To arrange the fractions from smallest to largest, we need to find a common denominator and compare the fractions based on their numerators:
1. First, find a common denominator for all fractions. The least common multiple of denominators 9, 4, 11, and 15 is 9*4*11*15 = 1980.
2. Convert each fraction to have a denominator of 1980:
a) \frac{2}{9} \times \frac{220}{220} = \frac{440}{1980}
b) \frac{1}{4} \times \frac{495}{495} = \frac{495}{1980}
c) \frac{3}{11} \times \frac{180}{180} = \frac{540}{1980}
d) \frac{4}{15} \times \frac{132}{132} = \frac{528}{1980}
3. Now, compare the fractions based on their numerators:
- \frac{440}{1980} = 0.222
- \frac{495}{1980} = 0.25
- \frac{540}{1980} = 0.2727
- \frac{528}{1980} = 0.2667
Arranging the fractions from smallest to largest: \frac{2}{9} < \frac{1}{4} < \frac{4}{15} < \frac{3}{11}
\boxed{\frac{2}{9} < \frac{1}{4} < \frac{4}{15} < \frac{3}{11}}