Solve 1/3(-(3/4-1/3)+1/6)

$$\frac { 1 } { 3 } ( - ( \frac { 3 } { 4 } - \frac { 1 } { 3 } ) + \frac { 1 } { 6 } )$$

Evaluate

$$-\frac{1}{12}\approx -0.083333333$$

Solution Steps

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

$$\frac{1}{3}\left(-\left(\frac{9}{12}-\frac{4}{12}\right)+\frac{1}{6}\right)$$

Since \frac{9}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\left(-\frac{9-4}{12}+\frac{1}{6}\right)$$

Subtract 4 from 9 to get 5.

$$\frac{1}{3}\left(-\frac{5}{12}+\frac{1}{6}\right)$$

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

$$\frac{1}{3}\left(-\frac{5}{12}+\frac{2}{12}\right)$$

Since -\frac{5}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

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

Add -5 and 2 to get -3.

$$\frac{1}{3}\times \frac{-3}{12}$$

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

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

Multiply \frac{1}{3} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-1\right)}{3\times 4}$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{3\times 4}.

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

Fraction \frac{-1}{12} can be rewritten as -\frac{1}{12} by extracting the negative sign.

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

Factor

$$-\frac{1}{12} = -0.08333333333333333$$