Solve 5/12+1/3+1/5+1/6

$$\frac{ 5 }{ 12 } + \frac{ 1 }{ 3 } + \frac{ 1 }{ 5 } + \frac{ 1 }{ 6 }$$

Evaluate

$$\frac{67}{60}\approx 1.116666667$$

Solution Steps

Least common multiple of 12 and 3 is 12. Convert \frac{5}{12} and \frac{1}{3} to fractions with denominator 12.

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

Since \frac{5}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

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

Add 5 and 4 to get 9.

$$\frac{9}{12}+\frac{1}{5}+\frac{1}{6}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

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

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{15}{20}+\frac{4}{20}+\frac{1}{6}$$

Since \frac{15}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{15+4}{20}+\frac{1}{6}$$

Add 15 and 4 to get 19.

$$\frac{19}{20}+\frac{1}{6}$$

Least common multiple of 20 and 6 is 60. Convert \frac{19}{20} and \frac{1}{6} to fractions with denominator 60.

$$\frac{57}{60}+\frac{10}{60}$$

Since \frac{57}{60} and \frac{10}{60} have the same denominator, add them by adding their numerators.

$$\frac{57+10}{60}$$

Add 57 and 10 to get 67.

$$\frac{67}{60}$$

Factor

$$\frac{67}{2 ^ {2} \cdot 3 \cdot 5} = 1\frac{7}{60} = 1.1166666666666667$$