Solve 2/3-1/6/-frac{3{4}-1/2}

$$\frac { \frac { 2 } { 3 } - \frac { 1 } { 6 } } { - \frac { 3 } { 4 } - \frac { 1 } { 2 } }$$

Evaluate

$$-\frac{2}{5}=-0.4$$

Solution Steps

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{\frac{4}{6}-\frac{1}{6}}{-\frac{3}{4}-\frac{1}{2}}$$

Since \frac{4}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-1}{6}}{-\frac{3}{4}-\frac{1}{2}}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{3}{6}}{-\frac{3}{4}-\frac{1}{2}}$$

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

$$\frac{\frac{1}{2}}{-\frac{3}{4}-\frac{1}{2}}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{\frac{1}{2}}{-\frac{3}{4}-\frac{2}{4}}$$

Since -\frac{3}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{2}}{\frac{-3-2}{4}}$$

Subtract 2 from -3 to get -5.

$$\frac{\frac{1}{2}}{-\frac{5}{4}}$$

Divide \frac{1}{2} by -\frac{5}{4} by multiplying \frac{1}{2} by the reciprocal of -\frac{5}{4}.

$$\frac{1}{2}\left(-\frac{4}{5}\right)$$

Multiply \frac{1}{2} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-4\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{2\times 5}.

$$\frac{-4}{10}$$

Reduce the fraction \frac{-4}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{5}$$

Factor

$$-\frac{2}{5} = -0.4$$