Solve 811/54+25/2-104/3+9-211/6-3

$$8 \frac { 11 } { 54 } + \frac { 25 } { 2 } - \frac { 104 } { 3 } + 9 - 2 \frac { 11 } { 6 } - 3$$

Evaluate

$$-\frac{637}{54}\approx -11.796296296$$

Solution Steps

Multiply 8 and 54 to get 432.

$$\frac{432+11}{54}+\frac{25}{2}-\frac{104}{3}+9-\frac{2\times 6+11}{6}-3$$

Add 432 and 11 to get 443.

$$\frac{443}{54}+\frac{25}{2}-\frac{104}{3}+9-\frac{2\times 6+11}{6}-3$$

Least common multiple of 54 and 2 is 54. Convert \frac{443}{54} and \frac{25}{2} to fractions with denominator 54.

$$\frac{443}{54}+\frac{675}{54}-\frac{104}{3}+9-\frac{2\times 6+11}{6}-3$$

Since \frac{443}{54} and \frac{675}{54} have the same denominator, add them by adding their numerators.

$$\frac{443+675}{54}-\frac{104}{3}+9-\frac{2\times 6+11}{6}-3$$

Add 443 and 675 to get 1118.

$$\frac{1118}{54}-\frac{104}{3}+9-\frac{2\times 6+11}{6}-3$$

Reduce the fraction \frac{1118}{54} to lowest terms by extracting and canceling out 2.

$$\frac{559}{27}-\frac{104}{3}+9-\frac{2\times 6+11}{6}-3$$

Least common multiple of 27 and 3 is 27. Convert \frac{559}{27} and \frac{104}{3} to fractions with denominator 27.

$$\frac{559}{27}-\frac{936}{27}+9-\frac{2\times 6+11}{6}-3$$

Since \frac{559}{27} and \frac{936}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{559-936}{27}+9-\frac{2\times 6+11}{6}-3$$

Subtract 936 from 559 to get -377.

$$-\frac{377}{27}+9-\frac{2\times 6+11}{6}-3$$

Convert 9 to fraction \frac{243}{27}.

$$-\frac{377}{27}+\frac{243}{27}-\frac{2\times 6+11}{6}-3$$

Since -\frac{377}{27} and \frac{243}{27} have the same denominator, add them by adding their numerators.

$$\frac{-377+243}{27}-\frac{2\times 6+11}{6}-3$$

Add -377 and 243 to get -134.

$$-\frac{134}{27}-\frac{2\times 6+11}{6}-3$$

Multiply 2 and 6 to get 12.

$$-\frac{134}{27}-\frac{12+11}{6}-3$$

Add 12 and 11 to get 23.

$$-\frac{134}{27}-\frac{23}{6}-3$$

Least common multiple of 27 and 6 is 54. Convert -\frac{134}{27} and \frac{23}{6} to fractions with denominator 54.

$$-\frac{268}{54}-\frac{207}{54}-3$$

Since -\frac{268}{54} and \frac{207}{54} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-268-207}{54}-3$$

Subtract 207 from -268 to get -475.

$$-\frac{475}{54}-3$$

Convert 3 to fraction \frac{162}{54}.

$$-\frac{475}{54}-\frac{162}{54}$$

Since -\frac{475}{54} and \frac{162}{54} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-475-162}{54}$$

Subtract 162 from -475 to get -637.

$$-\frac{637}{54}$$

Factor

$$-\frac{637}{54} = -11\frac{43}{54} = -11.796296296296296$$