Solve 5.12-1/5.12

$$5.12- \frac{ 1 }{ 5.12 }$$

Evaluate

$$4.9246875$$

Solution Steps

Expand \frac{1}{5.12} by multiplying both numerator and the denominator by 100.

$$5.12-\frac{100}{512}$$

Reduce the fraction \frac{100}{512} to lowest terms by extracting and canceling out 4.

$$5.12-\frac{25}{128}$$

Convert decimal number 5.12 to fraction \frac{512}{100}. Reduce the fraction \frac{512}{100} to lowest terms by extracting and canceling out 4.

$$\frac{128}{25}-\frac{25}{128}$$

Least common multiple of 25 and 128 is 3200. Convert \frac{128}{25} and \frac{25}{128} to fractions with denominator 3200.

$$\frac{16384}{3200}-\frac{625}{3200}$$

Since \frac{16384}{3200} and \frac{625}{3200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16384-625}{3200}$$

Subtract 625 from 16384 to get 15759.

$$\frac{15759}{3200}$$

Factor

$$\frac{17 \cdot 103 \cdot 3 ^ {2}}{2 ^ {7} \cdot 5 ^ {2}} = 4\frac{2959}{3200} = 4.9246875$$