Solve 1/4+1/5-1/6+1/12

$$\frac{ 1 }{ 4 } + \frac{ 1 }{ 5 } - \frac{ 1 }{ 6 } + \frac{ 1 }{ 12 }$$

Evaluate

$$\frac{11}{30}\approx 0.366666667$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{5}{20}+\frac{4}{20}-\frac{1}{6}+\frac{1}{12}$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{5+4}{20}-\frac{1}{6}+\frac{1}{12}$$

Add 5 and 4 to get 9.

$$\frac{9}{20}-\frac{1}{6}+\frac{1}{12}$$

Least common multiple of 20 and 6 is 60. Convert \frac{9}{20} and \frac{1}{6} to fractions with denominator 60.

$$\frac{27}{60}-\frac{10}{60}+\frac{1}{12}$$

Since \frac{27}{60} and \frac{10}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-10}{60}+\frac{1}{12}$$

Subtract 10 from 27 to get 17.

$$\frac{17}{60}+\frac{1}{12}$$

Least common multiple of 60 and 12 is 60. Convert \frac{17}{60} and \frac{1}{12} to fractions with denominator 60.

$$\frac{17}{60}+\frac{5}{60}$$

Since \frac{17}{60} and \frac{5}{60} have the same denominator, add them by adding their numerators.

$$\frac{17+5}{60}$$

Add 17 and 5 to get 22.

$$\frac{22}{60}$$

Reduce the fraction \frac{22}{60} to lowest terms by extracting and canceling out 2.

$$\frac{11}{30}$$

Factor

$$\frac{11}{2 \cdot 3 \cdot 5} = 0.36666666666666664$$