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

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

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

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

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

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

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

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

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

Add 3 and 2 to get 5.

$$\frac{\frac{3}{2}}{\frac{5}{3}}$$

Divide \frac{3}{2} by \frac{5}{3} by multiplying \frac{3}{2} by the reciprocal of \frac{5}{3}.

$$\frac{3}{2}\times \frac{3}{5}$$

Multiply \frac{3}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 3}{2\times 5}$$

Do the multiplications in the fraction \frac{3\times 3}{2\times 5}.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$