Solve [(1/8-1/6):(1/3-1/2)-frac{3}{2}]:frac{1}{4}-frac{1}{6}}*2-frac{1}{4}-(frac{1}{6}-frac{15}{4})

$$[ ( \frac { 1 } { 8 } - \frac { 1 } { 6 } ) : ( \frac { 1 } { 3 } - \frac { 1 } { 2 } ) - \frac { 3 } { 2 } ] : \frac { 1 } { 4 } - \frac { 1 } { 6 } \} \cdot 2 - \frac { 1 } { 4 } - ( \frac { 1 } { 6 } - \frac { 15 } { 4 } )$$

Evaluate

$$-\frac{31}{6}\approx -5.166666667$$

Solution Steps

Least common multiple of 8 and 6 is 24. Convert \frac{1}{8} and \frac{1}{6} to fractions with denominator 24.

$$\frac{\frac{\frac{3}{24}-\frac{4}{24}}{\frac{1}{3}-\frac{1}{2}}-\frac{3}{2}}{\frac{1}{4}}-\frac{1}{6}$$

Since \frac{3}{24} and \frac{4}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{3-4}{24}}{\frac{1}{3}-\frac{1}{2}}-\frac{3}{2}}{\frac{1}{4}}-\frac{1}{6}$$

Subtract 4 from 3 to get -1.

$$\frac{\frac{-\frac{1}{24}}{\frac{1}{3}-\frac{1}{2}}-\frac{3}{2}}{\frac{1}{4}}-\frac{1}{6}$$

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

$$\frac{\frac{-\frac{1}{24}}{\frac{2}{6}-\frac{3}{6}}-\frac{3}{2}}{\frac{1}{4}}-\frac{1}{6}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-\frac{1}{24}}{\frac{2-3}{6}}-\frac{3}{2}}{\frac{1}{4}}-\frac{1}{6}$$

Subtract 3 from 2 to get -1.

$$\frac{\frac{-\frac{1}{24}}{-\frac{1}{6}}-\frac{3}{2}}{\frac{1}{4}}-\frac{1}{6}$$

Divide -\frac{1}{24} by -\frac{1}{6} by multiplying -\frac{1}{24} by the reciprocal of -\frac{1}{6}.

$$\frac{-\frac{1}{24}\left(-6\right)-\frac{3}{2}}{\frac{1}{4}}-\frac{1}{6}$$

Express -\frac{1}{24}\left(-6\right) as a single fraction.

$$\frac{\frac{-\left(-6\right)}{24}-\frac{3}{2}}{\frac{1}{4}}-\frac{1}{6}$$

Multiply -1 and -6 to get 6.

$$\frac{\frac{6}{24}-\frac{3}{2}}{\frac{1}{4}}-\frac{1}{6}$$

Reduce the fraction \frac{6}{24} to lowest terms by extracting and canceling out 6.

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

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

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

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

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

Subtract 6 from 1 to get -5.

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

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

$$-\frac{5}{4}\times 4-\frac{1}{6}$$

Cancel out 4 and 4.

$$-5-\frac{1}{6}$$

Convert -5 to fraction -\frac{30}{6}.

$$-\frac{30}{6}-\frac{1}{6}$$

Since -\frac{30}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-30-1}{6}$$

Subtract 1 from -30 to get -31.

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

Factor

$$-\frac{31}{6} = -5\frac{1}{6} = -5.166666666666667$$