1. The problem is to perform the division for the first expression in exercise 607: $$\frac{1}{3} : \frac{1}{9}$$. 2. Recall the rule for dividing fractions: dividing by a fraction is the same as multiplying by its reciprocal. That is, $$a : b = a \times \frac{1}{b}$$. 3. Apply this rule: $$\frac{1}{3} : \frac{1}{9} = \frac{1}{3} \times \frac{9}{1}$$. 4. Multiply the numerators and denominators: $$= \frac{1 \times 9}{3 \times 1} = \frac{9}{3}$$. 5. Simplify the fraction: $$\frac{9}{3} = 3$$. 6. Therefore, the result of the division is 3.