Solve 2/3-5/6/-3+frac{3{4}}

$$\frac { \frac { 2 } { 3 } - \frac { 5 } { 6 } } { - 3 + \frac { 3 } { 4 } }$$

Evaluate

$$\frac{2}{27}\approx 0.074074074$$

Solution Steps

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

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

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

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

Subtract 5 from 4 to get -1.

$$\frac{-\frac{1}{6}}{-3+\frac{3}{4}}$$

Convert -3 to fraction -\frac{12}{4}.

$$\frac{-\frac{1}{6}}{-\frac{12}{4}+\frac{3}{4}}$$

Since -\frac{12}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{1}{6}}{\frac{-12+3}{4}}$$

Add -12 and 3 to get -9.

$$\frac{-\frac{1}{6}}{-\frac{9}{4}}$$

Divide -\frac{1}{6} by -\frac{9}{4} by multiplying -\frac{1}{6} by the reciprocal of -\frac{9}{4}.

$$-\frac{1}{6}\left(-\frac{4}{9}\right)$$

Multiply -\frac{1}{6} times -\frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-4\right)}{6\times 9}$$

Do the multiplications in the fraction \frac{-\left(-4\right)}{6\times 9}.

$$\frac{4}{54}$$

Reduce the fraction \frac{4}{54} to lowest terms by extracting and canceling out 2.

$$\frac{2}{27}$$

Factor

$$\frac{2}{3 ^ {3}} = 0.07407407407407407$$