Solve 1/3+3/5+5/7+7/9+frac{9}{11}

$$\frac { 1 } { 3 } + \frac { 3 } { 5 } + \frac { 5 } { 7 } + \frac { 7 } { 9 } + \frac { 9 } { 11 }$$

Evaluate

$$\frac{11239}{3465}\approx 3.243578644$$

Solution Steps

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

$$\frac{5}{15}+\frac{9}{15}+\frac{5}{7}+\frac{7}{9}+\frac{9}{11}$$

Since \frac{5}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{5+9}{15}+\frac{5}{7}+\frac{7}{9}+\frac{9}{11}$$

Add 5 and 9 to get 14.

$$\frac{14}{15}+\frac{5}{7}+\frac{7}{9}+\frac{9}{11}$$

Least common multiple of 15 and 7 is 105. Convert \frac{14}{15} and \frac{5}{7} to fractions with denominator 105.

$$\frac{98}{105}+\frac{75}{105}+\frac{7}{9}+\frac{9}{11}$$

Since \frac{98}{105} and \frac{75}{105} have the same denominator, add them by adding their numerators.

$$\frac{98+75}{105}+\frac{7}{9}+\frac{9}{11}$$

Add 98 and 75 to get 173.

$$\frac{173}{105}+\frac{7}{9}+\frac{9}{11}$$

Least common multiple of 105 and 9 is 315. Convert \frac{173}{105} and \frac{7}{9} to fractions with denominator 315.

$$\frac{519}{315}+\frac{245}{315}+\frac{9}{11}$$

Since \frac{519}{315} and \frac{245}{315} have the same denominator, add them by adding their numerators.

$$\frac{519+245}{315}+\frac{9}{11}$$

Add 519 and 245 to get 764.

$$\frac{764}{315}+\frac{9}{11}$$

Least common multiple of 315 and 11 is 3465. Convert \frac{764}{315} and \frac{9}{11} to fractions with denominator 3465.

$$\frac{8404}{3465}+\frac{2835}{3465}$$

Since \frac{8404}{3465} and \frac{2835}{3465} have the same denominator, add them by adding their numerators.

$$\frac{8404+2835}{3465}$$

Add 8404 and 2835 to get 11239.

$$\frac{11239}{3465}$$

Factor

$$\frac{11239}{3 ^ {2} \cdot 5 \cdot 7 \cdot 11} = 3\frac{844}{3465} = 3.2435786435786436$$