Solve -1/15+1/4-1/3+1/6

$$- \frac { 1 } { 15 } + \frac { 1 } { 4 } - \frac { 1 } { 3 } + \frac { 1 } { 6 }$$

Evaluate

$$\frac{1}{60}\approx 0.016666667$$

Solution Steps

Least common multiple of 15 and 4 is 60. Convert -\frac{1}{15} and \frac{1}{4} to fractions with denominator 60.

$$-\frac{4}{60}+\frac{15}{60}-\frac{1}{3}+\frac{1}{6}$$

Since -\frac{4}{60} and \frac{15}{60} have the same denominator, add them by adding their numerators.

$$\frac{-4+15}{60}-\frac{1}{3}+\frac{1}{6}$$

Add -4 and 15 to get 11.

$$\frac{11}{60}-\frac{1}{3}+\frac{1}{6}$$

Least common multiple of 60 and 3 is 60. Convert \frac{11}{60} and \frac{1}{3} to fractions with denominator 60.

$$\frac{11}{60}-\frac{20}{60}+\frac{1}{6}$$

Since \frac{11}{60} and \frac{20}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-20}{60}+\frac{1}{6}$$

Subtract 20 from 11 to get -9.

$$\frac{-9}{60}+\frac{1}{6}$$

Reduce the fraction \frac{-9}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{3}{20}+\frac{1}{6}$$

Least common multiple of 20 and 6 is 60. Convert -\frac{3}{20} and \frac{1}{6} to fractions with denominator 60.

$$-\frac{9}{60}+\frac{10}{60}$$

Since -\frac{9}{60} and \frac{10}{60} have the same denominator, add them by adding their numerators.

$$\frac{-9+10}{60}$$

Add -9 and 10 to get 1.

$$\frac{1}{60}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 3 \cdot 5} = 0.016666666666666666$$