Solve 1/3-3/4/frac{5{6}}=

$$\frac { \frac { 1 } { 3 } - \frac { 3 } { 4 } } { \frac { 5 } { 6 } } =$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

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

$$\frac{\frac{4}{12}-\frac{9}{12}}{\frac{5}{6}}$$

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

$$\frac{\frac{4-9}{12}}{\frac{5}{6}}$$

Subtract 9 from 4 to get -5.

$$\frac{-\frac{5}{12}}{\frac{5}{6}}$$

Divide -\frac{5}{12} by \frac{5}{6} by multiplying -\frac{5}{12} by the reciprocal of \frac{5}{6}.

$$-\frac{5}{12}\times \frac{6}{5}$$

Multiply -\frac{5}{12} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 6}{12\times 5}$$

Do the multiplications in the fraction \frac{-5\times 6}{12\times 5}.

$$\frac{-30}{60}$$

Reduce the fraction \frac{-30}{60} to lowest terms by extracting and canceling out 30.

$$-\frac{1}{2}$$

Factor

$$-\frac{1}{2} = -0.5$$