Solve 8-7/6-11{5-frac{2/4-frac{2{3}}}}

$$8- \frac{ 7 }{ 6- \frac{ 11 }{ 5- \frac{ 2 }{ 4- \frac{ 2 }{ 3 } } } }$$

Evaluate

$$6$$

Solution Steps

Convert 4 to fraction \frac{12}{3}.

$$8-\frac{7}{6-\frac{11}{5-\frac{2}{\frac{12}{3}-\frac{2}{3}}}}$$

Since \frac{12}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$8-\frac{7}{6-\frac{11}{5-\frac{2}{\frac{12-2}{3}}}}$$

Subtract 2 from 12 to get 10.

$$8-\frac{7}{6-\frac{11}{5-\frac{2}{\frac{10}{3}}}}$$

Divide 2 by \frac{10}{3} by multiplying 2 by the reciprocal of \frac{10}{3}.

$$8-\frac{7}{6-\frac{11}{5-2\times \frac{3}{10}}}$$

Express 2\times \frac{3}{10} as a single fraction.

$$8-\frac{7}{6-\frac{11}{5-\frac{2\times 3}{10}}}$$

Multiply 2 and 3 to get 6.

$$8-\frac{7}{6-\frac{11}{5-\frac{6}{10}}}$$

Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$8-\frac{7}{6-\frac{11}{5-\frac{3}{5}}}$$

Convert 5 to fraction \frac{25}{5}.

$$8-\frac{7}{6-\frac{11}{\frac{25}{5}-\frac{3}{5}}}$$

Since \frac{25}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$8-\frac{7}{6-\frac{11}{\frac{25-3}{5}}}$$

Subtract 3 from 25 to get 22.

$$8-\frac{7}{6-\frac{11}{\frac{22}{5}}}$$

Divide 11 by \frac{22}{5} by multiplying 11 by the reciprocal of \frac{22}{5}.

$$8-\frac{7}{6-11\times \frac{5}{22}}$$

Express 11\times \frac{5}{22} as a single fraction.

$$8-\frac{7}{6-\frac{11\times 5}{22}}$$

Multiply 11 and 5 to get 55.

$$8-\frac{7}{6-\frac{55}{22}}$$

Reduce the fraction \frac{55}{22} to lowest terms by extracting and canceling out 11.

$$8-\frac{7}{6-\frac{5}{2}}$$

Convert 6 to fraction \frac{12}{2}.

$$8-\frac{7}{\frac{12}{2}-\frac{5}{2}}$$

Since \frac{12}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$8-\frac{7}{\frac{12-5}{2}}$$

Subtract 5 from 12 to get 7.

$$8-\frac{7}{\frac{7}{2}}$$

Divide 7 by \frac{7}{2} by multiplying 7 by the reciprocal of \frac{7}{2}.

$$8-7\times \frac{2}{7}$$

Cancel out 7 and 7.

$$8-2$$

Subtract 2 from 8 to get 6.

$$6$$

Factor

$$2\times 3$$