Solve 5/11+3/7+8/13

$$\frac{ 5 }{ 11 } + \frac{ 3 }{ 7 } + \frac{ 8 }{ 13 }$$

Evaluate

$$\frac{1500}{1001}\approx 1.498501499$$

Solution Steps

Least common multiple of 11 and 7 is 77. Convert \frac{5}{11} and \frac{3}{7} to fractions with denominator 77.

$$\frac{35}{77}+\frac{33}{77}+\frac{8}{13}$$

Since \frac{35}{77} and \frac{33}{77} have the same denominator, add them by adding their numerators.

$$\frac{35+33}{77}+\frac{8}{13}$$

Add 35 and 33 to get 68.

$$\frac{68}{77}+\frac{8}{13}$$

Least common multiple of 77 and 13 is 1001. Convert \frac{68}{77} and \frac{8}{13} to fractions with denominator 1001.

$$\frac{884}{1001}+\frac{616}{1001}$$

Since \frac{884}{1001} and \frac{616}{1001} have the same denominator, add them by adding their numerators.

$$\frac{884+616}{1001}$$

Add 884 and 616 to get 1500.

$$\frac{1500}{1001}$$

Factor

$$\frac{2 ^ {2} \cdot 3 \cdot 5 ^ {3}}{7 \cdot 11 \cdot 13} = 1\frac{499}{1001} = 1.4985014985014986$$