Solve [-5/2][-4/3+1/6]

$$[ \frac { - 5 } { 2 } ] [ \frac { - 4 } { 3 } + \frac { 1 } { 6 } ]$$

Evaluate

$$\frac{35}{12}\approx 2.916666667$$

Solution Steps

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

Least common multiple of 3 and 6 is 6. Convert -\frac{4}{3} and \frac{1}{6} to fractions with denominator 6.

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

Since -\frac{8}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$-\frac{5}{2}\times \frac{-8+1}{6}$$

Add -8 and 1 to get -7.

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

Multiply -\frac{5}{2} times -\frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\left(-7\right)}{2\times 6}$$

Do the multiplications in the fraction \frac{-5\left(-7\right)}{2\times 6}.

$$\frac{35}{12}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {2} \cdot 3} = 2\frac{11}{12} = 2.9166666666666665$$