How many times have you gone to the fridge to use the tomato paste only to find some unwanted fuzzies on top because you haven't used any for a while? I wasted a lot of tomato paste until I came across this tip:
After opening your jar and using the tomato paste pour a layer of olive oil on top and evenly distribute. Replace the lid. The next time you use the tomato paste there will be a layer of solidified oil that is white, don't worry - it's only oil, just use the paste as normal. Do this after each use. Tomato paste lasts for absolutely ages in the fridge using this trick.