11/9 - 1/11

1. Find a common denominator: To subtract the fractions $\frac{11}{9} - \frac{1}{11}$, we need a common denominator. The least common multiple of 9 and 11 is $9 \times 11 = 99$.

2. Convert the fractions: Multiply the numerator and denominator of each fraction to have a denominator of 99:
$$\frac{11}{9} = \frac{11 \times 11}{9 \times 11} = \frac{121}{99}$$
$$\frac{1}{11} = \frac{1 \times 9}{11 \times 9} = \frac{9}{99}$$

3. Subtract the fractions: Now subtract the numerators while keeping the common denominator:
$$\frac{121}{99} - \frac{9}{99} = \frac{121 - 9}{99} = \frac{112}{99}$$

1. Convert to a mixed number: To convert $\frac{112}{99}$ to a mixed number, divide 112 by 99. $112 \div 99 = 1$ with a remainder of $112 - 99 = 13$. Thus, the mixed number is $1 \frac{13}{99}$.

1. Check for simplest form: The fraction $\frac{13}{99}$ cannot be simplified further because 13 is a prime number and is not a factor of 99.