Solve 1+1/9/1+1{1+frac{8/10}}

$$\frac { 1 + \frac { 1 } { 9 } } { 1 + \frac { 1 } { 1 + \frac { 8 } { 10 } } }$$

Evaluate

$$\frac{5}{7}\approx 0.714285714$$

Solution Steps

Convert 1 to fraction \frac{9}{9}.

$$\frac{\frac{9}{9}+\frac{1}{9}}{1+\frac{1}{1+\frac{8}{10}}}$$

Since \frac{9}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+1}{9}}{1+\frac{1}{1+\frac{8}{10}}}$$

Add 9 and 1 to get 10.

$$\frac{\frac{10}{9}}{1+\frac{1}{1+\frac{8}{10}}}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{10}{9}}{1+\frac{1}{1+\frac{4}{5}}}$$

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

$$\frac{\frac{10}{9}}{1+\frac{1}{\frac{5}{5}+\frac{4}{5}}}$$

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

$$\frac{\frac{10}{9}}{1+\frac{1}{\frac{5+4}{5}}}$$

Add 5 and 4 to get 9.

$$\frac{\frac{10}{9}}{1+\frac{1}{\frac{9}{5}}}$$

Divide 1 by \frac{9}{5} by multiplying 1 by the reciprocal of \frac{9}{5}.

$$\frac{\frac{10}{9}}{1+1\times \frac{5}{9}}$$

Multiply 1 and \frac{5}{9} to get \frac{5}{9}.

$$\frac{\frac{10}{9}}{1+\frac{5}{9}}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{\frac{10}{9}}{\frac{9}{9}+\frac{5}{9}}$$

Since \frac{9}{9} and \frac{5}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10}{9}}{\frac{9+5}{9}}$$

Add 9 and 5 to get 14.

$$\frac{\frac{10}{9}}{\frac{14}{9}}$$

Divide \frac{10}{9} by \frac{14}{9} by multiplying \frac{10}{9} by the reciprocal of \frac{14}{9}.

$$\frac{10}{9}\times \frac{9}{14}$$

Multiply \frac{10}{9} times \frac{9}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 9}{9\times 14}$$

Cancel out 9 in both numerator and denominator.

$$\frac{10}{14}$$

Reduce the fraction \frac{10}{14} to lowest terms by extracting and canceling out 2.

$$\frac{5}{7}$$

Factor

$$\frac{5}{7} = 0.7142857142857143$$