To find the possible ratios of dogs to cats, we simplify the ratio of 28 dogs to 56 cats:

$\text{Ratio} = \frac{28}{56} = \frac{1}{2}$

This means the simplest ratio of dogs to cats is 1:2. However, this ratio can be scaled up by multiplying both sides by any whole number to generate other possible ratios.

Here are all possible ratios of dogs to cats that can be made:

1. $1:2$ (simplest form)
2. $2:4$
3. $3:6$
4. $4:8$
5. $5:10$
6. $6:12$
7. $7:14$
8. $8:16$
9. $9:18$
10. $10:20$
11. $11:22$
12. $12:24$
13. $13:26$
14. $14:28$
15. $15:30$
16. $16:32$
17. $17:34$
18. $18:36$
19. $19:38$
20. $20:40$
21. $21:42$
22. $22:44$
23. $23:46$
24. $24:48$
25. $25:50$
26. $26:52$
27. $27:54$
28. $28:56$ (original form)

Each of these ratios maintains the same proportion of dogs to cats, though expressed with larger numbers.

Would you like further details on how ratios work, or do you have any questions?

Here are 5 related questions for you:

1. How do you simplify a ratio when the numbers are not as straightforward?
2. What are equivalent ratios, and how do they differ from fractions?
3. Can you create ratios in reverse (cats to dogs) for the given problem?
4. How would the ratios change if the number of cats increased to 84 but dogs stayed the same?
5. How can ratios be useful in real-world scenarios like pet daycares?

Tip: To simplify a ratio, always divide both terms by their greatest common divisor (GCD).