1. The problem demonstrates the concept of proportions, where two ratios are equal. Given the ratios $\frac{2}{4}$ and $\frac{3}{6}$, we verify if they are proportional. 2. Simplify each ratio: $$\frac{2}{4} = \frac{1}{2}$$ $$\frac{3}{6} = \frac{1}{2}$$ Both simplify to $\frac{1}{2}$, so they are proportional. 3. A proportional relationship means there is a constant ratio or rate between two quantities. For example, in the "apples - cost" table: - 1 apple costs 2 units, - 3 apples cost 6 units. 4. Confirm the constant of proportionality (rate) between cost and number of apples: $$\text{constant} = \frac{\text{cost}}{\text{number of apples}} = \frac{2}{1} = 2$$ 5. Check the second row with the constant: $$6 \div 3 = 2$$ The ratio remains the same, confirming the proportionality. 6. Similarly, the "hours - points" table represents a proportional relationship, with: $$\frac{10}{1} = 10$$ $$\frac{20}{2} = 10$$ 7. Since both ratios equal 10, the points earned per hour remain constant, showing a proportional relationship. Final Answer: The ratios given describe proportional relationships with constants of proportionality 2 (cost per apple) and 10 (points per hour) respectively.