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

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

Evaluate

$$-\frac{1}{3}\approx -0.333333333$$

Solution Steps

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

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

Since \frac{1}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 1 to get -1.

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

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

$$-\frac{1}{6}+\frac{4}{6}-\frac{5}{6}$$

Since -\frac{1}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{-1+4}{6}-\frac{5}{6}$$

Add -1 and 4 to get 3.

$$\frac{3}{6}-\frac{5}{6}$$

Since \frac{3}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-5}{6}$$

Subtract 5 from 3 to get -2.

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

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

$$-\frac{1}{3}$$

Factor

$$-\frac{1}{3} = -0.3333333333333333$$