Solve -(6/5+2*8/3)*(-1/4-3):5/2

$$- ( \frac { 6 } { 5 } + 2 \cdot \frac { 8 } { 3 } ) \cdot ( - \frac { 1 } { 4 } - 3 ) : \frac { 5 } { 2 }$$

Evaluate

$$\frac{637}{75}\approx 8.493333333$$

Solution Steps

Express 2\times \frac{8}{3} as a single fraction.

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

Multiply 2 and 8 to get 16.

$$\frac{\left(-\left(\frac{6}{5}+\frac{16}{3}\right)\right)\left(-\frac{1}{4}-3\right)}{\frac{5}{2}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{6}{5} and \frac{16}{3} to fractions with denominator 15.

$$\frac{\left(-\left(\frac{18}{15}+\frac{80}{15}\right)\right)\left(-\frac{1}{4}-3\right)}{\frac{5}{2}}$$

Since \frac{18}{15} and \frac{80}{15} have the same denominator, add them by adding their numerators.

$$\frac{\left(-\frac{18+80}{15}\right)\left(-\frac{1}{4}-3\right)}{\frac{5}{2}}$$

Add 18 and 80 to get 98.

$$\frac{-\frac{98}{15}\left(-\frac{1}{4}-3\right)}{\frac{5}{2}}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{-\frac{98}{15}\left(-\frac{1}{4}-\frac{12}{4}\right)}{\frac{5}{2}}$$

Since -\frac{1}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{98}{15}\times \frac{-1-12}{4}}{\frac{5}{2}}$$

Subtract 12 from -1 to get -13.

$$\frac{-\frac{98}{15}\left(-\frac{13}{4}\right)}{\frac{5}{2}}$$

Multiply -\frac{98}{15} times -\frac{13}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-98\left(-13\right)}{15\times 4}}{\frac{5}{2}}$$

Do the multiplications in the fraction \frac{-98\left(-13\right)}{15\times 4}.

$$\frac{\frac{1274}{60}}{\frac{5}{2}}$$

Reduce the fraction \frac{1274}{60} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{637}{30}}{\frac{5}{2}}$$

Divide \frac{637}{30} by \frac{5}{2} by multiplying \frac{637}{30} by the reciprocal of \frac{5}{2}.

$$\frac{637}{30}\times \frac{2}{5}$$

Multiply \frac{637}{30} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{637\times 2}{30\times 5}$$

Do the multiplications in the fraction \frac{637\times 2}{30\times 5}.

$$\frac{1274}{150}$$

Reduce the fraction \frac{1274}{150} to lowest terms by extracting and canceling out 2.

$$\frac{637}{75}$$

Factor

$$\frac{7 ^ {2} \cdot 13}{3 \cdot 5 ^ {2}} = 8\frac{37}{75} = 8.493333333333334$$