Solve 10-1/1-1{1+frac{5/4}}

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

Evaluate

$$\frac{41}{5}=8.2$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

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

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

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

Add 4 and 5 to get 9.

$$10-\frac{1}{1-\frac{1}{\frac{9}{4}}}$$

Divide 1 by \frac{9}{4} by multiplying 1 by the reciprocal of \frac{9}{4}.

$$10-\frac{1}{1-1\times \frac{4}{9}}$$

Multiply 1 and \frac{4}{9} to get \frac{4}{9}.

$$10-\frac{1}{1-\frac{4}{9}}$$

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

$$10-\frac{1}{\frac{9}{9}-\frac{4}{9}}$$

Since \frac{9}{9} and \frac{4}{9} have the same denominator, subtract them by subtracting their numerators.

$$10-\frac{1}{\frac{9-4}{9}}$$

Subtract 4 from 9 to get 5.

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

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

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

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

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

Convert 10 to fraction \frac{50}{5}.

$$\frac{50}{5}-\frac{9}{5}$$

Since \frac{50}{5} and \frac{9}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{50-9}{5}$$

Subtract 9 from 50 to get 41.

$$\frac{41}{5}$$

Factor

$$\frac{41}{5} = 8\frac{1}{5} = 8.2$$