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

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

Evaluate

$$\frac{8}{5}=1.6$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

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

Since \frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

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

Divide 1 by \frac{5}{3} by multiplying 1 by the reciprocal of \frac{5}{3}.

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

Multiply 1 and \frac{3}{5} to get \frac{3}{5}.

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

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

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

Since \frac{5}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

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

Add 5 and 3 to get 8.

$$\frac{8}{5}$$

Factor

$$\frac{2 ^ {3}}{5} = 1\frac{3}{5} = 1.6$$