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

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

Evaluate

$$\frac{31}{8}=3.875$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\frac{5}{1+\frac{1}{3+\frac{1}{\frac{8}{4}+\frac{1}{4}}}}$$

Since \frac{8}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{5}{1+\frac{1}{3+\frac{1}{\frac{8+1}{4}}}}$$

Add 8 and 1 to get 9.

$$\frac{5}{1+\frac{1}{3+\frac{1}{\frac{9}{4}}}}$$

Divide 1 by \frac{9}{4} by multiplying 1 by the reciprocal of \frac{9}{4}.

$$\frac{5}{1+\frac{1}{3+1\times \frac{4}{9}}}$$

Multiply 1 and \frac{4}{9} to get \frac{4}{9}.

$$\frac{5}{1+\frac{1}{3+\frac{4}{9}}}$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{5}{1+\frac{1}{\frac{27}{9}+\frac{4}{9}}}$$

Since \frac{27}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{5}{1+\frac{1}{\frac{27+4}{9}}}$$

Add 27 and 4 to get 31.

$$\frac{5}{1+\frac{1}{\frac{31}{9}}}$$

Divide 1 by \frac{31}{9} by multiplying 1 by the reciprocal of \frac{31}{9}.

$$\frac{5}{1+1\times \frac{9}{31}}$$

Multiply 1 and \frac{9}{31} to get \frac{9}{31}.

$$\frac{5}{1+\frac{9}{31}}$$

Convert 1 to fraction \frac{31}{31}.

$$\frac{5}{\frac{31}{31}+\frac{9}{31}}$$

Since \frac{31}{31} and \frac{9}{31} have the same denominator, add them by adding their numerators.

$$\frac{5}{\frac{31+9}{31}}$$

Add 31 and 9 to get 40.

$$\frac{5}{\frac{40}{31}}$$

Divide 5 by \frac{40}{31} by multiplying 5 by the reciprocal of \frac{40}{31}.

$$5\times \frac{31}{40}$$

Express 5\times \frac{31}{40} as a single fraction.

$$\frac{5\times 31}{40}$$

Multiply 5 and 31 to get 155.

$$\frac{155}{40}$$

Reduce the fraction \frac{155}{40} to lowest terms by extracting and canceling out 5.

$$\frac{31}{8}$$

Factor

$$\frac{31}{2 ^ {3}} = 3\frac{7}{8} = 3.875$$