Solve (1/2)^3+(1/3)^2-(5/6)

$$( \frac { 1 } { 2 } ) ^ { 3 } + ( \frac { 1 } { 3 } ) ^ { 2 } - ( \frac { 5 } { 6 } )$$

Evaluate

$$-\frac{43}{72}\approx -0.597222222$$

Solution Steps

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{1}{8}+\left(\frac{1}{3}\right)^{2}-\frac{5}{6}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{8}+\frac{1}{9}-\frac{5}{6}$$

Least common multiple of 8 and 9 is 72. Convert \frac{1}{8} and \frac{1}{9} to fractions with denominator 72.

$$\frac{9}{72}+\frac{8}{72}-\frac{5}{6}$$

Since \frac{9}{72} and \frac{8}{72} have the same denominator, add them by adding their numerators.

$$\frac{9+8}{72}-\frac{5}{6}$$

Add 9 and 8 to get 17.

$$\frac{17}{72}-\frac{5}{6}$$

Least common multiple of 72 and 6 is 72. Convert \frac{17}{72} and \frac{5}{6} to fractions with denominator 72.

$$\frac{17}{72}-\frac{60}{72}$$

Since \frac{17}{72} and \frac{60}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-60}{72}$$

Subtract 60 from 17 to get -43.

$$-\frac{43}{72}$$

Factor

$$-\frac{43}{72} = -0.5972222222222222$$