Solve -3^2div3+left(1/2-2/3right)12--1^2015

$$- { 3 }^{ 2 } \div 3+ \left( \frac{ 1 }{ 2 } - \frac{ 2 }{ 3 } \right) 12- { -1 }^{ 2015 }$$

Evaluate

$$-4$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{-9}{3}+\left(\frac{1}{2}-\frac{2}{3}\right)\times 12-\left(-1\right)^{2015}$$

Divide -9 by 3 to get -3.

$$-3+\left(\frac{1}{2}-\frac{2}{3}\right)\times 12-\left(-1\right)^{2015}$$

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

$$-3+\left(\frac{3}{6}-\frac{4}{6}\right)\times 12-\left(-1\right)^{2015}$$

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

$$-3+\frac{3-4}{6}\times 12-\left(-1\right)^{2015}$$

Subtract 4 from 3 to get -1.

$$-3-\frac{1}{6}\times 12-\left(-1\right)^{2015}$$

Express -\frac{1}{6}\times 12 as a single fraction.

$$-3+\frac{-12}{6}-\left(-1\right)^{2015}$$

Divide -12 by 6 to get -2.

$$-3-2-\left(-1\right)^{2015}$$

Subtract 2 from -3 to get -5.

$$-5-\left(-1\right)^{2015}$$

Calculate -1 to the power of 2015 and get -1.

$$-5-\left(-1\right)$$

The opposite of -1 is 1.

$$-5+1$$

Add -5 and 1 to get -4.

$$-4$$

Factor

$$-4$$