Solve 1/7+2/9+3/11+4/13

$$\frac { 1 } { 7 } + \frac { 2 } { 9 } + \frac { 3 } { 11 } + \frac { 4 } { 13 }$$

Evaluate

$$\frac{8518}{9009}\approx 0.945498945$$

Solution Steps

Least common multiple of 7 and 9 is 63. Convert \frac{1}{7} and \frac{2}{9} to fractions with denominator 63.

$$\frac{9}{63}+\frac{14}{63}+\frac{3}{11}+\frac{4}{13}$$

Since \frac{9}{63} and \frac{14}{63} have the same denominator, add them by adding their numerators.

$$\frac{9+14}{63}+\frac{3}{11}+\frac{4}{13}$$

Add 9 and 14 to get 23.

$$\frac{23}{63}+\frac{3}{11}+\frac{4}{13}$$

Least common multiple of 63 and 11 is 693. Convert \frac{23}{63} and \frac{3}{11} to fractions with denominator 693.

$$\frac{253}{693}+\frac{189}{693}+\frac{4}{13}$$

Since \frac{253}{693} and \frac{189}{693} have the same denominator, add them by adding their numerators.

$$\frac{253+189}{693}+\frac{4}{13}$$

Add 253 and 189 to get 442.

$$\frac{442}{693}+\frac{4}{13}$$

Least common multiple of 693 and 13 is 9009. Convert \frac{442}{693} and \frac{4}{13} to fractions with denominator 9009.

$$\frac{5746}{9009}+\frac{2772}{9009}$$

Since \frac{5746}{9009} and \frac{2772}{9009} have the same denominator, add them by adding their numerators.

$$\frac{5746+2772}{9009}$$

Add 5746 and 2772 to get 8518.

$$\frac{8518}{9009}$$

Factor

$$\frac{2 \cdot 4259}{3 ^ {2} \cdot 7 \cdot 11 \cdot 13} = 0.9454989454989455$$