Final answer:
By simplifying the ratios 5:1 and 15:3, as well as 10:2 and 25:5, we find that both pairs are equivalent because they simplify to the same number. However, 198:1287 and 2:13 are not equivalent as they simplify to different numbers.
Step-by-step explanation:
To determine if two pairs of equations are equivalent, we need to compare the ratios and see if they can be simplified to the same fraction. We do this by dividing the numerator by the denominator and checking if both equations yield the same result or by checking if the multiplication factor between the numerators is the same as the factor between the denominators.
For the pair 5:1 and 15:3, we can divide the numerators and the denominators of both ratios by the greatest common divisor of each pair, which in this case is 5 for the first ratio and 3 for the second. Doing so, we get 5/1 = 5 and 15/3 = 5. Since both ratios simplify to the same number, they are equivalent.
Similarly, for the pair 10:2 and 25:5, we can divide 10 by 2 and 25 by 5 to get 5 in both cases. Hence, these pairs are also equivalent.
Lastly, for the pair 198:1287 and 2:13, we divide both numbers in each ratio to check for equivalence. If we divide 198 by 1287, we do not get the same result as dividing 2 by 13. Therefore, these two ratios are not equivalent.