Solve (-10/9)div(-4/3)+4/15*(-5/2)

$$( - \frac { 10 } { 9 } ) \div ( - \frac { 4 } { 3 } ) + \frac { 4 } { 15 } \times ( - \frac { 5 } { 2 } )$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

Divide -\frac{10}{9} by -\frac{4}{3} by multiplying -\frac{10}{9} by the reciprocal of -\frac{4}{3}.

$$-\frac{10}{9}\left(-\frac{3}{4}\right)+\frac{4}{15}\left(-\frac{5}{2}\right)$$

Multiply -\frac{10}{9} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-10\left(-3\right)}{9\times 4}+\frac{4}{15}\left(-\frac{5}{2}\right)$$

Do the multiplications in the fraction \frac{-10\left(-3\right)}{9\times 4}.

$$\frac{30}{36}+\frac{4}{15}\left(-\frac{5}{2}\right)$$

Reduce the fraction \frac{30}{36} to lowest terms by extracting and canceling out 6.

$$\frac{5}{6}+\frac{4}{15}\left(-\frac{5}{2}\right)$$

Multiply \frac{4}{15} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{6}+\frac{4\left(-5\right)}{15\times 2}$$

Do the multiplications in the fraction \frac{4\left(-5\right)}{15\times 2}.

$$\frac{5}{6}+\frac{-20}{30}$$

Reduce the fraction \frac{-20}{30} to lowest terms by extracting and canceling out 10.

$$\frac{5}{6}-\frac{2}{3}$$

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

$$\frac{5}{6}-\frac{4}{6}$$

Since \frac{5}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-4}{6}$$

Subtract 4 from 5 to get 1.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$