Final answer:
To determine if the given ratios form a proportion, we can set the two length ratios equal to each other and the two width ratios equal to each other. If the resulting equations are true, then the ratios form a proportion.
Step-by-step explanation:
A proportion is created when two ratios are found to be equivalent or equal. To determine if the given ratios form a proportion, we can set the two length ratios equal to each other and the two width ratios equal to each other. If the resulting equations are true, then the ratios form a proportion.
Let's consider the first scenario with the given unit in inches:
Inches:
Length: 2/5 = 4/10
Width: 1/8 = 2/16
Setting the two length ratios equal to each other: 2/5 = 4/10. Simplifying, we have 2/5 = 2/5, which is true. Therefore, the length ratios form a proportion.
Setting the two width ratios equal to each other: 1/8 = 2/16. Simplifying, we have 1/8 = 1/8, which is true. Therefore, the width ratios form a proportion.
Since both the length ratios and the width ratios form a proportion, we can conclude that the given ratios form a proportion.