A thumb rule that very often works is that you can switch the word "Of" to multiplied. This is only when calculating with fractions. Do not use this all of the time because it is, as i said, does not work in every situation. But you can just keep it in mind when calculating with fractions.
When doing multiplication with fractions and the numerators are the same number you only multiply the denominator.
To chech if you are correct you can always switch the fractions to regular numbers but always answer in fractions(because it is more exact.) when calculating with fractions if no other instruction is given.
So first of all.
"half of the ticket holders will receive a prize."
This means that half of the 300 ticket holders will recieve prices. (300/2 = 150)
"the winners are equally likely to win one of the three prizes..."
This means that of those 150 winners, they will have a 1/3 chance of getting one of the three prices.
There are 150 winners and 1/3 of those will get a book, and 1/3 will recieve gift certificate to a restaurant, 1/3 will recieve a movie ticket. So a third of the 150 winners will recieve a movieticket(150/3=50)
I think i am correct, otherwise someone else will have to correct me