OK so one tablespoon (tbsp) is the equivalent of three teaspoons (tsp), 15 millilitres (ml)) or weight wise roughly half an ounce (oz) or 15 grams (g) based on water, in most of the world. In the USA a tablespoon is defined as 14.79ml while if you are in Australia a tablespoon is 20ml, things sure do change Down Under, so make sure if you are using a recipe book, that you know where it is from and adjust your figures accordingly.
On to the half cups now; half a cup is 125ml in Australia and Canada, 142.05ml in the UK and 118.3ml in the USA.
So if you are in the United States of America there are eight tbsps in a _ cup, there are 6.25 tablespoons in Australia, if you're in Canada it is 8.3 tablespoons in a half a cup while it's a whopping 9 _ in British _ Cup.
Why everybody has different sized cups and teaspoons is beyond me, must be some historical significance. It certainly explains why most of the world uses the metric system while cooking their dinner!