"Wir vergleichen ja gern und oft."
Just like your other recent question, this modal particle isn't easy to explain. I would suggest that "ja" supports the factor of trueness, like: We compare, we really do, happily and often. At the same time, it says "as you already know" – maybe because it is widely known or common sense even: "Sie wissen ja, wie Kinder sind" – or "as I mentioned or suggested before". And that just might be my personal perspective and someone else might find other tones in this single word. There's no way I could translate it.
Thank you. I think I'm getting the idea of modal particles generally, but it also seems as though I'll only really get the feel by seeing them often and well--and asking questions. I hope my questions aren't becoming too tiresome: I do appreciate the help very much.
They aren't and you're as welcome as always. Some question are just hard to answer. See Katherle's answer about 'mal'. All we can do is paraphrasing those particles and if that helps, it's well worth the effort.
Thank you. I understand that some things don't translate: the same is true of some English expressions, I think. But I think in time, with help and with reading things in more context, I'll get some feel for it. Thanks again.