How many five ninths are in one-third?

Solution:
1. Understand the fractions involved:
- We need to find out how many times \frac{5}{9} fits into \frac{1}{3}.

2. Use division of fractions:
- The task requires dividing \frac{1}{3} by \frac{5}{9}.

3. Perform the division:
- To divide by a fraction, multiply by its reciprocal.
- The reciprocal of \frac{5}{9} is \frac{9}{5}.

4. Carry out the multiplication:
- Multiply \frac{1}{3} by \frac{9}{5}:
\frac{1}{3} \times \frac{9}{5} = \frac{1 \times 9}{3 \times 5} = \frac{9}{15}

5. Simplify the result:
- Simplify \frac{9}{15} by dividing both the numerator and denominator by their greatest common divisor, 3:
\frac{9}{15} = \frac{3}{5}