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

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

Evaluate

$$-2$$

Solution Steps

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

$$2-6\left(\frac{3}{6}-\frac{4}{6}+\frac{5}{6}\right)$$

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

$$2-6\left(\frac{3-4}{6}+\frac{5}{6}\right)$$

Subtract 4 from 3 to get -1.

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

Since -\frac{1}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$2-6\times \frac{-1+5}{6}$$

Add -1 and 5 to get 4.

$$2-6\times \frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$2-6\times \frac{2}{3}$$

Express 6\times \frac{2}{3} as a single fraction.

$$2-\frac{6\times 2}{3}$$

Multiply 6 and 2 to get 12.

$$2-\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$2-4$$

Subtract 4 from 2 to get -2.

$$-2$$

Factor

$$-2$$