1. **State the problem:** Divide 5.5 in the ratio $\frac{1}{2} : \frac{1}{3}$. 2. **Understand the ratio:** The ratio parts are $\frac{1}{2}$ and $\frac{1}{3}$. To divide 5.5 in this ratio means to find two parts $x$ and $y$ such that $x:y = \frac{1}{2} : \frac{1}{3}$ and $x + y = 5.5$. 3. **Convert ratio to a common form:** To work with the ratio, express both parts with a common denominator: $$\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}$$ So the ratio is $3:2$. 4. **Set up the equation:** Let the common multiplier be $k$. Then: $$x = 3k, \quad y = 2k$$ Since $x + y = 5.5$, we have: $$3k + 2k = 5k = 5.5$$ 5. **Solve for $k$:** $$k = \frac{5.5}{5} = 1.1$$ 6. **Find the parts:** $$x = 3k = 3 \times 1.1 = 3.3$$ $$y = 2k = 2 \times 1.1 = 2.2$$ 7. **Check the sum:** $$3.3 + 2.2 = 5.5$$ which matches the total. **Final answer:** The two parts are $3.3$ and $2.2$.