The problem asks to identify the number line model that correctly represents the expression $\frac{3}{4} + (-\frac{1}{4})$.

1. Problem Description

The problem asks to identify the number line model that correctly represents the expression $\frac{3}{4} + (-\frac{1}{4})$.

2. Solution Steps

We need to evaluate the expression $\frac{3}{4} + (-\frac{1}{4})$.

Since we are adding a negative number, it is the same as subtraction:

$\frac{3}{4} + (-\frac{1}{4}) = \frac{3}{4} - \frac{1}{4} = \frac{3-1}{4} = \frac{2}{4} = \frac{1}{2}$

Now let's analyze the number line models:

A: Starts at $\frac{3}{4}$ and moves left (negative direction) by $\frac{1}{4}$. This results in $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$.

B: Starts at $\frac{3}{4}$ and moves right (positive direction) by $\frac{1}{4}$. This results in $\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1$.

C: Starts at $0$ and moves right (positive direction) by $\frac{3}{4}$, then moves left (negative direction) by $\frac{3}{4}$. This represents $\frac{3}{4} - \frac{3}{4} = 0$.

The correct number line model should start at $\frac{3}{4}$ and move to the left by $\frac{1}{4}$. Model A correctly represents this operation and the final answer is $\frac{2}{4}$ which is the same as $\frac{1}{2}$.

3. Final Answer

A