Solve (5/6*7/8*10/21)div(3-frac{7/2)}{frac{9}{8}-frac{13}{6}+frac{7}{4}-frac{25}{9}+frac{17}{18}}

$$\frac { ( \frac { 5 } { 6 } \cdot \frac { 7 } { 8 } \cdot \frac { 10 } { 21 } ) \div ( 3 - \frac { 7 } { 2 } ) } { \frac { 9 } { 8 } - \frac { 13 } { 6 } + \frac { 7 } { 4 } - \frac { 25 } { 9 } + \frac { 17 } { 18 } }$$

Evaluate

$$\frac{50}{81}\approx 0.617283951$$

Solution Steps

Multiply \frac{5}{6} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{5\times 7}{6\times 8}\times \frac{10}{21}}{3-\frac{7}{2}}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Do the multiplications in the fraction \frac{5\times 7}{6\times 8}.

$$\frac{\frac{\frac{35}{48}\times \frac{10}{21}}{3-\frac{7}{2}}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Multiply \frac{35}{48} times \frac{10}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{35\times 10}{48\times 21}}{3-\frac{7}{2}}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Do the multiplications in the fraction \frac{35\times 10}{48\times 21}.

$$\frac{\frac{\frac{350}{1008}}{3-\frac{7}{2}}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Reduce the fraction \frac{350}{1008} to lowest terms by extracting and canceling out 14.

$$\frac{\frac{\frac{25}{72}}{3-\frac{7}{2}}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{\frac{\frac{25}{72}}{\frac{6}{2}-\frac{7}{2}}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Since \frac{6}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{25}{72}}{\frac{6-7}{2}}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Subtract 7 from 6 to get -1.

$$\frac{\frac{\frac{25}{72}}{-\frac{1}{2}}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Divide \frac{25}{72} by -\frac{1}{2} by multiplying \frac{25}{72} by the reciprocal of -\frac{1}{2}.

$$\frac{\frac{25}{72}\left(-2\right)}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Express \frac{25}{72}\left(-2\right) as a single fraction.

$$\frac{\frac{25\left(-2\right)}{72}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Multiply 25 and -2 to get -50.

$$\frac{\frac{-50}{72}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Reduce the fraction \frac{-50}{72} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{25}{36}}{\frac{9}{8}-\frac{13}{6}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Least common multiple of 8 and 6 is 24. Convert \frac{9}{8} and \frac{13}{6} to fractions with denominator 24.

$$\frac{-\frac{25}{36}}{\frac{27}{24}-\frac{52}{24}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Since \frac{27}{24} and \frac{52}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{25}{36}}{\frac{27-52}{24}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Subtract 52 from 27 to get -25.

$$\frac{-\frac{25}{36}}{-\frac{25}{24}+\frac{7}{4}-\frac{25}{9}+\frac{17}{18}}$$

Least common multiple of 24 and 4 is 24. Convert -\frac{25}{24} and \frac{7}{4} to fractions with denominator 24.

$$\frac{-\frac{25}{36}}{-\frac{25}{24}+\frac{42}{24}-\frac{25}{9}+\frac{17}{18}}$$

Since -\frac{25}{24} and \frac{42}{24} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{25}{36}}{\frac{-25+42}{24}-\frac{25}{9}+\frac{17}{18}}$$

Add -25 and 42 to get 17.

$$\frac{-\frac{25}{36}}{\frac{17}{24}-\frac{25}{9}+\frac{17}{18}}$$

Least common multiple of 24 and 9 is 72. Convert \frac{17}{24} and \frac{25}{9} to fractions with denominator 72.

$$\frac{-\frac{25}{36}}{\frac{51}{72}-\frac{200}{72}+\frac{17}{18}}$$

Since \frac{51}{72} and \frac{200}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{25}{36}}{\frac{51-200}{72}+\frac{17}{18}}$$

Subtract 200 from 51 to get -149.

$$\frac{-\frac{25}{36}}{-\frac{149}{72}+\frac{17}{18}}$$

Least common multiple of 72 and 18 is 72. Convert -\frac{149}{72} and \frac{17}{18} to fractions with denominator 72.

$$\frac{-\frac{25}{36}}{-\frac{149}{72}+\frac{68}{72}}$$

Since -\frac{149}{72} and \frac{68}{72} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{25}{36}}{\frac{-149+68}{72}}$$

Add -149 and 68 to get -81.

$$\frac{-\frac{25}{36}}{\frac{-81}{72}}$$

Reduce the fraction \frac{-81}{72} to lowest terms by extracting and canceling out 9.

$$\frac{-\frac{25}{36}}{-\frac{9}{8}}$$

Divide -\frac{25}{36} by -\frac{9}{8} by multiplying -\frac{25}{36} by the reciprocal of -\frac{9}{8}.

$$-\frac{25}{36}\left(-\frac{8}{9}\right)$$

Multiply -\frac{25}{36} times -\frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-25\left(-8\right)}{36\times 9}$$

Do the multiplications in the fraction \frac{-25\left(-8\right)}{36\times 9}.

$$\frac{200}{324}$$

Reduce the fraction \frac{200}{324} to lowest terms by extracting and canceling out 4.

$$\frac{50}{81}$$

Factor

$$\frac{2 \cdot 5 ^ {2}}{3 ^ {4}} = 0.6172839506172839$$