Solve (65/36+33/8*18/11)div(46/9-frac{63}{8}divfrac{189}{20})

$$( \frac { 65 } { 36 } + \frac { 33 } { 8 } \times \frac { 18 } { 11 } ) \div ( \frac { 46 } { 9 } - \frac { 63 } { 8 } \div \frac { 189 } { 20 } )$$

Evaluate

$$2$$

Solution Steps

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

$$\frac{\frac{65}{36}+\frac{33\times 18}{8\times 11}}{\frac{46}{9}-\frac{\frac{63}{8}}{\frac{189}{20}}}$$

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

$$\frac{\frac{65}{36}+\frac{594}{88}}{\frac{46}{9}-\frac{\frac{63}{8}}{\frac{189}{20}}}$$

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

$$\frac{\frac{65}{36}+\frac{27}{4}}{\frac{46}{9}-\frac{\frac{63}{8}}{\frac{189}{20}}}$$

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

$$\frac{\frac{65}{36}+\frac{243}{36}}{\frac{46}{9}-\frac{\frac{63}{8}}{\frac{189}{20}}}$$

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

$$\frac{\frac{65+243}{36}}{\frac{46}{9}-\frac{\frac{63}{8}}{\frac{189}{20}}}$$

Add 65 and 243 to get 308.

$$\frac{\frac{308}{36}}{\frac{46}{9}-\frac{\frac{63}{8}}{\frac{189}{20}}}$$

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

$$\frac{\frac{77}{9}}{\frac{46}{9}-\frac{\frac{63}{8}}{\frac{189}{20}}}$$

Divide \frac{63}{8} by \frac{189}{20} by multiplying \frac{63}{8} by the reciprocal of \frac{189}{20}.

$$\frac{\frac{77}{9}}{\frac{46}{9}-\frac{63}{8}\times \frac{20}{189}}$$

Multiply \frac{63}{8} times \frac{20}{189} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{77}{9}}{\frac{46}{9}-\frac{63\times 20}{8\times 189}}$$

Do the multiplications in the fraction \frac{63\times 20}{8\times 189}.

$$\frac{\frac{77}{9}}{\frac{46}{9}-\frac{1260}{1512}}$$

Reduce the fraction \frac{1260}{1512} to lowest terms by extracting and canceling out 252.

$$\frac{\frac{77}{9}}{\frac{46}{9}-\frac{5}{6}}$$

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

$$\frac{\frac{77}{9}}{\frac{92}{18}-\frac{15}{18}}$$

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

$$\frac{\frac{77}{9}}{\frac{92-15}{18}}$$

Subtract 15 from 92 to get 77.

$$\frac{\frac{77}{9}}{\frac{77}{18}}$$

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

$$\frac{77}{9}\times \frac{18}{77}$$

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

$$\frac{77\times 18}{9\times 77}$$

Cancel out 77 in both numerator and denominator.

$$\frac{18}{9}$$

Divide 18 by 9 to get 2.

$$2$$

Factor

$$2$$