1. **Stating the problem:** We want to arrange fractions in order of size, from smallest to largest or vice versa. 2. **Formula and rules:** To compare fractions, we can use the common denominator method or convert fractions to decimals. 3. **Common denominator method:** Find the least common denominator (LCD) of the fractions. 4. **Convert each fraction:** Rewrite each fraction with the LCD as the denominator. 5. **Compare numerators:** The fraction with the larger numerator is the larger fraction. 6. **Example:** Arrange $\frac{2}{3}$, $\frac{3}{4}$, and $\frac{1}{2}$ in order. 7. Find LCD of 3, 4, and 2, which is 12. 8. Convert fractions: $$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$ $$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$ $$\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$$ 9. Compare numerators: 6, 8, 9. 10. Order from smallest to largest: $\frac{1}{2} < \frac{2}{3} < \frac{3}{4}$. This method works for any set of fractions.