\frac{2}{\frac{15+4}{5}}$$

Add 15 and 4 to get 19.

$$3+\frac{2}{\frac{19}{5}}$$

Divide 2 by \frac{19}{5} by multiplying 2 by the reciprocal of \frac{19}{5}.

$$3+2\times \frac{5}{19}$$

Express 2\times \frac{5}{19} as a single fraction.

$$3+\frac{2\times 5}{19}$$

Multiply 2 and 5 to get 10.

$$3+\frac{10}{19}$$

Convert 3 to fraction \frac{57}{19}.

$$\frac{57}{19}+\frac{10}{19}$$

Since \frac{57}{19} and \frac{10}{19} have the same denominator, add them by adding their numerators.

$$\frac{57+10}{19}$$

Add 57 and 10 to get 67.

$$\frac{67}{19}$$

Factor

$$\frac{67}{19} = 3\frac{10}{19} = 3.526315789473684$$