Solve (-5/12+1/4-2):(-1/2)

$$( - \frac { 5 } { 12 } + \frac { 1 } { 4 } - 2 ) : ( - \frac { 1 } { 2 } )$$

Evaluate

$$\frac{13}{3}\approx 4.333333333$$

Solution Steps

Least common multiple of 12 and 4 is 12. Convert -\frac{5}{12} and \frac{1}{4} to fractions with denominator 12.

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

Since -\frac{5}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

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

Add -5 and 3 to get -2.

$$\frac{\frac{-2}{12}-2}{-\frac{1}{2}}$$

Reduce the fraction \frac{-2}{12} to lowest terms by extracting and canceling out 2.

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

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

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

Since -\frac{1}{6} and \frac{12}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 12 from -1 to get -13.

$$\frac{-\frac{13}{6}}{-\frac{1}{2}}$$

Divide -\frac{13}{6} by -\frac{1}{2} by multiplying -\frac{13}{6} by the reciprocal of -\frac{1}{2}.

$$-\frac{13}{6}\left(-2\right)$$

Express -\frac{13}{6}\left(-2\right) as a single fraction.

$$\frac{-13\left(-2\right)}{6}$$

Multiply -13 and -2 to get 26.

$$\frac{26}{6}$$

Reduce the fraction \frac{26}{6} to lowest terms by extracting and canceling out 2.

$$\frac{13}{3}$$

Factor

$$\frac{13}{3} = 4\frac{1}{3} = 4.333333333333333$$