Solve (7/12+3/4):(-8/27)+(2-32/5)*frac{25}{28}

$$( \frac { 7 } { 12 } + \frac { 3 } { 4 } ) : ( - \frac { 8 } { 27 } ) + ( 2 - 3 \frac { 2 } { 5 } ) \cdot \frac { 25 } { 28 }$$

Evaluate

$$-\frac{23}{4}=-5.75$$

Solution Steps

Least common multiple of 12 and 4 is 12. Convert \frac{7}{12} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{7}{12}+\frac{9}{12}}{-\frac{8}{27}}+\left(2-\frac{3\times 5+2}{5}\right)\times \frac{25}{28}$$

Since \frac{7}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7+9}{12}}{-\frac{8}{27}}+\left(2-\frac{3\times 5+2}{5}\right)\times \frac{25}{28}$$

Add 7 and 9 to get 16.

$$\frac{\frac{16}{12}}{-\frac{8}{27}}+\left(2-\frac{3\times 5+2}{5}\right)\times \frac{25}{28}$$

Reduce the fraction \frac{16}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{4}{3}}{-\frac{8}{27}}+\left(2-\frac{3\times 5+2}{5}\right)\times \frac{25}{28}$$

Divide \frac{4}{3} by -\frac{8}{27} by multiplying \frac{4}{3} by the reciprocal of -\frac{8}{27}.

$$\frac{4}{3}\left(-\frac{27}{8}\right)+\left(2-\frac{3\times 5+2}{5}\right)\times \frac{25}{28}$$

Multiply \frac{4}{3} times -\frac{27}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-27\right)}{3\times 8}+\left(2-\frac{3\times 5+2}{5}\right)\times \frac{25}{28}$$

Do the multiplications in the fraction \frac{4\left(-27\right)}{3\times 8}.

$$\frac{-108}{24}+\left(2-\frac{3\times 5+2}{5}\right)\times \frac{25}{28}$$

Reduce the fraction \frac{-108}{24} to lowest terms by extracting and canceling out 12.

$$-\frac{9}{2}+\left(2-\frac{3\times 5+2}{5}\right)\times \frac{25}{28}$$

Multiply 3 and 5 to get 15.

$$-\frac{9}{2}+\left(2-\frac{15+2}{5}\right)\times \frac{25}{28}$$

Add 15 and 2 to get 17.

$$-\frac{9}{2}+\left(2-\frac{17}{5}\right)\times \frac{25}{28}$$

Convert 2 to fraction \frac{10}{5}.

$$-\frac{9}{2}+\left(\frac{10}{5}-\frac{17}{5}\right)\times \frac{25}{28}$$

Since \frac{10}{5} and \frac{17}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{9}{2}+\frac{10-17}{5}\times \frac{25}{28}$$

Subtract 17 from 10 to get -7.

$$-\frac{9}{2}-\frac{7}{5}\times \frac{25}{28}$$

Multiply -\frac{7}{5} times \frac{25}{28} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{9}{2}+\frac{-7\times 25}{5\times 28}$$

Do the multiplications in the fraction \frac{-7\times 25}{5\times 28}.

$$-\frac{9}{2}+\frac{-175}{140}$$

Reduce the fraction \frac{-175}{140} to lowest terms by extracting and canceling out 35.

$$-\frac{9}{2}-\frac{5}{4}$$

Least common multiple of 2 and 4 is 4. Convert -\frac{9}{2} and \frac{5}{4} to fractions with denominator 4.

$$-\frac{18}{4}-\frac{5}{4}$$

Since -\frac{18}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-18-5}{4}$$

Subtract 5 from -18 to get -23.

$$-\frac{23}{4}$$

Factor

$$-\frac{23}{4} = -5\frac{3}{4} = -5.75$$