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

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

Evaluate

$$\frac{13}{6}\approx 2.166666667$$

Solution Steps

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

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

Convert 1 to fraction \frac{2}{2}.

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

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

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

Add 2 and 1 to get 3.

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

Convert 1 to fraction \frac{2}{2}.

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

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

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

Add 2 and 1 to get 3.

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

Divide 1 by \frac{3}{2} by multiplying 1 by the reciprocal of \frac{3}{2}.

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

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

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

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{9}{6}+\frac{4}{6}$$

Since \frac{9}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+4}{6}$$

Add 9 and 4 to get 13.

$$\frac{13}{6}$$

Factor

$$\frac{13}{2 \cdot 3} = 2\frac{1}{6} = 2.1666666666666665$$