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

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

Evaluate

$$1$$

Solution Steps

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

$$1-\frac{1}{1+\frac{2}{\frac{6}{2}-\frac{1}{2}}}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{1}{1+\frac{2}{\frac{6-1}{2}}}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

Subtract 1 from 6 to get 5.

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

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

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

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

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

Multiply 2 and 2 to get 4.

$$1-\frac{1}{1+\frac{4}{5}}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

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

$$1-\frac{1}{\frac{5}{5}+\frac{4}{5}}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

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

$$1-\frac{1}{\frac{5+4}{5}}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

Add 5 and 4 to get 9.

$$1-\frac{1}{\frac{9}{5}}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

Divide 1 by \frac{9}{5} by multiplying 1 by the reciprocal of \frac{9}{5}.

$$1-1\times \frac{5}{9}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

Multiply 1 and \frac{5}{9} to get \frac{5}{9}.

$$1-\frac{5}{9}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{9}{9}-\frac{5}{9}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

Since \frac{9}{9} and \frac{5}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-5}{9}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

Subtract 5 from 9 to get 4.

$$\frac{4}{9}+\frac{1}{1+\frac{1}{1+\frac{1}{4}}}$$

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

$$\frac{4}{9}+\frac{1}{1+\frac{1}{\frac{4}{4}+\frac{1}{4}}}$$

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

$$\frac{4}{9}+\frac{1}{1+\frac{1}{\frac{4+1}{4}}}$$

Add 4 and 1 to get 5.

$$\frac{4}{9}+\frac{1}{1+\frac{1}{\frac{5}{4}}}$$

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

$$\frac{4}{9}+\frac{1}{1+1\times \frac{4}{5}}$$

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

$$\frac{4}{9}+\frac{1}{1+\frac{4}{5}}$$

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

$$\frac{4}{9}+\frac{1}{\frac{5}{5}+\frac{4}{5}}$$

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

$$\frac{4}{9}+\frac{1}{\frac{5+4}{5}}$$

Add 5 and 4 to get 9.

$$\frac{4}{9}+\frac{1}{\frac{9}{5}}$$

Divide 1 by \frac{9}{5} by multiplying 1 by the reciprocal of \frac{9}{5}.

$$\frac{4}{9}+1\times \frac{5}{9}$$

Multiply 1 and \frac{5}{9} to get \frac{5}{9}.

$$\frac{4}{9}+\frac{5}{9}$$

Since \frac{4}{9} and \frac{5}{9} have the same denominator, add them by adding their numerators.

$$\frac{4+5}{9}$$

Add 4 and 5 to get 9.

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

Divide 9 by 9 to get 1.

$$1$$

Factor

$$1$$