To solve the expression [tex]\(-5 - (-2)\)[/tex] using integer tiles, here's a structured approach that Allison should follow:
1. Start with the Initial Tiles:
- Begin with 5 negative tiles representing [tex]\(-5\)[/tex].
2. Understand the Operation:
- The expression [tex]\(-5 - (-2)\)[/tex] can be interpreted as subtracting negative 2 from negative 5.
3. Convert the Subtraction of a Negative to Addition:
- Subtracting a negative number is the same as adding its positive counterpart.
- Therefore, [tex]\(-5 - (-2)\)[/tex] simplifies to [tex]\(-5 + 2\)[/tex].
4. Add the Positive Tiles:
- Allison should now add 2 positive tiles to the existing 5 negative tiles.
5. Combine the Tiles:
- Combine the negative and positive tiles accordingly.
- Combining 5 negative tiles with 2 positive tiles essentially means reducing the number of negative tiles by 2.
6. Resulting Tiles:
- After combining, Allison will have 3 negative tiles left.
Thus, to evaluate the expression [tex]\(-5 - (-2)\)[/tex], Allison should remove 2 negative tiles. This is because adding 2 positive tiles cancels out 2 of the negative tiles, effectively leaving her with 3 negative tiles to represent the answer, [tex]\(-3\)[/tex].
