The problem states that Emily is thinking of a number, which she calls $n$. She then finds $\frac{1}{4}$ of the number and subtracts 3.

To write an algebraic expression for this, we follow the steps:

1. Emily finds $\frac{1}{4}$ of the number $n$. This part can be represented as: $\frac{1}{4}n$
2. Then, she subtracts 3 from this result, giving: $\frac{1}{4}n - 3$

So, the expression that represents Emily's number is $\frac{1}{4}n - 3$.

Would you like further details on how to work with such expressions, or have any questions?

Here are 5 follow-up questions to deepen your understanding:

1. What happens if Emily adds 3 instead of subtracting it?
2. How would the expression change if Emily finds $\frac{1}{2}$ of the number instead of $\frac{1}{4}$?
3. How can you evaluate the expression if Emily's number $n$ is 12?
4. What is the general process to simplify expressions involving fractions?
5. How would the expression change if she multiplied the result by 2 instead of subtracting 3?

Tip: When working with expressions involving fractions, always perform the operations in sequence to avoid errors.