google play store - Out Of Space error

For at least 3 years now, my Samsung Galaxy Tab 2.0 running Jelly Bean is running into some problems. Ever since I hit ~300 MB left, every app I try to download from my device or the web version of Google Play has shown the error 'insufficient storage space availible'. I have tried the following so far:

1. Clearing Google Play cache


2. Clearing Google Play data


3. Removing Google Play updates


4. Uninstalling some apps


5. Clearing device cache


6. Memory Booster app

Any app seems to do this unless I have about 8x the required amount of storage left. By the way, I can't root my tablet.

(and yes, I know this has been asked before.)

Thanks!

EDIT: I now have 360 MB remaining, and I am now trying to download a 15 MB app. After trying to download with no Google play data, cache, and with Google play 1.0, something must be wrong.(Edit- No, duh.)

NOTE TO MOREAKI: unfortunately, no. I do not have a rooted tablet. Memory booster seems to work downloading other apps, but most apps will not download.

Please comment if you oppose anything I have said.

Sometime I will try to root my Galaxy tab to see if that solves the problem.

Edit again: I never did.