Solve (17/18*52/5-8:15/7):4frac{1/4}{5frac{3}{4}-3frac{11}{12}}+frac{2frac{11}{12}-3:(2frac{2}{7}*3frac{1}{2}-3frac{1}{2})}{2frac{2}{5}*1frac{7}{8}:3frac{3}{11}}

$$\frac { ( 1 \frac { 7 } { 18 } \cdot 5 \frac { 2 } { 5 } - 8 : 1 \frac { 5 } { 7 } ) : 4 \frac { 1 } { 4 } } { 5 \frac { 3 } { 4 } - 3 \frac { 11 } { 12 } } + \frac { 2 \frac { 11 } { 12 } - 3 : ( 2 \frac { 2 } { 7 } \cdot 3 \frac { 1 } { 2 } - 3 \frac { 1 } { 2 } ) } { 2 \frac { 2 } { 5 } \cdot 1 \frac { 7 } { 8 } : 3 \frac { 3 } { 11 } }$$

Evaluate

$$2$$

Solution Steps

Multiply 1 and 18 to get 18.

$$\frac{\frac{\frac{18+7}{18}\times \frac{5\times 5+2}{5}-\frac{8}{\frac{1\times 7+5}{7}}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 18 and 7 to get 25.

$$\frac{\frac{\frac{25}{18}\times \frac{5\times 5+2}{5}-\frac{8}{\frac{1\times 7+5}{7}}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 5 and 5 to get 25.

$$\frac{\frac{\frac{25}{18}\times \frac{25+2}{5}-\frac{8}{\frac{1\times 7+5}{7}}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 25 and 2 to get 27.

$$\frac{\frac{\frac{25}{18}\times \frac{27}{5}-\frac{8}{\frac{1\times 7+5}{7}}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply \frac{25}{18} times \frac{27}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{25\times 27}{18\times 5}-\frac{8}{\frac{1\times 7+5}{7}}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Do the multiplications in the fraction \frac{25\times 27}{18\times 5}.

$$\frac{\frac{\frac{675}{90}-\frac{8}{\frac{1\times 7+5}{7}}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Reduce the fraction \frac{675}{90} to lowest terms by extracting and canceling out 45.

$$\frac{\frac{\frac{15}{2}-\frac{8}{\frac{1\times 7+5}{7}}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Divide 8 by \frac{1\times 7+5}{7} by multiplying 8 by the reciprocal of \frac{1\times 7+5}{7}.

$$\frac{\frac{\frac{15}{2}-\frac{8\times 7}{1\times 7+5}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 8 and 7 to get 56.

$$\frac{\frac{\frac{15}{2}-\frac{56}{1\times 7+5}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 1 and 7 to get 7.

$$\frac{\frac{\frac{15}{2}-\frac{56}{7+5}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 7 and 5 to get 12.

$$\frac{\frac{\frac{15}{2}-\frac{56}{12}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Reduce the fraction \frac{56}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{\frac{15}{2}-\frac{14}{3}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{15}{2} and \frac{14}{3} to fractions with denominator 6.

$$\frac{\frac{\frac{45}{6}-\frac{28}{6}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Since \frac{45}{6} and \frac{28}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{45-28}{6}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Subtract 28 from 45 to get 17.

$$\frac{\frac{\frac{17}{6}}{\frac{4\times 4+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 4 and 4 to get 16.

$$\frac{\frac{\frac{17}{6}}{\frac{16+1}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 16 and 1 to get 17.

$$\frac{\frac{\frac{17}{6}}{\frac{17}{4}}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Divide \frac{17}{6} by \frac{17}{4} by multiplying \frac{17}{6} by the reciprocal of \frac{17}{4}.

$$\frac{\frac{17}{6}\times \frac{4}{17}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply \frac{17}{6} times \frac{4}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{17\times 4}{6\times 17}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Cancel out 17 in both numerator and denominator.

$$\frac{\frac{4}{6}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{3}}{\frac{5\times 4+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{2}{3}}{\frac{20+3}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 20 and 3 to get 23.

$$\frac{\frac{2}{3}}{\frac{23}{4}-\frac{3\times 12+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 3 and 12 to get 36.

$$\frac{\frac{2}{3}}{\frac{23}{4}-\frac{36+11}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 36 and 11 to get 47.

$$\frac{\frac{2}{3}}{\frac{23}{4}-\frac{47}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Least common multiple of 4 and 12 is 12. Convert \frac{23}{4} and \frac{47}{12} to fractions with denominator 12.

$$\frac{\frac{2}{3}}{\frac{69}{12}-\frac{47}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Since \frac{69}{12} and \frac{47}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{3}}{\frac{69-47}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Subtract 47 from 69 to get 22.

