Solve 27/540+31/540+25/540+20/540+frac{18}{540}+frac{14}{540}+frac{14}{540}+frac{7}{540}+frac{11}{540}+frac{3}{540}=

$$\frac{ 27 }{ 540 } + \frac{ 31 }{ 540 } + \frac{ 25 }{ 540 } + \frac{ 20 }{ 540 } + \frac{ 18 }{ 540 } + \frac{ 14 }{ 540 } + \frac{ 14 }{ 540 } + \frac{ 7 }{ 540 } + \frac{ 11 }{ 540 } + \frac{ 3 }{ 540 } =$$

Evaluate

$$\frac{17}{54}\approx 0.314814815$$

Solution Steps

Since \frac{27}{540} and \frac{31}{540} have the same denominator, add them by adding their numerators.

$$\frac{27+31}{540}+\frac{25}{540}+\frac{20}{540}+\frac{18}{540}+\frac{14}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Add 27 and 31 to get 58.

$$\frac{58}{540}+\frac{25}{540}+\frac{20}{540}+\frac{18}{540}+\frac{14}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Since \frac{58}{540} and \frac{25}{540} have the same denominator, add them by adding their numerators.

$$\frac{58+25}{540}+\frac{20}{540}+\frac{18}{540}+\frac{14}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Add 58 and 25 to get 83.

$$\frac{83}{540}+\frac{20}{540}+\frac{18}{540}+\frac{14}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Since \frac{83}{540} and \frac{20}{540} have the same denominator, add them by adding their numerators.

$$\frac{83+20}{540}+\frac{18}{540}+\frac{14}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Add 83 and 20 to get 103.

$$\frac{103}{540}+\frac{18}{540}+\frac{14}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Since \frac{103}{540} and \frac{18}{540} have the same denominator, add them by adding their numerators.

$$\frac{103+18}{540}+\frac{14}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Add 103 and 18 to get 121.

$$\frac{121}{540}+\frac{14}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Since \frac{121}{540} and \frac{14}{540} have the same denominator, add them by adding their numerators.

$$\frac{121+14}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Add 121 and 14 to get 135.

$$\frac{135}{540}+\frac{14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Since \frac{135}{540} and \frac{14}{540} have the same denominator, add them by adding their numerators.

$$\frac{135+14}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Add 135 and 14 to get 149.

$$\frac{149}{540}+\frac{7}{540}+\frac{11}{540}+\frac{3}{540}$$

Since \frac{149}{540} and \frac{7}{540} have the same denominator, add them by adding their numerators.

$$\frac{149+7}{540}+\frac{11}{540}+\frac{3}{540}$$

Add 149 and 7 to get 156.

$$\frac{156}{540}+\frac{11}{540}+\frac{3}{540}$$

Since \frac{156}{540} and \frac{11}{540} have the same denominator, add them by adding their numerators.

$$\frac{156+11}{540}+\frac{3}{540}$$

Add 156 and 11 to get 167.

$$\frac{167}{540}+\frac{3}{540}$$

Since \frac{167}{540} and \frac{3}{540} have the same denominator, add them by adding their numerators.

$$\frac{167+3}{540}$$

Add 167 and 3 to get 170.

$$\frac{170}{540}$$

Reduce the fraction \frac{170}{540} to lowest terms by extracting and canceling out 10.

$$\frac{17}{54}$$

Factor

$$\frac{17}{2 \cdot 3 ^ {3}} = 0.3148148148148148$$