Solve -2/9-2/3--3^/4+1/6+frac{17}{36}

$$- \frac{ 2 }{ 9 } - \frac{ 2 }{ 3 } -- \frac{ { 3 }^{ } }{ 4 } + \frac{ 1 }{ 6 } + \frac{ 17 }{ 36 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Least common multiple of 9 and 3 is 9. Convert -\frac{2}{9} and \frac{2}{3} to fractions with denominator 9.

$$-\frac{2}{9}-\frac{6}{9}-\left(-\frac{3^{1}}{4}\right)+\frac{1}{6}+\frac{17}{36}$$

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

$$\frac{-2-6}{9}-\left(-\frac{3^{1}}{4}\right)+\frac{1}{6}+\frac{17}{36}$$

Subtract 6 from -2 to get -8.

$$-\frac{8}{9}-\left(-\frac{3^{1}}{4}\right)+\frac{1}{6}+\frac{17}{36}$$

Calculate 3 to the power of 1 and get 3.

$$-\frac{8}{9}-\left(-\frac{3}{4}\right)+\frac{1}{6}+\frac{17}{36}$$

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

$$-\frac{8}{9}+\frac{3}{4}+\frac{1}{6}+\frac{17}{36}$$

Least common multiple of 9 and 4 is 36. Convert -\frac{8}{9} and \frac{3}{4} to fractions with denominator 36.

$$-\frac{32}{36}+\frac{27}{36}+\frac{1}{6}+\frac{17}{36}$$

Since -\frac{32}{36} and \frac{27}{36} have the same denominator, add them by adding their numerators.

$$\frac{-32+27}{36}+\frac{1}{6}+\frac{17}{36}$$

Add -32 and 27 to get -5.

$$-\frac{5}{36}+\frac{1}{6}+\frac{17}{36}$$

Least common multiple of 36 and 6 is 36. Convert -\frac{5}{36} and \frac{1}{6} to fractions with denominator 36.

$$-\frac{5}{36}+\frac{6}{36}+\frac{17}{36}$$

Since -\frac{5}{36} and \frac{6}{36} have the same denominator, add them by adding their numerators.

$$\frac{-5+6}{36}+\frac{17}{36}$$

Add -5 and 6 to get 1.

$$\frac{1}{36}+\frac{17}{36}$$

Since \frac{1}{36} and \frac{17}{36} have the same denominator, add them by adding their numerators.

$$\frac{1+17}{36}$$

Add 1 and 17 to get 18.

$$\frac{18}{36}$$

Reduce the fraction \frac{18}{36} to lowest terms by extracting and canceling out 18.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$