Having trouble with how to solve questions like this:
in a recent student government election, the ratio of students who voted for the winner to all the students who voted was 0.95
.
the number of students who voted was 60
.
how many votes did the winner get?

In this question there is a small trick that needs to be understood. Basically the ratio in the question is given as a decimal. It can be expressed as a ratio as well.
Ratio of students that voted for winner to the total number of voters = 95:100
The total number of students that voted = 60
Let us assume the common ratio to be = x
then
100x = 60
x = 60/100
   = 0.6
Then
The number of votes that the winner got = 95 * 0.6
                                                                 = 57
So 57 students voted for the winning candidate.