The problem asks which number line model represents the expression $- \frac{1}{2} + \frac{5}{4}$.

1. Problem Description

The problem asks which number line model represents the expression $- \frac{1}{2} + \frac{5}{4}$.

2. Solution Steps

First, convert $-\frac{1}{2}$ to a fraction with a denominator of

4. $-\frac{1}{2} = -\frac{2}{4}$

The given expression can be rewritten as:

$-\frac{2}{4} + \frac{5}{4}$

The first part of the expression is $-\frac{2}{4}$. This means starting at 0 and moving to the left by $\frac{2}{4}$. The number line model must show this movement.

The second part of the expression is $+\frac{5}{4}$. This means from the location $-\frac{2}{4}$, we must move to the right by $\frac{5}{4}$.

The final location will be $-\frac{2}{4} + \frac{5}{4} = \frac{3}{4}$.

We examine each number line option:

A:

The first arrow moves from 0 to $-\frac{2}{4}$. This is correct.

The second arrow moves from $-\frac{2}{4}$ to $\frac{3}{4}$. This is correct since the length of the second arrow is $\frac{5}{4}$.

B:

The first arrow moves from 0 to $-\frac{2}{4}$. This is correct.

The second arrow moves from $-\frac{2}{4}$ to $\frac{2}{4}$. This is incorrect because the length of the second arrow is not $\frac{5}{4}$.

C:

The first arrow moves from 0 to $-\frac{3}{4}$. This is incorrect since it should be $-\frac{2}{4}$.

The only correct option is A.

3. Final Answer

A