1. We are asked to compare the fractions $\frac{2}{3}$ and $\frac{3}{4}$. 2. To compare fractions, we find a common denominator or convert them to decimals. 3. The denominators are 3 and 4, so the least common denominator (LCD) is 12. 4. Convert each fraction to have denominator 12: $$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$ $$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$ 5. Now compare the numerators: 8 and 9. 6. Since $8 < 9$, it follows that $\frac{8}{12} < \frac{9}{12}$, therefore $$\frac{2}{3} < \frac{3}{4}$$ Final answer: $\boxed{\frac{2}{3} < \frac{3}{4}}$.