Four students are running for class president: liz, sam, sue, and tom. the probabilities of sam, sue, and tom winning are 7⁄25 , 3⁄10 and 21⁄100 , respectively. what is the probability of liz winning?

First, we need to convert all the fractions to have the same denominator. 10 and 25 are both multiples of 100, so 100 would be appropriate. 

Sam has a 7/25 chance. Because we want ?/100, something needs to change. To get from 25 to 100, you need to times 25 by 4, right? So, do the same with the 7.
7 x 4 = 28. Therefore Sam has a 28/100 chance.

Sue has 3/10. Using the same method, we can see that 3 needs to be multiplied by 10 (because 10 times 10 = 100). So Sue has a 30/100 chance.

Tom is already in the fraction we like, so just keep this as 21/100. 

Now, add 28/100, 30/100 and 21/100 to get 79/100. 

Because won of them will get the role of class president, we know that the probability adds to 1. To get a full probability (100/100, or 1), what needs to be added to 79/100? 

Another way of going about this is 100/100-79/100. The answer is 21/100

The probability of Liz winning is 21/100. 

Let me know if this is still unclear, I would be more than happy to explain in more detail if necessary :)