Solve 5.2-1/5.2

$$5.2- \frac{ 1 }{ 5.2 }$$

Evaluate

$$\frac{651}{130}\approx 5.007692308$$

Solution Steps

Expand \frac{1}{5.2} by multiplying both numerator and the denominator by 10.

$$5.2-\frac{10}{52}$$

Reduce the fraction \frac{10}{52} to lowest terms by extracting and canceling out 2.

$$5.2-\frac{5}{26}$$

Convert decimal number 5.2 to fraction \frac{52}{10}. Reduce the fraction \frac{52}{10} to lowest terms by extracting and canceling out 2.

$$\frac{26}{5}-\frac{5}{26}$$

Least common multiple of 5 and 26 is 130. Convert \frac{26}{5} and \frac{5}{26} to fractions with denominator 130.

$$\frac{676}{130}-\frac{25}{130}$$

Since \frac{676}{130} and \frac{25}{130} have the same denominator, subtract them by subtracting their numerators.

$$\frac{676-25}{130}$$

Subtract 25 from 676 to get 651.

$$\frac{651}{130}$$

Factor

$$\frac{3 \cdot 7 \cdot 31}{2 \cdot 5 \cdot 13} = 5\frac{1}{130} = 5.007692307692308$$