Solve 1+1/2+1/3+1/4+1/5+frac{1}{6}

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

Evaluate

$$\frac{49}{20}=2.45$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

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

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

$$\frac{9}{6}+\frac{2}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}$$

Since \frac{9}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}$$

Add 9 and 2 to get 11.

$$\frac{11}{6}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}$$

Least common multiple of 6 and 4 is 12. Convert \frac{11}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{22}{12}+\frac{3}{12}+\frac{1}{5}+\frac{1}{6}$$

Since \frac{22}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{22+3}{12}+\frac{1}{5}+\frac{1}{6}$$

Add 22 and 3 to get 25.

$$\frac{25}{12}+\frac{1}{5}+\frac{1}{6}$$

Least common multiple of 12 and 5 is 60. Convert \frac{25}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{125}{60}+\frac{12}{60}+\frac{1}{6}$$

Since \frac{125}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$\frac{125+12}{60}+\frac{1}{6}$$

Add 125 and 12 to get 137.

$$\frac{137}{60}+\frac{1}{6}$$

Least common multiple of 60 and 6 is 60. Convert \frac{137}{60} and \frac{1}{6} to fractions with denominator 60.

$$\frac{137}{60}+\frac{10}{60}$$

Since \frac{137}{60} and \frac{10}{60} have the same denominator, add them by adding their numerators.

$$\frac{137+10}{60}$$

Add 137 and 10 to get 147.

$$\frac{147}{60}$$

Reduce the fraction \frac{147}{60} to lowest terms by extracting and canceling out 3.

$$\frac{49}{20}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {2} \cdot 5} = 2\frac{9}{20} = 2.45$$