Solve 1/3+1/5+1/7+1/11+frac{1}{13}+frac{12}{17}

$$\frac { 1 } { 3 } + \frac { 1 } { 5 } + \frac { 1 } { 7 } + \frac { 1 } { 11 } + \frac { 1 } { 13 } + \frac { 12 } { 17 }$$

Evaluate

$$\frac{395621}{255255}\approx 1.549904997$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{5}{15}+\frac{3}{15}+\frac{1}{7}+\frac{1}{11}+\frac{1}{13}+\frac{12}{17}$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{5+3}{15}+\frac{1}{7}+\frac{1}{11}+\frac{1}{13}+\frac{12}{17}$$

Add 5 and 3 to get 8.

$$\frac{8}{15}+\frac{1}{7}+\frac{1}{11}+\frac{1}{13}+\frac{12}{17}$$

Least common multiple of 15 and 7 is 105. Convert \frac{8}{15} and \frac{1}{7} to fractions with denominator 105.

$$\frac{56}{105}+\frac{15}{105}+\frac{1}{11}+\frac{1}{13}+\frac{12}{17}$$

Since \frac{56}{105} and \frac{15}{105} have the same denominator, add them by adding their numerators.

$$\frac{56+15}{105}+\frac{1}{11}+\frac{1}{13}+\frac{12}{17}$$

Add 56 and 15 to get 71.

$$\frac{71}{105}+\frac{1}{11}+\frac{1}{13}+\frac{12}{17}$$

Least common multiple of 105 and 11 is 1155. Convert \frac{71}{105} and \frac{1}{11} to fractions with denominator 1155.

$$\frac{781}{1155}+\frac{105}{1155}+\frac{1}{13}+\frac{12}{17}$$

Since \frac{781}{1155} and \frac{105}{1155} have the same denominator, add them by adding their numerators.

$$\frac{781+105}{1155}+\frac{1}{13}+\frac{12}{17}$$

Add 781 and 105 to get 886.

$$\frac{886}{1155}+\frac{1}{13}+\frac{12}{17}$$

Least common multiple of 1155 and 13 is 15015. Convert \frac{886}{1155} and \frac{1}{13} to fractions with denominator 15015.

$$\frac{11518}{15015}+\frac{1155}{15015}+\frac{12}{17}$$

Since \frac{11518}{15015} and \frac{1155}{15015} have the same denominator, add them by adding their numerators.

$$\frac{11518+1155}{15015}+\frac{12}{17}$$

Add 11518 and 1155 to get 12673.

$$\frac{12673}{15015}+\frac{12}{17}$$

Least common multiple of 15015 and 17 is 255255. Convert \frac{12673}{15015} and \frac{12}{17} to fractions with denominator 255255.

$$\frac{215441}{255255}+\frac{180180}{255255}$$

Since \frac{215441}{255255} and \frac{180180}{255255} have the same denominator, add them by adding their numerators.

$$\frac{215441+180180}{255255}$$

Add 215441 and 180180 to get 395621.

$$\frac{395621}{255255}$$

Factor

$$\frac{395621}{3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17} = 1\frac{140366}{255255} = 1.5499049969638206$$