Solve 1/2+1/3+1/3+1/4+frac{1}{5}

$$\frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } + \frac{ 1 }{ 3 } + \frac{ 1 }{ 4 } + \frac{ 1 }{ 5 }$$

Evaluate

$$\frac{97}{60}\approx 1.616666667$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{2}{6}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{6}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}$$

Add 3 and 2 to get 5.

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

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{5}{6}+\frac{2}{6}+\frac{1}{4}+\frac{1}{5}$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{5+2}{6}+\frac{1}{4}+\frac{1}{5}$$

Add 5 and 2 to get 7.

$$\frac{7}{6}+\frac{1}{4}+\frac{1}{5}$$

Least common multiple of 6 and 4 is 12. Convert \frac{7}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{14}{12}+\frac{3}{12}+\frac{1}{5}$$

Since \frac{14}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{14+3}{12}+\frac{1}{5}$$

Add 14 and 3 to get 17.

$$\frac{17}{12}+\frac{1}{5}$$

Least common multiple of 12 and 5 is 60. Convert \frac{17}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{85}{60}+\frac{12}{60}$$

Since \frac{85}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$\frac{85+12}{60}$$

Add 85 and 12 to get 97.

$$\frac{97}{60}$$

Factor

$$\frac{97}{2 ^ {2} \cdot 3 \cdot 5} = 1\frac{37}{60} = 1.6166666666666667$$