Solve [(5/6-1/4)div11/3]*(-2/3)

$$[ ( \frac { 5 } { 6 } - \frac { 1 } { 4 } ) \div 1 \frac { 1 } { 3 } ] \times ( - \frac { 2 } { 3 } )$$

Evaluate

$$-\frac{7}{24}\approx -0.291666667$$

Solution Steps

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{10}{12}-\frac{3}{12}}{\frac{1\times 3+1}{3}}\left(-\frac{2}{3}\right)$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-3}{12}}{\frac{1\times 3+1}{3}}\left(-\frac{2}{3}\right)$$

Subtract 3 from 10 to get 7.

$$\frac{\frac{7}{12}}{\frac{1\times 3+1}{3}}\left(-\frac{2}{3}\right)$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{7}{12}}{\frac{3+1}{3}}\left(-\frac{2}{3}\right)$$

Add 3 and 1 to get 4.

$$\frac{\frac{7}{12}}{\frac{4}{3}}\left(-\frac{2}{3}\right)$$

Divide \frac{7}{12} by \frac{4}{3} by multiplying \frac{7}{12} by the reciprocal of \frac{4}{3}.

$$\frac{7}{12}\times \frac{3}{4}\left(-\frac{2}{3}\right)$$

Multiply \frac{7}{12} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 3}{12\times 4}\left(-\frac{2}{3}\right)$$

Do the multiplications in the fraction \frac{7\times 3}{12\times 4}.

$$\frac{21}{48}\left(-\frac{2}{3}\right)$$

Reduce the fraction \frac{21}{48} to lowest terms by extracting and canceling out 3.

$$\frac{7}{16}\left(-\frac{2}{3}\right)$$

Multiply \frac{7}{16} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-2\right)}{16\times 3}$$

Do the multiplications in the fraction \frac{7\left(-2\right)}{16\times 3}.

$$\frac{-14}{48}$$

Reduce the fraction \frac{-14}{48} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{24}$$

Factor

$$-\frac{7}{24} = -0.2916666666666667$$