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

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

Evaluate

$$\frac{19}{5}=3.8$$

Solution Steps

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

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

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

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

Add 4 and 1 to get 5.

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

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

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

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

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

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

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

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

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

Add 15 and 4 to get 19.

$$\frac{19}{5}$$

Factor

$$\frac{19}{5} = 3\frac{4}{5} = 3.8$$