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

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

Evaluate

$$\frac{21}{67}\approx 0.313432836$$

Solution Steps

Convert 5 to fraction \frac{20}{4}.

$$\frac{1}{3+\frac{1}{\frac{20}{4}+\frac{1}{4}}}$$

Since \frac{20}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{3+\frac{1}{\frac{20+1}{4}}}$$

Add 20 and 1 to get 21.

$$\frac{1}{3+\frac{1}{\frac{21}{4}}}$$

Divide 1 by \frac{21}{4} by multiplying 1 by the reciprocal of \frac{21}{4}.

$$\frac{1}{3+1\times \frac{4}{21}}$$

Multiply 1 and \frac{4}{21} to get \frac{4}{21}.

$$\frac{1}{3+\frac{4}{21}}$$

Convert 3 to fraction \frac{63}{21}.

$$\frac{1}{\frac{63}{21}+\frac{4}{21}}$$

Since \frac{63}{21} and \frac{4}{21} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{63+4}{21}}$$

Add 63 and 4 to get 67.

$$\frac{1}{\frac{67}{21}}$$

Divide 1 by \frac{67}{21} by multiplying 1 by the reciprocal of \frac{67}{21}.

$$1\times \frac{21}{67}$$

Multiply 1 and \frac{21}{67} to get \frac{21}{67}.

$$\frac{21}{67}$$

Factor

$$\frac{3 \cdot 7}{67} = 0.31343283582089554$$