Solve [2(-1)^3/-3-(-1)^2/2-3(-1)]

$$[ \frac { 2 ( - 1 ) ^ { 3 } } { - 3 } - \frac { ( - 1 ) ^ { 2 } } { 2 } - 3 ( - 1 ) ]$$

Evaluate

$$\frac{19}{6}\approx 3.166666667$$

Solution Steps

Calculate -1 to the power of 3 and get -1.

$$\frac{2\left(-1\right)}{-3}-\frac{\left(-1\right)^{2}}{2}-3\left(-1\right)$$

Multiply 2 and -1 to get -2.

$$\frac{-2}{-3}-\frac{\left(-1\right)^{2}}{2}-3\left(-1\right)$$

Fraction \frac{-2}{-3} can be simplified to \frac{2}{3} by removing the negative sign from both the numerator and the denominator.

$$\frac{2}{3}-\frac{\left(-1\right)^{2}}{2}-3\left(-1\right)$$

Calculate -1 to the power of 2 and get 1.

$$\frac{2}{3}-\frac{1}{2}-3\left(-1\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{4}{6}-\frac{3}{6}-3\left(-1\right)$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{6}-3\left(-1\right)$$

Subtract 3 from 4 to get 1.

$$\frac{1}{6}-3\left(-1\right)$$

Multiply 3 and -1 to get -3.

$$\frac{1}{6}-\left(-3\right)$$

The opposite of -3 is 3.

$$\frac{1}{6}+3$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{1}{6}+\frac{18}{6}$$

Since \frac{1}{6} and \frac{18}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+18}{6}$$

Add 1 and 18 to get 19.

$$\frac{19}{6}$$

Factor

$$\frac{19}{2 \cdot 3} = 3\frac{1}{6} = 3.1666666666666665$$