To evaluate the expression [tex]\( -5 - (-2) \)[/tex] using integer tiles, we need to follow a series of steps. Let's break it down:
1. Initial Setup:
- Allison begins with 5 negative tiles, which represent [tex]\(-5\)[/tex].
2. Understanding the Operation:
- The expression to evaluate is [tex]\( -5 - (-2) \)[/tex]. In mathematics, subtracting a negative number is equivalent to adding its positive counterpart. Therefore, [tex]\( - (-2) \)[/tex] is the same as adding 2. This changes our expression to [tex]\( -5 + 2 \)[/tex].
3. Applying the Operation:
- To add 2 to [tex]\(-5\)[/tex], Allison should add 2 positive tiles to her existing 5 negative tiles.
4. Visualizing Integer Tiles:
- When Allison adds 2 positive tiles to the 5 negative tiles she already has, each positive tile will cancel out one negative tile. This is because adding a positive tile to a negative tile essentially "zeros out" one of each pair (i.e., -1 + 1 = 0).
- After adding 2 positive tiles, she will have 3 negative tiles remaining (since 2 out of the 5 negative tiles will be neutralized by the 2 positive tiles).
5. Conclusion:
- Therefore, after Allison adds 2 positive tiles to her original 5 negative tiles, she effectively has 3 negative tiles left.
Thus, Allison should:
- Remove nothing (incorrect choices), she should add 2 negative tiles (correct choice).
Therefore, the correct action for Allison to take next to find the value of the expression [tex]\( -5 - (-2) \)[/tex] would be:
- Add 2 negative tiles.
The final answer is:
- The value of the expression [tex]\( -5 - (-2) \)[/tex] is [tex]\(-3\)[/tex].
