To find equivalent ratios, one of two things must apply:
There are common factors of both the numerator and denominator
The numerator and denominator are common factors of other numbers.
ex. 36 and 48 are both divisible by 2, 3, 6, and 12. If you divide both the numerator and denominator by 2, your ratio is 18:24. If the numerator and denominator were divided by 3, the ratio would be 12:16. Divided by 6 would give you a ratio of 6:8, and dividing by 12 results in a ratio of 4:3.
On the other side of the spectrum, if you, say, needed five or six options, then you can multiply both the numerator and denominator by a non-zero number (You are really multiplying by one, ex. 2/2, so the ratio is equivalent. It just seems larger.) So if you did multiply it by 2/2, then your ratio would be 72:96. Hope this helps.
