Question

In order to attract more advertisers to the arena during the sports events, the arena plans to offer advertising space as corporate prizes.
720 companies enter.
8 companies win.
What is the probability of a company winning?
Give your answer as a fraction.

Answer 1

8/720 but simplified is 1/90

Answer 2

You have 8 chances to win. There are 720 entries. Therefore, your chances of winning are 8/720.

Now ask, "am I done, or can I simplify this fraction?" In this case, yes, you can simplify the fraction. How?

You want to find the largest number by which you can divide both your numerator and denominator. Generally, if you haven't a clue where to start, make the numerator a 1. To do that in your example, divide 8 by itself (any number divided by itself = 1). 

Now, can you divide 720 by 8? Of course. You could use a calculator, but you definitely don't need to because 720 should remind you of a very simple number, whose equation you have memorized: 72, or 9*8, because what is 720 except 9*8*10? 

To simplify 720, divide 72 by 8, and then add a 0 after your single digit answer (the equivalent of multiplying by 10). 72/8 = 9, so your denominator = 90 (9*10=90). 

Thus, your final answer is 1/90 probability of winning.