The winner in a vote for class president received $\dfrac{3}{4}$ of the $240$ votes. How many votes did the winner receive?

Hint: We will multiply the received votes in fraction with the total votes to get the exact number of votes the winner received. Suppose that we have a total of $x$ objects and we have taken $n$ out of the $x$ objects. So, we will say that we have taken $n$ by $x$ objects.

Complete step by step solution:
We are asked to find the exact number of votes the winner received when he received $\dfrac{3}{4}$ of the $240$ votes.
Suppose that we have a total of $x$ objects and we have taken $n$ of them. Then we say that we have taken $n$ out of the $x$ objects. That can be written as $n$ by $x.$
Mathematically, it is written as $\dfrac{n}{x}.$
We need to consider the whole as $1.$ So, we are supposed to find the above value in terms of $1.$ That is, for $x,$ the value is $\dfrac{n}{x}.$ So, when we consider the whole as $1,$ the value will be a simplified form of $\dfrac{n}{x}.$
Let us suppose that this value is $p.$ So, we will get $\dfrac{n}{x}=p.$
Now, in such situations, we usually transpose the values to find the unknowns.
If we compare the values of the equation written above with the values given in the question, we will get $x=240$ and $p=\dfrac{3}{4}.$
So, we need to calculate the value of $n.$
We are going to transpose $x$ from the LHS to the RHS, $n=px=\dfrac{3}{4}\times 240=3\times 60=180.$

Hence the winner received $180$ votes.

Note: When we say that $x$ of $n$ items, we mean to say that the exact value can be found by multiplying the value $x$ with the value $n.$ In fact, the quotient $\dfrac{x}{n}$ is called the ratio of the value $x$ to the value $n.$