Solve -2/9-[2/3-(-3^3/4+2/6)]+frac{17}{36}

$$- \frac { 2 } { 9 } - [ \frac { 2 } { 3 } - ( - \frac { 3 ^ { 3 } } { 4 } + \frac { 2 } { 6 } ) ] + \frac { 17 } { 36 }$$

Evaluate

$$-\frac{41}{6}\approx -6.833333333$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$-\frac{2}{9}-\left(\frac{2}{3}-\left(-\frac{27}{4}+\frac{2}{6}\right)\right)+\frac{17}{36}$$

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

$$-\frac{2}{9}-\left(\frac{2}{3}-\left(-\frac{27}{4}+\frac{1}{3}\right)\right)+\frac{17}{36}$$

Least common multiple of 4 and 3 is 12. Convert -\frac{27}{4} and \frac{1}{3} to fractions with denominator 12.

$$-\frac{2}{9}-\left(\frac{2}{3}-\left(-\frac{81}{12}+\frac{4}{12}\right)\right)+\frac{17}{36}$$

Since -\frac{81}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$-\frac{2}{9}-\left(\frac{2}{3}-\frac{-81+4}{12}\right)+\frac{17}{36}$$

Add -81 and 4 to get -77.

$$-\frac{2}{9}-\left(\frac{2}{3}-\left(-\frac{77}{12}\right)\right)+\frac{17}{36}$$

The opposite of -\frac{77}{12} is \frac{77}{12}.

$$-\frac{2}{9}-\left(\frac{2}{3}+\frac{77}{12}\right)+\frac{17}{36}$$

Least common multiple of 3 and 12 is 12. Convert \frac{2}{3} and \frac{77}{12} to fractions with denominator 12.

$$-\frac{2}{9}-\left(\frac{8}{12}+\frac{77}{12}\right)+\frac{17}{36}$$

Since \frac{8}{12} and \frac{77}{12} have the same denominator, add them by adding their numerators.

$$-\frac{2}{9}-\frac{8+77}{12}+\frac{17}{36}$$

Add 8 and 77 to get 85.

$$-\frac{2}{9}-\frac{85}{12}+\frac{17}{36}$$

Least common multiple of 9 and 12 is 36. Convert -\frac{2}{9} and \frac{85}{12} to fractions with denominator 36.

$$-\frac{8}{36}-\frac{255}{36}+\frac{17}{36}$$

Since -\frac{8}{36} and \frac{255}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-8-255}{36}+\frac{17}{36}$$

Subtract 255 from -8 to get -263.

$$-\frac{263}{36}+\frac{17}{36}$$

Since -\frac{263}{36} and \frac{17}{36} have the same denominator, add them by adding their numerators.

$$\frac{-263+17}{36}$$

Add -263 and 17 to get -246.

$$\frac{-246}{36}$$

Reduce the fraction \frac{-246}{36} to lowest terms by extracting and canceling out 6.

$$-\frac{41}{6}$$

Factor

$$-\frac{41}{6} = -6\frac{5}{6} = -6.833333333333333$$