Solve 1/2+3{1+frac{4/5}}

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

Evaluate

$$\frac{3}{11}\approx 0.272727273$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

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

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

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

Add 5 and 4 to get 9.

$$\frac{1}{2+\frac{3}{\frac{9}{5}}}$$

Divide 3 by \frac{9}{5} by multiplying 3 by the reciprocal of \frac{9}{5}.

$$\frac{1}{2+3\times \frac{5}{9}}$$

Express 3\times \frac{5}{9} as a single fraction.

$$\frac{1}{2+\frac{3\times 5}{9}}$$

Multiply 3 and 5 to get 15.

$$\frac{1}{2+\frac{15}{9}}$$

Reduce the fraction \frac{15}{9} to lowest terms by extracting and canceling out 3.

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

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

$$\frac{1}{\frac{6}{3}+\frac{5}{3}}$$

Since \frac{6}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{6+5}{3}}$$

Add 6 and 5 to get 11.

$$\frac{1}{\frac{11}{3}}$$

Divide 1 by \frac{11}{3} by multiplying 1 by the reciprocal of \frac{11}{3}.

$$1\times \frac{3}{11}$$

Multiply 1 and \frac{3}{11} to get \frac{3}{11}.

$$\frac{3}{11}$$

Factor

$$\frac{3}{11} = 0.2727272727272727$$