Solve 1/5+1/15+1/10+1/20

$$\frac{ 1 }{ 5 } + \frac{ 1 }{ 15 } + \frac{ 1 }{ 10 } + \frac{ 1 }{ 20 }$$

Evaluate

$$\frac{5}{12}\approx 0.416666667$$

Solution Steps

Least common multiple of 5 and 15 is 15. Convert \frac{1}{5} and \frac{1}{15} to fractions with denominator 15.

$$\frac{3}{15}+\frac{1}{15}+\frac{1}{10}+\frac{1}{20}$$

Since \frac{3}{15} and \frac{1}{15} have the same denominator, add them by adding their numerators.

$$\frac{3+1}{15}+\frac{1}{10}+\frac{1}{20}$$

Add 3 and 1 to get 4.

$$\frac{4}{15}+\frac{1}{10}+\frac{1}{20}$$

Least common multiple of 15 and 10 is 30. Convert \frac{4}{15} and \frac{1}{10} to fractions with denominator 30.

$$\frac{8}{30}+\frac{3}{30}+\frac{1}{20}$$

Since \frac{8}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{8+3}{30}+\frac{1}{20}$$

Add 8 and 3 to get 11.

$$\frac{11}{30}+\frac{1}{20}$$

Least common multiple of 30 and 20 is 60. Convert \frac{11}{30} and \frac{1}{20} to fractions with denominator 60.

$$\frac{22}{60}+\frac{3}{60}$$

Since \frac{22}{60} and \frac{3}{60} have the same denominator, add them by adding their numerators.

$$\frac{22+3}{60}$$

Add 22 and 3 to get 25.

$$\frac{25}{60}$$

Reduce the fraction \frac{25}{60} to lowest terms by extracting and canceling out 5.

$$\frac{5}{12}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3} = 0.4166666666666667$$