Solve (-2711/9)div9-(1/2+2/3-3/4-frac{11}{12})*(-24)

$$(- 27 \frac { 11 } { 9 } ) \div 9-( \frac{ 1 }{ 2 } + \frac{ 2 }{ 3 } - \frac{ 3 }{ 4 } - \frac{ 11 }{ 12 } ) \times (-24)$$

Evaluate

$$-\frac{1226}{81}\approx -15.135802469$$

Solution Steps

Multiply 27 and 9 to get 243.

$$\frac{-\frac{243+11}{9}}{9}-\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\left(-24\right)$$

Add 243 and 11 to get 254.

$$\frac{-\frac{254}{9}}{9}-\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\left(-24\right)$$

Express \frac{-\frac{254}{9}}{9} as a single fraction.

$$\frac{-254}{9\times 9}-\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\left(-24\right)$$

Multiply 9 and 9 to get 81.

$$\frac{-254}{81}-\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\left(-24\right)$$

Fraction \frac{-254}{81} can be rewritten as -\frac{254}{81} by extracting the negative sign.

$$-\frac{254}{81}-\left(\frac{1}{2}+\frac{2}{3}-\frac{3}{4}-\frac{11}{12}\right)\left(-24\right)$$

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

$$-\frac{254}{81}-\left(\frac{3}{6}+\frac{4}{6}-\frac{3}{4}-\frac{11}{12}\right)\left(-24\right)$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$-\frac{254}{81}-\left(\frac{3+4}{6}-\frac{3}{4}-\frac{11}{12}\right)\left(-24\right)$$

Add 3 and 4 to get 7.

$$-\frac{254}{81}-\left(\frac{7}{6}-\frac{3}{4}-\frac{11}{12}\right)\left(-24\right)$$

Least common multiple of 6 and 4 is 12. Convert \frac{7}{6} and \frac{3}{4} to fractions with denominator 12.

$$-\frac{254}{81}-\left(\frac{14}{12}-\frac{9}{12}-\frac{11}{12}\right)\left(-24\right)$$

Since \frac{14}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{254}{81}-\left(\frac{14-9}{12}-\frac{11}{12}\right)\left(-24\right)$$

Subtract 9 from 14 to get 5.

$$-\frac{254}{81}-\left(\frac{5}{12}-\frac{11}{12}\right)\left(-24\right)$$

Since \frac{5}{12} and \frac{11}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{254}{81}-\frac{5-11}{12}\left(-24\right)$$

Subtract 11 from 5 to get -6.

$$-\frac{254}{81}-\frac{-6}{12}\left(-24\right)$$

Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.

$$-\frac{254}{81}-\left(-\frac{1}{2}\left(-24\right)\right)$$

Express -\frac{1}{2}\left(-24\right) as a single fraction.

$$-\frac{254}{81}-\frac{-\left(-24\right)}{2}$$

Multiply -1 and -24 to get 24.

$$-\frac{254}{81}-\frac{24}{2}$$

Divide 24 by 2 to get 12.

$$-\frac{254}{81}-12$$

Convert 12 to fraction \frac{972}{81}.

$$-\frac{254}{81}-\frac{972}{81}$$

Since -\frac{254}{81} and \frac{972}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-254-972}{81}$$

Subtract 972 from -254 to get -1226.

$$-\frac{1226}{81}$$

Factor

$$-\frac{1226}{81} = -15\frac{11}{81} = -15.135802469135802$$