Solve 1/9+9/100-1/75

$$\frac{ 1 }{ 9 } + \frac{ 9 }{ 100 } - \frac{ 1 }{ 75 }$$

Evaluate

$$\frac{169}{900}\approx 0.187777778$$

Solution Steps

Least common multiple of 9 and 100 is 900. Convert \frac{1}{9} and \frac{9}{100} to fractions with denominator 900.

$$\frac{100}{900}+\frac{81}{900}-\frac{1}{75}$$

Since \frac{100}{900} and \frac{81}{900} have the same denominator, add them by adding their numerators.

$$\frac{100+81}{900}-\frac{1}{75}$$

Add 100 and 81 to get 181.

$$\frac{181}{900}-\frac{1}{75}$$

Least common multiple of 900 and 75 is 900. Convert \frac{181}{900} and \frac{1}{75} to fractions with denominator 900.

$$\frac{181}{900}-\frac{12}{900}$$

Since \frac{181}{900} and \frac{12}{900} have the same denominator, subtract them by subtracting their numerators.

$$\frac{181-12}{900}$$

Subtract 12 from 181 to get 169.

$$\frac{169}{900}$$

Factor

$$\frac{13 ^ {2}}{2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {2}} = 0.18777777777777777$$