Solve (-27/3+9/2-3)-(1/3+1/2+1)

$$( \frac{ -27 }{ 3 } + \frac{ 9 }{ 2 } -3)-( \frac{ 1 }{ 3 } + \frac{ 1 }{ 2 } +1)$$

Evaluate

$$-\frac{28}{3}\approx -9.333333333$$

Solution Steps

Divide -27 by 3 to get -9.

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

Convert -9 to fraction -\frac{18}{2}.

$$-\frac{18}{2}+\frac{9}{2}-3-\left(\frac{1}{3}+\frac{1}{2}+1\right)$$

Since -\frac{18}{2} and \frac{9}{2} have the same denominator, add them by adding their numerators.

$$\frac{-18+9}{2}-3-\left(\frac{1}{3}+\frac{1}{2}+1\right)$$

Add -18 and 9 to get -9.

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

Convert 3 to fraction \frac{6}{2}.

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

Since -\frac{9}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 6 from -9 to get -15.

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

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

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

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

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

Add 2 and 3 to get 5.

$$-\frac{15}{2}-\left(\frac{5}{6}+1\right)$$

Convert 1 to fraction \frac{6}{6}.

$$-\frac{15}{2}-\left(\frac{5}{6}+\frac{6}{6}\right)$$

Since \frac{5}{6} and \frac{6}{6} have the same denominator, add them by adding their numerators.

$$-\frac{15}{2}-\frac{5+6}{6}$$

Add 5 and 6 to get 11.

$$-\frac{15}{2}-\frac{11}{6}$$

Least common multiple of 2 and 6 is 6. Convert -\frac{15}{2} and \frac{11}{6} to fractions with denominator 6.

$$-\frac{45}{6}-\frac{11}{6}$$

Since -\frac{45}{6} and \frac{11}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-45-11}{6}$$

Subtract 11 from -45 to get -56.

$$\frac{-56}{6}$$

Reduce the fraction \frac{-56}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{28}{3}$$

Factor

$$-\frac{28}{3} = -9\frac{1}{3} = -9.333333333333334$$