Question: Divide $1/9 \div 9/4 \div 4/3$. Write your answer as whole number or fraction in lowest terms.
1. **State the problem**
We need to divide $\frac{1}{9} \div \frac{9}{4} \div \frac{4}{3}$.
2. **Use the rule for dividing fractions**
To divide by a fraction, multiply by its reciprocal.
So,
$$\frac{1}{9} \div \frac{9}{4} \div \frac{4}{3} = \frac{1}{9} \times \frac{4}{9} \times \frac{3}{4}$$
3. **Multiply step by step**
First multiply the numerators and denominators:
$$\frac{1 \cdot 4 \cdot 3}{9 \cdot 9 \cdot 4}$$
4. **Cancel common factors**
$$\frac{1 \cdot \cancel{4} \cdot 3}{9 \cdot 9 \cdot \cancel{4}}$$
Now simplify what is left:
$$\frac{3}{81}$$
5. **Reduce the fraction**
$$\frac{3}{81} = \frac{1}{27}$$
6. **Final answer**
The answer is $\frac{1}{27}$.