Solve 3/5.8+3/8.11+3/11.14

$$\frac{ 3 }{ 5.8 } + \frac{ 3 }{ 8.11 } + \frac{ 3 }{ 11.14 }$$

Evaluate

$$\frac{15149655}{13100083}\approx 1.156454887$$

Solution Steps

Expand \frac{3}{5.8} by multiplying both numerator and the denominator by 10.

$$\frac{30}{58}+\frac{3}{8.11}+\frac{3}{11.14}$$

Reduce the fraction \frac{30}{58} to lowest terms by extracting and canceling out 2.

$$\frac{15}{29}+\frac{3}{8.11}+\frac{3}{11.14}$$

Expand \frac{3}{8.11} by multiplying both numerator and the denominator by 100.

$$\frac{15}{29}+\frac{300}{811}+\frac{3}{11.14}$$

Least common multiple of 29 and 811 is 23519. Convert \frac{15}{29} and \frac{300}{811} to fractions with denominator 23519.

$$\frac{12165}{23519}+\frac{8700}{23519}+\frac{3}{11.14}$$

Since \frac{12165}{23519} and \frac{8700}{23519} have the same denominator, add them by adding their numerators.

$$\frac{12165+8700}{23519}+\frac{3}{11.14}$$

Add 12165 and 8700 to get 20865.

$$\frac{20865}{23519}+\frac{3}{11.14}$$

Expand \frac{3}{11.14} by multiplying both numerator and the denominator by 100.

$$\frac{20865}{23519}+\frac{300}{1114}$$

Reduce the fraction \frac{300}{1114} to lowest terms by extracting and canceling out 2.

$$\frac{20865}{23519}+\frac{150}{557}$$

Least common multiple of 23519 and 557 is 13100083. Convert \frac{20865}{23519} and \frac{150}{557} to fractions with denominator 13100083.

$$\frac{11621805}{13100083}+\frac{3527850}{13100083}$$

Since \frac{11621805}{13100083} and \frac{3527850}{13100083} have the same denominator, add them by adding their numerators.

$$\frac{11621805+3527850}{13100083}$$

Add 11621805 and 3527850 to get 15149655.

$$\frac{15149655}{13100083}$$

Factor

$$\frac{5 \cdot 61 \cdot 5519 \cdot 3 ^ {2}}{29 \cdot 557 \cdot 811} = 1\frac{2049572}{13100083} = 1.1564548865835431$$