Solve (129/36+41/8*17/11)div(5frac{1/9-7frac{7}{8}div9frac{9}{20})}{3frac{1}{5}divfrac{9}{2}text{of}5frac{1}{3}}

$$\frac { ( 1 \frac { 29 } { 36 } + 4 \frac { 1 } { 8 } \times 1 \frac { 7 } { 11 } ) \div ( 5 \frac { 1 } { 9 } - 7 \frac { 7 } { 8 } \div 9 \frac { 9 } { 20 } ) } { 3 \frac { 1 } { 5 } \div \frac { 9 } { 2 } \text { of } 5 \frac { 1 } { 3 } }$$

Evaluate

$$\frac{135}{256}=0.52734375$$

Solution Steps

Multiply 1 and 36 to get 36.

$$\frac{\frac{\frac{36+29}{36}+\frac{4\times 8+1}{8}\times \frac{1\times 11+7}{11}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Add 36 and 29 to get 65.

$$\frac{\frac{\frac{65}{36}+\frac{4\times 8+1}{8}\times \frac{1\times 11+7}{11}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Multiply 4 and 8 to get 32.

$$\frac{\frac{\frac{65}{36}+\frac{32+1}{8}\times \frac{1\times 11+7}{11}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Add 32 and 1 to get 33.

$$\frac{\frac{\frac{65}{36}+\frac{33}{8}\times \frac{1\times 11+7}{11}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Multiply 1 and 11 to get 11.

$$\frac{\frac{\frac{65}{36}+\frac{33}{8}\times \frac{11+7}{11}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Add 11 and 7 to get 18.

$$\frac{\frac{\frac{65}{36}+\frac{33}{8}\times \frac{18}{11}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Multiply \frac{33}{8} times \frac{18}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{65}{36}+\frac{33\times 18}{8\times 11}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Do the multiplications in the fraction \frac{33\times 18}{8\times 11}.

$$\frac{\frac{\frac{65}{36}+\frac{594}{88}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Reduce the fraction \frac{594}{88} to lowest terms by extracting and canceling out 22.

$$\frac{\frac{\frac{65}{36}+\frac{27}{4}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Least common multiple of 36 and 4 is 36. Convert \frac{65}{36} and \frac{27}{4} to fractions with denominator 36.

$$\frac{\frac{\frac{65}{36}+\frac{243}{36}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Since \frac{65}{36} and \frac{243}{36} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{65+243}{36}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Add 65 and 243 to get 308.

$$\frac{\frac{\frac{308}{36}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Reduce the fraction \frac{308}{36} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{\frac{77}{9}}{\frac{5\times 9+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Multiply 5 and 9 to get 45.

$$\frac{\frac{\frac{77}{9}}{\frac{45+1}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Add 45 and 1 to get 46.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{\frac{7\times 8+7}{8}}{\frac{9\times 20+9}{20}}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Divide \frac{7\times 8+7}{8} by \frac{9\times 20+9}{20} by multiplying \frac{7\times 8+7}{8} by the reciprocal of \frac{9\times 20+9}{20}.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{\left(7\times 8+7\right)\times 20}{8\left(9\times 20+9\right)}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{5\left(7+7\times 8\right)}{2\left(9+9\times 20\right)}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Multiply 7 and 8 to get 56.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{5\left(7+56\right)}{2\left(9+9\times 20\right)}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Add 7 and 56 to get 63.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{5\times 63}{2\left(9+9\times 20\right)}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Multiply 5 and 63 to get 315.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{315}{2\left(9+9\times 20\right)}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Multiply 9 and 20 to get 180.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{315}{2\left(9+180\right)}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Add 9 and 180 to get 189.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{315}{2\times 189}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Multiply 2 and 189 to get 378.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{315}{378}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Reduce the fraction \frac{315}{378} to lowest terms by extracting and canceling out 63.

$$\frac{\frac{\frac{77}{9}}{\frac{46}{9}-\frac{5}{6}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Least common multiple of 9 and 6 is 18. Convert \frac{46}{9} and \frac{5}{6} to fractions with denominator 18.

$$\frac{\frac{\frac{77}{9}}{\frac{92}{18}-\frac{15}{18}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Since \frac{92}{18} and \frac{15}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{77}{9}}{\frac{92-15}{18}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Subtract 15 from 92 to get 77.

$$\frac{\frac{\frac{77}{9}}{\frac{77}{18}}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Divide \frac{77}{9} by \frac{77}{18} by multiplying \frac{77}{9} by the reciprocal of \frac{77}{18}.

$$\frac{\frac{77}{9}\times \frac{18}{77}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Multiply \frac{77}{9} times \frac{18}{77} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{77\times 18}{9\times 77}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Cancel out 77 in both numerator and denominator.

$$\frac{\frac{18}{9}}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Divide 18 by 9 to get 2.

$$\frac{2}{\frac{\frac{3\times 5+1}{5}}{\frac{9}{2}}\times \frac{5\times 3+1}{3}}$$

Divide \frac{3\times 5+1}{5} by \frac{9}{2} by multiplying \frac{3\times 5+1}{5} by the reciprocal of \frac{9}{2}.

$$\frac{2}{\frac{\left(3\times 5+1\right)\times 2}{5\times 9}\times \frac{5\times 3+1}{3}}$$

Multiply 3 and 5 to get 15.

$$\frac{2}{\frac{\left(15+1\right)\times 2}{5\times 9}\times \frac{5\times 3+1}{3}}$$

Add 15 and 1 to get 16.

$$\frac{2}{\frac{16\times 2}{5\times 9}\times \frac{5\times 3+1}{3}}$$

Multiply 16 and 2 to get 32.

$$\frac{2}{\frac{32}{5\times 9}\times \frac{5\times 3+1}{3}}$$

Multiply 5 and 9 to get 45.

$$\frac{2}{\frac{32}{45}\times \frac{5\times 3+1}{3}}$$

Multiply 5 and 3 to get 15.

$$\frac{2}{\frac{32}{45}\times \frac{15+1}{3}}$$

Add 15 and 1 to get 16.

$$\frac{2}{\frac{32}{45}\times \frac{16}{3}}$$

Multiply \frac{32}{45} times \frac{16}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{\frac{32\times 16}{45\times 3}}$$

Do the multiplications in the fraction \frac{32\times 16}{45\times 3}.

$$\frac{2}{\frac{512}{135}}$$

Divide 2 by \frac{512}{135} by multiplying 2 by the reciprocal of \frac{512}{135}.

$$2\times \frac{135}{512}$$

Express 2\times \frac{135}{512} as a single fraction.

$$\frac{2\times 135}{512}$$

Multiply 2 and 135 to get 270.

$$\frac{270}{512}$$

Reduce the fraction \frac{270}{512} to lowest terms by extracting and canceling out 2.

$$\frac{135}{256}$$

Factor

$$\frac{3 ^ {3} \cdot 5}{2 ^ {8}} = 0.52734375$$