Solve 1/5+1/4+1/3+1/6

$$\frac { 1 } { 5 } + \frac { 1 } { 4 } + \frac { 1 } { 3 } + \frac { 1 } { 6 }$$

Evaluate

$$\frac{19}{20}=0.95$$

Solution Steps

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

$$\frac{4}{20}+\frac{5}{20}+\frac{1}{3}+\frac{1}{6}$$

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

$$\frac{4+5}{20}+\frac{1}{3}+\frac{1}{6}$$

Add 4 and 5 to get 9.

$$\frac{9}{20}+\frac{1}{3}+\frac{1}{6}$$

Least common multiple of 20 and 3 is 60. Convert \frac{9}{20} and \frac{1}{3} to fractions with denominator 60.

$$\frac{27}{60}+\frac{20}{60}+\frac{1}{6}$$

Since \frac{27}{60} and \frac{20}{60} have the same denominator, add them by adding their numerators.

$$\frac{27+20}{60}+\frac{1}{6}$$

Add 27 and 20 to get 47.

$$\frac{47}{60}+\frac{1}{6}$$

Least common multiple of 60 and 6 is 60. Convert \frac{47}{60} and \frac{1}{6} to fractions with denominator 60.

$$\frac{47}{60}+\frac{10}{60}$$

Since \frac{47}{60} and \frac{10}{60} have the same denominator, add them by adding their numerators.

$$\frac{47+10}{60}$$

Add 47 and 10 to get 57.

$$\frac{57}{60}$$

Reduce the fraction \frac{57}{60} to lowest terms by extracting and canceling out 3.

$$\frac{19}{20}$$

Factor

$$\frac{19}{2 ^ {2} \cdot 5} = 0.95$$