Solve 1/214.8+1/215.5+1/218.5

$$\frac{ 1 }{ 214.8 } + \frac{ 1 }{ 215.5 } + \frac{ 1 }{ 218.5 }$$

Evaluate

$$\frac{2806199}{202284678}\approx 0.013872524$$

Solution Steps

Expand \frac{1}{214.8} by multiplying both numerator and the denominator by 10.

$$\frac{10}{2148}+\frac{1}{215.5}+\frac{1}{218.5}$$

Reduce the fraction \frac{10}{2148} to lowest terms by extracting and canceling out 2.

$$\frac{5}{1074}+\frac{1}{215.5}+\frac{1}{218.5}$$

Expand \frac{1}{215.5} by multiplying both numerator and the denominator by 10.

$$\frac{5}{1074}+\frac{10}{2155}+\frac{1}{218.5}$$

Reduce the fraction \frac{10}{2155} to lowest terms by extracting and canceling out 5.

$$\frac{5}{1074}+\frac{2}{431}+\frac{1}{218.5}$$

Least common multiple of 1074 and 431 is 462894. Convert \frac{5}{1074} and \frac{2}{431} to fractions with denominator 462894.

$$\frac{2155}{462894}+\frac{2148}{462894}+\frac{1}{218.5}$$

Since \frac{2155}{462894} and \frac{2148}{462894} have the same denominator, add them by adding their numerators.

$$\frac{2155+2148}{462894}+\frac{1}{218.5}$$

Add 2155 and 2148 to get 4303.

$$\frac{4303}{462894}+\frac{1}{218.5}$$

Expand \frac{1}{218.5} by multiplying both numerator and the denominator by 10.

$$\frac{4303}{462894}+\frac{10}{2185}$$

Reduce the fraction \frac{10}{2185} to lowest terms by extracting and canceling out 5.

$$\frac{4303}{462894}+\frac{2}{437}$$

Least common multiple of 462894 and 437 is 202284678. Convert \frac{4303}{462894} and \frac{2}{437} to fractions with denominator 202284678.

$$\frac{1880411}{202284678}+\frac{925788}{202284678}$$

Since \frac{1880411}{202284678} and \frac{925788}{202284678} have the same denominator, add them by adding their numerators.

$$\frac{1880411+925788}{202284678}$$

Add 1880411 and 925788 to get 2806199.

$$\frac{2806199}{202284678}$$

Factor

$$\frac{11 \cdot 337 \cdot 757}{2 \cdot 3 \cdot 19 \cdot 23 \cdot 179 \cdot 431} = 0.013872523750909102$$