Solve 125/4(-8/5)*1/10-4/3:(-2)-frac{5}{8}-(-frac{5}{12})*(-frac{7}{2})=

$$\frac { 125 } { 4 } ( - \frac { 8 } { 5 } ) \cdot \frac { 1 } { 10 } - \frac { 4 } { 3 } : ( - 2 ) - \frac { 5 } { 8 } - ( - \frac { 5 } { 12 } ) \cdot ( - \frac { 7 } { 2 } ) =$$

Evaluate

$$-\frac{77}{12}\approx -6.416666667$$

Solution Steps

Multiply \frac{125}{4} times -\frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{125\left(-8\right)}{4\times 5}\times \frac{1}{10}-\frac{\frac{4}{3}}{-2}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Do the multiplications in the fraction \frac{125\left(-8\right)}{4\times 5}.

$$\frac{-1000}{20}\times \frac{1}{10}-\frac{\frac{4}{3}}{-2}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Divide -1000 by 20 to get -50.

$$-50\times \frac{1}{10}-\frac{\frac{4}{3}}{-2}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Multiply -50 and \frac{1}{10} to get \frac{-50}{10}.

$$\frac{-50}{10}-\frac{\frac{4}{3}}{-2}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Divide -50 by 10 to get -5.

$$-5-\frac{\frac{4}{3}}{-2}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Express \frac{\frac{4}{3}}{-2} as a single fraction.

$$-5-\frac{4}{3\left(-2\right)}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Multiply 3 and -2 to get -6.

$$-5-\frac{4}{-6}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Reduce the fraction \frac{4}{-6} to lowest terms by extracting and canceling out 2.

$$-5-\left(-\frac{2}{3}\right)-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$-5+\frac{2}{3}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

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

$$-\frac{15}{3}+\frac{2}{3}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Since -\frac{15}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{-15+2}{3}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Add -15 and 2 to get -13.

$$-\frac{13}{3}-\frac{5}{8}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Least common multiple of 3 and 8 is 24. Convert -\frac{13}{3} and \frac{5}{8} to fractions with denominator 24.

$$-\frac{104}{24}-\frac{15}{24}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Since -\frac{104}{24} and \frac{15}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-104-15}{24}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Subtract 15 from -104 to get -119.

$$-\frac{119}{24}-\left(-\frac{5}{12}\left(-\frac{7}{2}\right)\right)$$

Multiply -\frac{5}{12} times -\frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{119}{24}-\frac{-5\left(-7\right)}{12\times 2}$$

Do the multiplications in the fraction \frac{-5\left(-7\right)}{12\times 2}.

$$-\frac{119}{24}-\frac{35}{24}$$

Since -\frac{119}{24} and \frac{35}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-119-35}{24}$$

Subtract 35 from -119 to get -154.

$$\frac{-154}{24}$$

Reduce the fraction \frac{-154}{24} to lowest terms by extracting and canceling out 2.

$$-\frac{77}{12}$$

Factor

$$-\frac{77}{12} = -6\frac{5}{12} = -6.416666666666667$$