Final answer:
The ratio that forms a proportional relationship with 15 is 10/25 (Option d), as both ratios reduce to 2/5, which indicates that they are proportional to each other.
Step-by-step explanation:
To determine which ratios form a proportional relationship with 15, you can start by expressing 15 as a ratio of 15 to something. Since 1 is a neutral element in multiplication and division, 15 can be thought of as a ratio of 15/1. Next, compare each given ratio to this by cross-multiplying and checking if the products are equal.
For ratio a, 2/5 = 15/1? Cross-multiplication gives 2 * 1 = 5 * 15. So, 2 ≠ 75, which means they don't form a proportional relationship.
For ratio b, 12/20 = 15/1? Simplify 12/20 to 3/5 and then cross-multiply to get 3 * 1 = 5 * 15. So, 3 ≠ 75, which means they don't form a proportional relationship.
For ratio c, 4/6 = 15/1? Simplify 4/6 to 2/3 and then cross-multiply to get 2 * 1 = 3 * 15. So, 2 ≠ 45, which means they don't form a proportional relationship.
For ratio d, 10/25 = 15/1? Simplify 10/25 to 2/5 and then cross-multiply to get 2 * 1 = 5 * 15. So, 2 ≠ 75, which means they do form a proportional relationship because both 10/25 and 15/1 reduce to 2/5.
Therefore, the ratio that forms a proportional relationship with 15 is 10/25 (Option d).