Solve -2/12+8/12--9/12(-15/12+frac{27}{12})

$$- \frac{ 2 }{ 12 } + \frac{ 8 }{ 12 } -- \frac{ 9 }{ 12 } ( \frac{ -15 }{ 12 } + \frac{ 27 }{ 12 } )$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

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

$$-\frac{1}{6}+\frac{8}{12}-\left(-\frac{9}{12}\right)\left(\frac{-15}{12}+\frac{27}{12}\right)$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{6}+\frac{2}{3}-\left(-\frac{9}{12}\right)\left(\frac{-15}{12}+\frac{27}{12}\right)$$

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

$$-\frac{1}{6}+\frac{4}{6}-\left(-\frac{9}{12}\right)\left(\frac{-15}{12}+\frac{27}{12}\right)$$

Since -\frac{1}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{-1+4}{6}-\left(-\frac{9}{12}\right)\left(\frac{-15}{12}+\frac{27}{12}\right)$$

Add -1 and 4 to get 3.

$$\frac{3}{6}-\left(-\frac{9}{12}\right)\left(\frac{-15}{12}+\frac{27}{12}\right)$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}-\left(-\frac{9}{12}\right)\left(\frac{-15}{12}+\frac{27}{12}\right)$$

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

$$\frac{1}{2}-\left(-\frac{3}{4}\left(\frac{-15}{12}+\frac{27}{12}\right)\right)$$

Reduce the fraction \frac{-15}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}-\left(-\frac{3}{4}\left(-\frac{5}{4}+\frac{27}{12}\right)\right)$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}-\left(-\frac{3}{4}\left(-\frac{5}{4}+\frac{9}{4}\right)\right)$$

Since -\frac{5}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\left(-\frac{3}{4}\times \frac{-5+9}{4}\right)$$

Add -5 and 9 to get 4.

$$\frac{1}{2}-\left(-\frac{3}{4}\times \frac{4}{4}\right)$$

Divide 4 by 4 to get 1.

$$\frac{1}{2}-\left(-\frac{3}{4}\right)$$

The opposite of -\frac{3}{4} is \frac{3}{4}.

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

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

$$\frac{2}{4}+\frac{3}{4}$$

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

$$\frac{2+3}{4}$$

Add 2 and 3 to get 5.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$