Solve 2+1/2+frac{1{2}}

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

Evaluate

$$\frac{12}{5}=2.4$$

Solution Steps

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

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

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

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

Divide 1 by \frac{5}{2} by multiplying 1 by the reciprocal of \frac{5}{2}.

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

Multiply 1 and \frac{2}{5} to get \frac{2}{5}.

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

Convert 2 to fraction \frac{10}{5}.

$$\frac{10}{5}+\frac{2}{5}$$

Since \frac{10}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{10+2}{5}$$

Add 10 and 2 to get 12.

$$\frac{12}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{5} = 2\frac{2}{5} = 2.4$$