Help Installing Sims 3 Expansions? (The installers won't open)

I have a mac and I'm a newbie to installing Sims on my mac, but I've successfully got the Sims 3 base game installed from games4theworld. I downloaded Late Night, Showtime, Master Suite Stuff, and made disc images. I followed the Games4TheWorld mac guide installation and my folders look just as theirs do. But I open the sims 3 late night dmg file that is on my desktop. The crack, installation guide and the installer is inside like it should be. But, once I click on the installer, the little icon will come up in my dock at the bottom of my screen and then nothing else will come up. But if I click on it in the dock, it will exit. The installation hasn't come up.

Please help, I'd be rather grateful. I've been trying to get this to work all day.

If it helps, I use Keka to unrar my rar files, would that be causing my problem? But it worked, showed me all the folders that were supposed to be inside, so I don't know if that would be a factor. I would use the stuffit expander, but its no longer available. And if I do have to use that program, can someone direct me to a way to get it so I can install this? I used Keka because that's what I use to install my custom content.