Solve {l}{1/5+1/15+1/20}{+1/10}

$$\left. \begin{array} { l } { \frac { 1 } { 5 } + \frac { 1 } { 15 } + \frac { 1 } { 20 } } \\ { + \frac { 1 } { 10 } } \end{array} \right.$$

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.

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

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

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

Add 3 and 1 to get 4.

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

Least common multiple of 15 and 20 is 60. Convert \frac{4}{15} and \frac{1}{20} to fractions with denominator 60.

$$\frac{16}{60}+\frac{3}{60}+\frac{1}{10}$$

Since \frac{16}{60} and \frac{3}{60} have the same denominator, add them by adding their numerators.

$$\frac{16+3}{60}+\frac{1}{10}$$

Add 16 and 3 to get 19.

$$\frac{19}{60}+\frac{1}{10}$$

Least common multiple of 60 and 10 is 60. Convert \frac{19}{60} and \frac{1}{10} to fractions with denominator 60.

$$\frac{19}{60}+\frac{6}{60}$$

Since \frac{19}{60} and \frac{6}{60} have the same denominator, add them by adding their numerators.

$$\frac{19+6}{60}$$

Add 19 and 6 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

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