Solve (-2/3)^3-(1/3+71/6)

$$( - \frac { 2 } { 3 } ) ^ { 3 } - ( \frac { 1 } { 3 } + 7 \frac { 1 } { 6 } )$$

Evaluate

$$-\frac{421}{54}\approx -7.796296296$$

Solution Steps

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$-\frac{8}{27}-\left(\frac{1}{3}+\frac{7\times 6+1}{6}\right)$$

Multiply 7 and 6 to get 42.

$$-\frac{8}{27}-\left(\frac{1}{3}+\frac{42+1}{6}\right)$$

Add 42 and 1 to get 43.

$$-\frac{8}{27}-\left(\frac{1}{3}+\frac{43}{6}\right)$$

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{43}{6} to fractions with denominator 6.

$$-\frac{8}{27}-\left(\frac{2}{6}+\frac{43}{6}\right)$$

Since \frac{2}{6} and \frac{43}{6} have the same denominator, add them by adding their numerators.

$$-\frac{8}{27}-\frac{2+43}{6}$$

Add 2 and 43 to get 45.

$$-\frac{8}{27}-\frac{45}{6}$$

Reduce the fraction \frac{45}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{8}{27}-\frac{15}{2}$$

Least common multiple of 27 and 2 is 54. Convert -\frac{8}{27} and \frac{15}{2} to fractions with denominator 54.

$$-\frac{16}{54}-\frac{405}{54}$$

Since -\frac{16}{54} and \frac{405}{54} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-16-405}{54}$$

Subtract 405 from -16 to get -421.

$$-\frac{421}{54}$$

Factor

$$-\frac{421}{54} = -7\frac{43}{54} = -7.796296296296297$$