Solve (1/3-3/4)div(-5/9)=

$$( \frac { 1 } { 3 } - \frac { 3 } { 4 } ) \div ( - \frac { 5 } { 9 } ) =$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{4}{12}-\frac{9}{12}}{-\frac{5}{9}}$$

Since \frac{4}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-9}{12}}{-\frac{5}{9}}$$

Subtract 9 from 4 to get -5.

$$\frac{-\frac{5}{12}}{-\frac{5}{9}}$$

Divide -\frac{5}{12} by -\frac{5}{9} by multiplying -\frac{5}{12} by the reciprocal of -\frac{5}{9}.

$$-\frac{5}{12}\left(-\frac{9}{5}\right)$$

Multiply -\frac{5}{12} times -\frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\left(-9\right)}{12\times 5}$$

Do the multiplications in the fraction \frac{-5\left(-9\right)}{12\times 5}.

$$\frac{45}{60}$$

Reduce the fraction \frac{45}{60} to lowest terms by extracting and canceling out 15.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$