What is Bayes' theorem?

In maths, this is a theory of probability, where the second event is conditional on the first. The chance of picking a jack at random from a pack of cards is 4/52. If it is, the chance of getting another jack is 3/52, if not, it is 4/51. Hence the probability of this second one is dependent on the first. Bayes theorem gives the probability that given the second card is an ace, the first card is also.

How do you divide a fraction by a fraction?

To divide a fraction by a fraction, you simply change the symbol to a multiplication symbol and flip the second fraction.

Therefore to divide a half by a half, which looks like this:
1/2 divided by 1/2
flip it so you get
1/2 x 2/1 which is clearly 2 / 2 which is 1.