Solve (2/3--7/2-5/6+1/4)div(-frac{4}{3}+frac{2}{3}-frac{1}{6})=

$$( \frac { 2 } { 3 } - \frac { - 7 } { 2 } - \frac { 5 } { 6 } + \frac { 1 } { 4 } ) \div ( - \frac { 4 } { 3 } + \frac { 2 } { 3 } - \frac { 1 } { 6 } ) =$$

Evaluate

$$-\frac{43}{10}=-4.3$$

Solution Steps

Fraction \frac{-7}{2} can be rewritten as -\frac{7}{2} by extracting the negative sign.

$$\frac{\frac{2}{3}-\left(-\frac{7}{2}\right)-\frac{5}{6}+\frac{1}{4}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

The opposite of -\frac{7}{2} is \frac{7}{2}.

$$\frac{\frac{2}{3}+\frac{7}{2}-\frac{5}{6}+\frac{1}{4}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{\frac{4}{6}+\frac{21}{6}-\frac{5}{6}+\frac{1}{4}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

Since \frac{4}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+21}{6}-\frac{5}{6}+\frac{1}{4}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

Add 4 and 21 to get 25.

$$\frac{\frac{25}{6}-\frac{5}{6}+\frac{1}{4}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

Since \frac{25}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25-5}{6}+\frac{1}{4}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

Subtract 5 from 25 to get 20.

$$\frac{\frac{20}{6}+\frac{1}{4}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{10}{3}+\frac{1}{4}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{10}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{40}{12}+\frac{3}{12}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

Since \frac{40}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{40+3}{12}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

Add 40 and 3 to get 43.

$$\frac{\frac{43}{12}}{-\frac{4}{3}+\frac{2}{3}-\frac{1}{6}}$$

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

$$\frac{\frac{43}{12}}{\frac{-4+2}{3}-\frac{1}{6}}$$

Add -4 and 2 to get -2.

$$\frac{\frac{43}{12}}{-\frac{2}{3}-\frac{1}{6}}$$

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

$$\frac{\frac{43}{12}}{-\frac{4}{6}-\frac{1}{6}}$$

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

$$\frac{\frac{43}{12}}{\frac{-4-1}{6}}$$

Subtract 1 from -4 to get -5.

$$\frac{\frac{43}{12}}{-\frac{5}{6}}$$

Divide \frac{43}{12} by -\frac{5}{6} by multiplying \frac{43}{12} by the reciprocal of -\frac{5}{6}.

$$\frac{43}{12}\left(-\frac{6}{5}\right)$$

Multiply \frac{43}{12} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{43\left(-6\right)}{12\times 5}$$

Do the multiplications in the fraction \frac{43\left(-6\right)}{12\times 5}.

$$\frac{-258}{60}$$

Reduce the fraction \frac{-258}{60} to lowest terms by extracting and canceling out 6.

$$-\frac{43}{10}$$

Factor

$$-\frac{43}{10} = -4\frac{3}{10} = -4.3$$