$$\frac{\frac{2}{3}}{\frac{22}{12}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Reduce the fraction \frac{22}{12} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{3}}{\frac{11}{6}}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Divide \frac{2}{3} by \frac{11}{6} by multiplying \frac{2}{3} by the reciprocal of \frac{11}{6}.

$$\frac{2}{3}\times \frac{6}{11}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply \frac{2}{3} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 6}{3\times 11}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Do the multiplications in the fraction \frac{2\times 6}{3\times 11}.

$$\frac{12}{33}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Reduce the fraction \frac{12}{33} to lowest terms by extracting and canceling out 3.

$$\frac{4}{11}+\frac{\frac{2\times 12+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 2 and 12 to get 24.

$$\frac{4}{11}+\frac{\frac{24+11}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 24 and 11 to get 35.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{2\times 7+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 2 and 7 to get 14.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{14+2}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 14 and 2 to get 16.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{16}{7}\times \frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 3 and 2 to get 6.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{16}{7}\times \frac{6+1}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 6 and 1 to get 7.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{16}{7}\times \frac{7}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply \frac{16}{7} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{16\times 7}{7\times 2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Cancel out 7 in both numerator and denominator.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{16}{2}-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Divide 16 by 2 to get 8.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{8-\frac{3\times 2+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 3 and 2 to get 6.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{8-\frac{6+1}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 6 and 1 to get 7.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{8-\frac{7}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Convert 8 to fraction \frac{16}{2}.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{16}{2}-\frac{7}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Since \frac{16}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{16-7}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Subtract 7 from 16 to get 9.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3}{\frac{9}{2}}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Divide 3 by \frac{9}{2} by multiplying 3 by the reciprocal of \frac{9}{2}.

$$\frac{4}{11}+\frac{\frac{35}{12}-3\times \frac{2}{9}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Express 3\times \frac{2}{9} as a single fraction.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{3\times 2}{9}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 3 and 2 to get 6.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{6}{9}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{2}{3}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Least common multiple of 12 and 3 is 12. Convert \frac{35}{12} and \frac{2}{3} to fractions with denominator 12.

$$\frac{4}{11}+\frac{\frac{35}{12}-\frac{8}{12}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Since \frac{35}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{11}+\frac{\frac{35-8}{12}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Subtract 8 from 35 to get 27.

$$\frac{4}{11}+\frac{\frac{27}{12}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{2\times 5+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 2 and 5 to get 10.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{10+2}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 10 and 2 to get 12.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{12}{5}\times \frac{1\times 8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply 1 and 8 to get 8.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{12}{5}\times \frac{8+7}{8}}{\frac{3\times 11+3}{11}}}$$

Add 8 and 7 to get 15.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{12}{5}\times \frac{15}{8}}{\frac{3\times 11+3}{11}}}$$

Multiply \frac{12}{5} times \frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{12\times 15}{5\times 8}}{\frac{3\times 11+3}{11}}}$$

Do the multiplications in the fraction \frac{12\times 15}{5\times 8}.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{180}{40}}{\frac{3\times 11+3}{11}}}$$

Reduce the fraction \frac{180}{40} to lowest terms by extracting and canceling out 20.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{9}{2}}{\frac{3\times 11+3}{11}}}$$

Multiply 3 and 11 to get 33.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{9}{2}}{\frac{33+3}{11}}}$$

Add 33 and 3 to get 36.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{\frac{9}{2}}{\frac{36}{11}}}$$

Divide \frac{9}{2} by \frac{36}{11} by multiplying \frac{9}{2} by the reciprocal of \frac{36}{11}.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{9}{2}\times \frac{11}{36}}$$

Multiply \frac{9}{2} times \frac{11}{36} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{9\times 11}{2\times 36}}$$

Do the multiplications in the fraction \frac{9\times 11}{2\times 36}.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{99}{72}}$$

Reduce the fraction \frac{99}{72} to lowest terms by extracting and canceling out 9.

$$\frac{4}{11}+\frac{\frac{9}{4}}{\frac{11}{8}}$$

Divide \frac{9}{4} by \frac{11}{8} by multiplying \frac{9}{4} by the reciprocal of \frac{11}{8}.

$$\frac{4}{11}+\frac{9}{4}\times \frac{8}{11}$$

Multiply \frac{9}{4} times \frac{8}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{11}+\frac{9\times 8}{4\times 11}$$

Do the multiplications in the fraction \frac{9\times 8}{4\times 11}.

$$\frac{4}{11}+\frac{72}{44}$$

Reduce the fraction \frac{72}{44} to lowest terms by extracting and canceling out 4.

$$\frac{4}{11}+\frac{18}{11}$$

Since \frac{4}{11} and \frac{18}{11} have the same denominator, add them by adding their numerators.

$$\frac{4+18}{11}$$

Add 4 and 18 to get 22.

$$\frac{22}{11}$$

Divide 22 by 11 to get 2.

$$2$$

Factor

$$2$$