Equivalent means "equal".
1:3 and 5:2 are by no means equal in any way shape or form. Neither are 2:6 and 10:4.
The problems you have can be solved (I think), though those examples have seemingly nothing to do with anything (if they do, then I'm totally off).
For the first problem,
First off, a ratio can be though of as three differnt ways. Let's use 3:1 as an example
3:1 and 3 to 1.
All mean the same thing. Simply, a number of things (thing 1) compared to a number of other things (thing 2).
Thing 1 as 3 geese. Thing 2 as 1 hunter.
This can be said as "for every three geese there is 1 hunter", "there are three times as many geese than hunters", "there are three geese to one hunter."
3 and 15 have can both be divided by 3. Or in fancy terminology 3 and 15 are divisible by 3.
This is how you know the rations are equivalent, because they can both be divided by a certain number (typically less than 10).
This easiest way is to divide the second number, 15, by the divisible number (in this case 3).
After you do that, pick a simple number you can easily work with (say 2) and plug it into the first part.
Now, using the answer of the second number (15) divided by the divisible number (3) multiply the second number (2) by it.
If you didn't get my explanation, here are the steps in order:
3 (blank) ........ 15 (blank)
Find divisible number. 3/3 = whole number (good; it's divisible) 15/3 = whole number (5).
Take a number.
3:2 .......... 15: (blank)
Multiply new number (2) by the answer of 15/the divisible number we've been working with for 50 years now.
Get 3:2 ......... 15: 10.
That's a rather strange problem with even stranger examples.
Is this the "reform math" or "fuzzy math"?
Beware of that stuff.