Given that the raffle prize is to be divided equally, the amount of money each person will receive will be equal to the total raffle prize (14x^(2)/15) divided by the number of people (7x). Thus, we get:
(14x^(2)/15) / 7x
= (14x^(2)/15) * (1/7x)
= 14x^(2)/15*7x
= 14x^(2)/105x
= 2x/15 (Divide both the numerator and denominator by 7x)
Therefor, each person would receive 2x/15 dollars.
If you know how to cancel when dealing with fractions, you can get to this step much easier, however this way also works. The idea with cancelling would be that when you had (14x^(2)/15) / 7x, you would recognise that 14x^2 may be divided by 7x straight away to get 2x. Then you would have 2x/15 as your answer.