Solve {c}{1331/6184+242/3456+11/5184}{+1/20116}

$$\left. \begin{array} { c } { \frac { 1331 } { 6184 } + \frac { 242 } { 3456 } + \frac { 11 } { 5184 } } \\ { + \frac { 1 } { 20116 } } \end{array} \right.$$

Evaluate

$$\frac{2896173959}{10076184864}\approx 0.287427632$$

Solution Steps

Reduce the fraction \frac{242}{3456} to lowest terms by extracting and canceling out 2.

$$\frac{1331}{6184}+\frac{121}{1728}+\frac{11}{5184}+\frac{1}{20116}$$

Least common multiple of 6184 and 1728 is 1335744. Convert \frac{1331}{6184} and \frac{121}{1728} to fractions with denominator 1335744.

$$\frac{287496}{1335744}+\frac{93533}{1335744}+\frac{11}{5184}+\frac{1}{20116}$$

Since \frac{287496}{1335744} and \frac{93533}{1335744} have the same denominator, add them by adding their numerators.

$$\frac{287496+93533}{1335744}+\frac{11}{5184}+\frac{1}{20116}$$

Add 287496 and 93533 to get 381029.

$$\frac{381029}{1335744}+\frac{11}{5184}+\frac{1}{20116}$$

Least common multiple of 1335744 and 5184 is 4007232. Convert \frac{381029}{1335744} and \frac{11}{5184} to fractions with denominator 4007232.

$$\frac{1143087}{4007232}+\frac{8503}{4007232}+\frac{1}{20116}$$

Since \frac{1143087}{4007232} and \frac{8503}{4007232} have the same denominator, add them by adding their numerators.

$$\frac{1143087+8503}{4007232}+\frac{1}{20116}$$

Add 1143087 and 8503 to get 1151590.

$$\frac{1151590}{4007232}+\frac{1}{20116}$$

Reduce the fraction \frac{1151590}{4007232} to lowest terms by extracting and canceling out 2.

$$\frac{575795}{2003616}+\frac{1}{20116}$$

Least common multiple of 2003616 and 20116 is 10076184864. Convert \frac{575795}{2003616} and \frac{1}{20116} to fractions with denominator 10076184864.

$$\frac{2895673055}{10076184864}+\frac{500904}{10076184864}$$

Since \frac{2895673055}{10076184864} and \frac{500904}{10076184864} have the same denominator, add them by adding their numerators.

$$\frac{2895673055+500904}{10076184864}$$

Add 2895673055 and 500904 to get 2896173959.

$$\frac{2896173959}{10076184864}$$

Factor

$$\frac{7 ^ {2} \cdot 67 \cdot 882173}{2 ^ {5} \cdot 3 ^ {4} \cdot 47 \cdot 107 \cdot 773} = 0.2874276323916401$$