Solve 1/38+4/171+2/855+4/171+frac{14}{855}

$$\frac { 1 } { 38 } + \frac { 4 } { 171 } + \frac { 2 } { 855 } + \frac { 4 } { 171 } + \frac { 14 } { 855 }$$

Evaluate

$$\frac{157}{1710}\approx 0.091812865$$

Solution Steps

Least common multiple of 38 and 171 is 342. Convert \frac{1}{38} and \frac{4}{171} to fractions with denominator 342.

$$\frac{9}{342}+\frac{8}{342}+\frac{2}{855}+\frac{4}{171}+\frac{14}{855}$$

Since \frac{9}{342} and \frac{8}{342} have the same denominator, add them by adding their numerators.

$$\frac{9+8}{342}+\frac{2}{855}+\frac{4}{171}+\frac{14}{855}$$

Add 9 and 8 to get 17.

$$\frac{17}{342}+\frac{2}{855}+\frac{4}{171}+\frac{14}{855}$$

Least common multiple of 342 and 855 is 1710. Convert \frac{17}{342} and \frac{2}{855} to fractions with denominator 1710.

$$\frac{85}{1710}+\frac{4}{1710}+\frac{4}{171}+\frac{14}{855}$$

Since \frac{85}{1710} and \frac{4}{1710} have the same denominator, add them by adding their numerators.

$$\frac{85+4}{1710}+\frac{4}{171}+\frac{14}{855}$$

Add 85 and 4 to get 89.

$$\frac{89}{1710}+\frac{4}{171}+\frac{14}{855}$$

Least common multiple of 1710 and 171 is 1710. Convert \frac{89}{1710} and \frac{4}{171} to fractions with denominator 1710.

$$\frac{89}{1710}+\frac{40}{1710}+\frac{14}{855}$$

Since \frac{89}{1710} and \frac{40}{1710} have the same denominator, add them by adding their numerators.

$$\frac{89+40}{1710}+\frac{14}{855}$$

Add 89 and 40 to get 129.

$$\frac{129}{1710}+\frac{14}{855}$$

Reduce the fraction \frac{129}{1710} to lowest terms by extracting and canceling out 3.

$$\frac{43}{570}+\frac{14}{855}$$

Least common multiple of 570 and 855 is 1710. Convert \frac{43}{570} and \frac{14}{855} to fractions with denominator 1710.

$$\frac{129}{1710}+\frac{28}{1710}$$

Since \frac{129}{1710} and \frac{28}{1710} have the same denominator, add them by adding their numerators.

$$\frac{129+28}{1710}$$

Add 129 and 28 to get 157.

$$\frac{157}{1710}$$

Factor

$$\frac{157}{2 \cdot 3 ^ {2} \cdot 5 \cdot 19} = 0.09181286549707603$$