Solve (4/3-7/6+1-17/12)(frac{7/4-5+frac{7}{2}-frac{2}{6})}{(frac{8}{5}-3)+(frac{16}{25}*frac{125}{8}*frac{1}{12}*frac{3}{4})}

$$\frac { ( \frac { 4 } { 3 } - \frac { 7 } { 6 } + 1 - \frac { 17 } { 12 } ) ( \frac { 7 } { 4 } - 5 + \frac { 7 } { 2 } - \frac { 2 } { 6 } ) } { ( \frac { 8 } { 5 } - 3 ) + ( \frac { 16 } { 25 } \cdot \frac { 125 } { 8 } \cdot \frac { 1 } { 12 } \cdot \frac { 3 } { 4 } ) }$$

Evaluate

$$-\frac{5}{186}\approx -0.02688172$$

Solution Steps

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{7}{6} to fractions with denominator 6.

$$\frac{\left(\frac{8}{6}-\frac{7}{6}+1-\frac{17}{12}\right)\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Since \frac{8}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\frac{8-7}{6}+1-\frac{17}{12}\right)\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Subtract 7 from 8 to get 1.

$$\frac{\left(\frac{1}{6}+1-\frac{17}{12}\right)\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{\left(\frac{1}{6}+\frac{6}{6}-\frac{17}{12}\right)\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Since \frac{1}{6} and \frac{6}{6} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{1+6}{6}-\frac{17}{12}\right)\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Add 1 and 6 to get 7.

$$\frac{\left(\frac{7}{6}-\frac{17}{12}\right)\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Least common multiple of 6 and 12 is 12. Convert \frac{7}{6} and \frac{17}{12} to fractions with denominator 12.

$$\frac{\left(\frac{14}{12}-\frac{17}{12}\right)\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Since \frac{14}{12} and \frac{17}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14-17}{12}\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Subtract 17 from 14 to get -3.

$$\frac{\frac{-3}{12}\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

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

$$\frac{-\frac{1}{4}\left(\frac{7}{4}-5+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{-\frac{1}{4}\left(\frac{7}{4}-\frac{20}{4}+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Since \frac{7}{4} and \frac{20}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{4}\left(\frac{7-20}{4}+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Subtract 20 from 7 to get -13.

$$\frac{-\frac{1}{4}\left(-\frac{13}{4}+\frac{7}{2}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{13}{4} and \frac{7}{2} to fractions with denominator 4.

$$\frac{-\frac{1}{4}\left(-\frac{13}{4}+\frac{14}{4}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Since -\frac{13}{4} and \frac{14}{4} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{4}\left(\frac{-13+14}{4}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Add -13 and 14 to get 1.

$$\frac{-\frac{1}{4}\left(\frac{1}{4}-\frac{2}{6}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

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

$$\frac{-\frac{1}{4}\left(\frac{1}{4}-\frac{1}{3}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{-\frac{1}{4}\left(\frac{3}{12}-\frac{4}{12}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Since \frac{3}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{4}\times \frac{3-4}{12}}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Subtract 4 from 3 to get -1.

$$\frac{-\frac{1}{4}\left(-\frac{1}{12}\right)}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Multiply -\frac{1}{4} times -\frac{1}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-\left(-1\right)}{4\times 12}}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{4\times 12}.

$$\frac{\frac{1}{48}}{\frac{8}{5}-3+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{\frac{1}{48}}{\frac{8}{5}-\frac{15}{5}+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Since \frac{8}{5} and \frac{15}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{48}}{\frac{8-15}{5}+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Subtract 15 from 8 to get -7.

$$\frac{\frac{1}{48}}{-\frac{7}{5}+\frac{16}{25}\times \frac{125}{8}\times \frac{1}{12}\times \frac{3}{4}}$$

Multiply \frac{16}{25} times \frac{125}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{48}}{-\frac{7}{5}+\frac{16\times 125}{25\times 8}\times \frac{1}{12}\times \frac{3}{4}}$$

Do the multiplications in the fraction \frac{16\times 125}{25\times 8}.

$$\frac{\frac{1}{48}}{-\frac{7}{5}+\frac{2000}{200}\times \frac{1}{12}\times \frac{3}{4}}$$

Divide 2000 by 200 to get 10.

$$\frac{\frac{1}{48}}{-\frac{7}{5}+10\times \frac{1}{12}\times \frac{3}{4}}$$

Multiply 10 and \frac{1}{12} to get \frac{10}{12}.

$$\frac{\frac{1}{48}}{-\frac{7}{5}+\frac{10}{12}\times \frac{3}{4}}$$

Reduce the fraction \frac{10}{12} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{48}}{-\frac{7}{5}+\frac{5}{6}\times \frac{3}{4}}$$

Multiply \frac{5}{6} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{48}}{-\frac{7}{5}+\frac{5\times 3}{6\times 4}}$$

Do the multiplications in the fraction \frac{5\times 3}{6\times 4}.

$$\frac{\frac{1}{48}}{-\frac{7}{5}+\frac{15}{24}}$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{48}}{-\frac{7}{5}+\frac{5}{8}}$$

Least common multiple of 5 and 8 is 40. Convert -\frac{7}{5} and \frac{5}{8} to fractions with denominator 40.

$$\frac{\frac{1}{48}}{-\frac{56}{40}+\frac{25}{40}}$$

Since -\frac{56}{40} and \frac{25}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{48}}{\frac{-56+25}{40}}$$

Add -56 and 25 to get -31.

$$\frac{\frac{1}{48}}{-\frac{31}{40}}$$

Divide \frac{1}{48} by -\frac{31}{40} by multiplying \frac{1}{48} by the reciprocal of -\frac{31}{40}.

$$\frac{1}{48}\left(-\frac{40}{31}\right)$$

Multiply \frac{1}{48} times -\frac{40}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-40\right)}{48\times 31}$$

Do the multiplications in the fraction \frac{1\left(-40\right)}{48\times 31}.

$$\frac{-40}{1488}$$

Reduce the fraction \frac{-40}{1488} to lowest terms by extracting and canceling out 8.

$$-\frac{5}{186}$$

Factor

$$-\frac{5}{186} = -0.026881720430107527$$