Solve (4/5*(1/6-3/8)):(5/12*(frac{1}{10}+frac{7}{4}))=

$$( \frac { 4 } { 5 } \cdot ( \frac { 1 } { 6 } - \frac { 3 } { 8 } ) ) : ( \frac { 5 } { 12 } \cdot ( \frac { 1 } { 10 } + \frac { 7 } { 4 } ) ) =$$

Evaluate

$$-\frac{8}{37}\approx -0.216216216$$

Solution Steps

Least common multiple of 6 and 8 is 24. Convert \frac{1}{6} and \frac{3}{8} to fractions with denominator 24.

$$\frac{\frac{4}{5}\left(\frac{4}{24}-\frac{9}{24}\right)}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Since \frac{4}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{5}\times \frac{4-9}{24}}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Subtract 9 from 4 to get -5.

$$\frac{\frac{4}{5}\left(-\frac{5}{24}\right)}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Multiply \frac{4}{5} times -\frac{5}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\left(-5\right)}{5\times 24}}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Do the multiplications in the fraction \frac{4\left(-5\right)}{5\times 24}.

$$\frac{\frac{-20}{120}}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Reduce the fraction \frac{-20}{120} to lowest terms by extracting and canceling out 20.

$$\frac{-\frac{1}{6}}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Least common multiple of 10 and 4 is 20. Convert \frac{1}{10} and \frac{7}{4} to fractions with denominator 20.

$$\frac{-\frac{1}{6}}{\frac{5}{12}\left(\frac{2}{20}+\frac{35}{20}\right)}$$

Since \frac{2}{20} and \frac{35}{20} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{6}}{\frac{5}{12}\times \frac{2+35}{20}}$$

Add 2 and 35 to get 37.

$$\frac{-\frac{1}{6}}{\frac{5}{12}\times \frac{37}{20}}$$

Multiply \frac{5}{12} times \frac{37}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{1}{6}}{\frac{5\times 37}{12\times 20}}$$

Do the multiplications in the fraction \frac{5\times 37}{12\times 20}.

$$\frac{-\frac{1}{6}}{\frac{185}{240}}$$

Reduce the fraction \frac{185}{240} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{1}{6}}{\frac{37}{48}}$$

Divide -\frac{1}{6} by \frac{37}{48} by multiplying -\frac{1}{6} by the reciprocal of \frac{37}{48}.

$$-\frac{1}{6}\times \frac{48}{37}$$

Multiply -\frac{1}{6} times \frac{48}{37} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-48}{6\times 37}$$

Do the multiplications in the fraction \frac{-48}{6\times 37}.

$$\frac{-48}{222}$$

Reduce the fraction \frac{-48}{222} to lowest terms by extracting and canceling out 6.

$$-\frac{8}{37}$$

Factor

$$-\frac{8}{37} = -0.21621621621621623$$