Solve 4/3div(1/6-13/5)

$$\frac { 4 } { 3 } \div ( \frac { 1 } { 6 } - \frac { 13 } { 5 } )$$

Evaluate

$$-\frac{40}{73}\approx -0.547945205$$

Solution Steps

Least common multiple of 6 and 5 is 30. Convert \frac{1}{6} and \frac{13}{5} to fractions with denominator 30.

$$\frac{\frac{4}{3}}{\frac{5}{30}-\frac{78}{30}}$$

Since \frac{5}{30} and \frac{78}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{3}}{\frac{5-78}{30}}$$

Subtract 78 from 5 to get -73.

$$\frac{\frac{4}{3}}{-\frac{73}{30}}$$

Divide \frac{4}{3} by -\frac{73}{30} by multiplying \frac{4}{3} by the reciprocal of -\frac{73}{30}.

$$\frac{4}{3}\left(-\frac{30}{73}\right)$$

Multiply \frac{4}{3} times -\frac{30}{73} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-30\right)}{3\times 73}$$

Do the multiplications in the fraction \frac{4\left(-30\right)}{3\times 73}.

$$\frac{-120}{219}$$

Reduce the fraction \frac{-120}{219} to lowest terms by extracting and canceling out 3.

$$-\frac{40}{73}$$

Factor

$$-\frac{40}{73} = -0.547945205479452$$