1. State the problem. Problem: Compare $\frac{2}{3}$ and $\frac{3}{4}$. 2. Formula and rule. Use cross-multiplication: for $\frac{a}{b}$ and $\frac{c}{d}$ compare $ad$ and $bc$. 3. Apply the formula to these fractions. Compute $2\times4=8$ and $3\times3=9$. 4. Convert to a common denominator and simplify. $\frac{2}{3}=\frac{8}{12}$ and $\frac{3}{4}=\frac{9}{12}$. $\frac{8}{12}=\frac{\cancel{4}\cdot2}{\cancel{4}\cdot3}=\frac{2}{3}$. 5. Compare the cross-products. Since $8<9$, we conclude $\frac{2}{3}<\frac{3}{4}$. 6. Final answer. Answer: $\frac{2}{3} < \frac{3}{4}$.