Solve (2/3+5/6)div(4/9-8/3)

$$( \frac { 2 } { 3 } + \frac { 5 } { 6 } ) \div ( \frac { 4 } { 9 } - \frac { 8 } { 3 } )$$

Evaluate

$$-\frac{27}{40}=-0.675$$

Solution Steps

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

$$\frac{\frac{4}{6}+\frac{5}{6}}{\frac{4}{9}-\frac{8}{3}}$$

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

$$\frac{\frac{4+5}{6}}{\frac{4}{9}-\frac{8}{3}}$$

Add 4 and 5 to get 9.

$$\frac{\frac{9}{6}}{\frac{4}{9}-\frac{8}{3}}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{2}}{\frac{4}{9}-\frac{8}{3}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{8}{3} to fractions with denominator 9.

$$\frac{\frac{3}{2}}{\frac{4}{9}-\frac{24}{9}}$$

Since \frac{4}{9} and \frac{24}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{2}}{\frac{4-24}{9}}$$

Subtract 24 from 4 to get -20.

$$\frac{\frac{3}{2}}{-\frac{20}{9}}$$

Divide \frac{3}{2} by -\frac{20}{9} by multiplying \frac{3}{2} by the reciprocal of -\frac{20}{9}.

$$\frac{3}{2}\left(-\frac{9}{20}\right)$$

Multiply \frac{3}{2} times -\frac{9}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-9\right)}{2\times 20}$$

Do the multiplications in the fraction \frac{3\left(-9\right)}{2\times 20}.

$$\frac{-27}{40}$$

Fraction \frac{-27}{40} can be rewritten as -\frac{27}{40} by extracting the negative sign.

$$-\frac{27}{40}$$

Factor

$$-\frac{27}{40} = -0.675$$