Solve 5/12+(1/2+3/5)*(-8/3)

$$\frac { 5 } { 12 } + ( \frac { 1 } { 2 } + \frac { 3 } { 5 } ) \cdot ( \frac { - 8 } { 3 } )$$

Evaluate

$$-\frac{151}{60}\approx -2.516666667$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{3}{5} to fractions with denominator 10.

$$\frac{5}{12}+\left(\frac{5}{10}+\frac{6}{10}\right)\times \frac{-8}{3}$$

Since \frac{5}{10} and \frac{6}{10} have the same denominator, add them by adding their numerators.

$$\frac{5}{12}+\frac{5+6}{10}\times \frac{-8}{3}$$

Add 5 and 6 to get 11.

$$\frac{5}{12}+\frac{11}{10}\times \frac{-8}{3}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{5}{12}+\frac{11}{10}\left(-\frac{8}{3}\right)$$

Multiply \frac{11}{10} times -\frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{12}+\frac{11\left(-8\right)}{10\times 3}$$

Do the multiplications in the fraction \frac{11\left(-8\right)}{10\times 3}.

$$\frac{5}{12}+\frac{-88}{30}$$

Reduce the fraction \frac{-88}{30} to lowest terms by extracting and canceling out 2.

$$\frac{5}{12}-\frac{44}{15}$$

Least common multiple of 12 and 15 is 60. Convert \frac{5}{12} and \frac{44}{15} to fractions with denominator 60.

$$\frac{25}{60}-\frac{176}{60}$$

Since \frac{25}{60} and \frac{176}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-176}{60}$$

Subtract 176 from 25 to get -151.

$$-\frac{151}{60}$$

Factor

$$-\frac{151}{60} = -2\frac{31}{60} = -2.5166666666666666$$