Solve 5.11-1/5.11

$$5.11- \frac{ 1 }{ 5.11 }$$

Evaluate

$$\frac{251121}{51100}\approx 4.914305284$$

Solution Steps

Expand \frac{1}{5.11} by multiplying both numerator and the denominator by 100.

$$5.11-\frac{100}{511}$$

Convert decimal number 5.11 to fraction \frac{511}{100}.

$$\frac{511}{100}-\frac{100}{511}$$

Least common multiple of 100 and 511 is 51100. Convert \frac{511}{100} and \frac{100}{511} to fractions with denominator 51100.

$$\frac{261121}{51100}-\frac{10000}{51100}$$

Since \frac{261121}{51100} and \frac{10000}{51100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{261121-10000}{51100}$$

Subtract 10000 from 261121 to get 251121.

$$\frac{251121}{51100}$$

Factor

$$\frac{3 \cdot 13 \cdot 47 \cdot 137}{7 \cdot 73 \cdot 2 ^ {2} \cdot 5 ^ {2}} = 4\frac{46721}{51100} = 4.914305283757338$$