Solve [2/5*(-10/3)+5/2]:5/8-frac{12}{5}=

$$[ \frac { 2 } { 5 } \cdot ( - \frac { 10 } { 3 } ) + \frac { 5 } { 2 } ] : \frac { 5 } { 8 } - \frac { 12 } { 5 } =$$

Evaluate

$$-\frac{8}{15}\approx -0.533333333$$

Solution Steps

Multiply \frac{2}{5} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{2\left(-10\right)}{5\times 3}+\frac{5}{2}}{\frac{5}{8}}-\frac{12}{5}$$

Do the multiplications in the fraction \frac{2\left(-10\right)}{5\times 3}.

$$\frac{\frac{-20}{15}+\frac{5}{2}}{\frac{5}{8}}-\frac{12}{5}$$

Reduce the fraction \frac{-20}{15} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{4}{3}+\frac{5}{2}}{\frac{5}{8}}-\frac{12}{5}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{4}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{-\frac{8}{6}+\frac{15}{6}}{\frac{5}{8}}-\frac{12}{5}$$

Since -\frac{8}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-8+15}{6}}{\frac{5}{8}}-\frac{12}{5}$$

Add -8 and 15 to get 7.

$$\frac{\frac{7}{6}}{\frac{5}{8}}-\frac{12}{5}$$

Divide \frac{7}{6} by \frac{5}{8} by multiplying \frac{7}{6} by the reciprocal of \frac{5}{8}.

$$\frac{7}{6}\times \frac{8}{5}-\frac{12}{5}$$

Multiply \frac{7}{6} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 8}{6\times 5}-\frac{12}{5}$$

Do the multiplications in the fraction \frac{7\times 8}{6\times 5}.

$$\frac{56}{30}-\frac{12}{5}$$

Reduce the fraction \frac{56}{30} to lowest terms by extracting and canceling out 2.

$$\frac{28}{15}-\frac{12}{5}$$

Least common multiple of 15 and 5 is 15. Convert \frac{28}{15} and \frac{12}{5} to fractions with denominator 15.

$$\frac{28}{15}-\frac{36}{15}$$

Since \frac{28}{15} and \frac{36}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-36}{15}$$

Subtract 36 from 28 to get -8.

$$-\frac{8}{15}$$

Factor

$$-\frac{8}{15} = -0.5333333333333333$$