Solve (1/12-5/6+1/2)div(-1/24)

$$( \frac { 1 } { 12 } - \frac { 5 } { 6 } + \frac { 1 } { 2 } ) \div ( - \frac { 1 } { 24 } )$$

Evaluate

$$6$$

Solution Steps

Least common multiple of 12 and 6 is 12. Convert \frac{1}{12} and \frac{5}{6} to fractions with denominator 12.

$$\frac{\frac{1}{12}-\frac{10}{12}+\frac{1}{2}}{-\frac{1}{24}}$$

Since \frac{1}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-10}{12}+\frac{1}{2}}{-\frac{1}{24}}$$

Subtract 10 from 1 to get -9.

$$\frac{\frac{-9}{12}+\frac{1}{2}}{-\frac{1}{24}}$$

Reduce the fraction \frac{-9}{12} to lowest terms by extracting and canceling out 3.

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

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

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

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

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

Add -3 and 2 to get -1.

$$\frac{-\frac{1}{4}}{-\frac{1}{24}}$$

Divide -\frac{1}{4} by -\frac{1}{24} by multiplying -\frac{1}{4} by the reciprocal of -\frac{1}{24}.

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

Express -\frac{1}{4}\left(-24\right) as a single fraction.

$$\frac{-\left(-24\right)}{4}$$

Multiply -1 and -24 to get 24.

$$\frac{24}{4}$$

Divide 24 by 4 to get 6.

$$6$$

Factor

$$2\times 3$$