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

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

Evaluate

$$\frac{31}{42}\approx 0.738095238$$

Solution Steps

Since \frac{3}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 7 from 3 to get -4.

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

Divide -4 by 2 to get -2.

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

Convert -2 to fraction -\frac{12}{6}.

$$\frac{-\frac{12}{6}-\frac{5}{6}+\frac{1}{4}}{-4+\frac{2}{3}-\frac{1}{6}}$$

Since -\frac{12}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-12-5}{6}+\frac{1}{4}}{-4+\frac{2}{3}-\frac{1}{6}}$$

Subtract 5 from -12 to get -17.

$$\frac{-\frac{17}{6}+\frac{1}{4}}{-4+\frac{2}{3}-\frac{1}{6}}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{17}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{-\frac{34}{12}+\frac{3}{12}}{-4+\frac{2}{3}-\frac{1}{6}}$$

Since -\frac{34}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-34+3}{12}}{-4+\frac{2}{3}-\frac{1}{6}}$$

Add -34 and 3 to get -31.

$$\frac{-\frac{31}{12}}{-4+\frac{2}{3}-\frac{1}{6}}$$

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

$$\frac{-\frac{31}{12}}{-\frac{12}{3}+\frac{2}{3}-\frac{1}{6}}$$

Since -\frac{12}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{31}{12}}{\frac{-12+2}{3}-\frac{1}{6}}$$

Add -12 and 2 to get -10.

$$\frac{-\frac{31}{12}}{-\frac{10}{3}-\frac{1}{6}}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{10}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{-\frac{31}{12}}{-\frac{20}{6}-\frac{1}{6}}$$

Since -\frac{20}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{31}{12}}{\frac{-20-1}{6}}$$

Subtract 1 from -20 to get -21.

$$\frac{-\frac{31}{12}}{\frac{-21}{6}}$$

Reduce the fraction \frac{-21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{31}{12}}{-\frac{7}{2}}$$

Divide -\frac{31}{12} by -\frac{7}{2} by multiplying -\frac{31}{12} by the reciprocal of -\frac{7}{2}.

$$-\frac{31}{12}\left(-\frac{2}{7}\right)$$

Multiply -\frac{31}{12} times -\frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-31\left(-2\right)}{12\times 7}$$

Do the multiplications in the fraction \frac{-31\left(-2\right)}{12\times 7}.

$$\frac{62}{84}$$

Reduce the fraction \frac{62}{84} to lowest terms by extracting and canceling out 2.

$$\frac{31}{42}$$

Factor

$$\frac{31}{2 \cdot 3 \cdot 7} = 0.7380952380952381$$