2 4/15-(2-1 1/15):4/9

Let's solve the expression step by step.

1. Convert mixed numbers to improper fractions:

   For \(2 \frac{4}{15}\): \[ 2 \frac{4}{15} = \frac{2 \times 15 + 4}{15} = \frac{30 + 4}{15} = \frac{34}{15} \]

   For \(1 \frac{1}{15}\): \[ 1 \frac{1}{15} = \frac{1 \times 15 + 1}{15} = \frac{15 + 1}{15} = \frac{16}{15} \]

2. Substitute into the expression and simplify: \[ 2 \frac{4}{15} - (2 - 1 \frac{1}{15}) = \frac{34}{15} - \left(2 - \frac{16}{15}\right) \] First, convert 2 to a fraction with a denominator of 15: \[ 2 = \frac{30}{15} \] Now subtract: \[ 2 - 1 \frac{1}{15} = \frac{30}{15} - \frac{16}{15} = \frac{30 - 16}{15} = \frac{14}{15} \]

   Now, we have: \[ \frac{34}{15} - \frac{14}{15} = \frac{34 - 14}{15} = \frac{20}{15} \] Simplifying \(\frac{20}{15}\): \[ \frac{20}{15} = \frac{4}{3} \]

3. Now divide by \( \frac{4}{9} \): \[ \frac{4}{3} \div \frac{4}{9} = \frac{4}{3} \times \frac{9}{4} \] The 4's cancel out: \[ = \frac{9}{3} = 3 \]

Final answer: \[ \boxed{3} \]