I wonder if I might be able to jump in and help here.
I've followed Red's steps and managed to find the division sign, so I'll try and explain how I did it.
As you've done, go to the International System Preferences. Select the 'Input Menu' tab/button.
You should then see a list of languages and flags etc., but at the top of the list should be the 'keyboard viewer' option. Select it by clicking the 'On' tickbox on the far left. Make sure also that the option at the bottom of the pane 'Show input menu in menu bar' is also selected.
If it wasn't there already there will be a flag in your menu bar. Click on it, and one of the menu listings should be 'Keyboard viewer'. Click on it to open the viewer.
What looks like a miniature keyboard appears. It allows you to try out various modifier keys (alt, command, ctrl, shift, etc) to see what effect that has on the character that will be inputted. If you try holding down alt, you should see that the '/' key becomes '÷', so you know that alt+/ will give you ÷.
One caveat, though. I think both Red and I are using a British keyboard; this maybe why the wrong symbol is being produced for you. In any case, keyboard viewer should let you see what does what.
Hope this goes some way to helping.
Yours,
W.