Simplify `27-[18-{16-(5-4-1)}]`

Options

A. `28`
B. `13`
C. `22`
D. `23`

Answer

To simplify the expression `27 - [18 - {16 - (5 - 4 - 1)}]`, we will follow the order of operations, which prioritizes calculations inside brackets first.

### Step-by-Step Solution:

1. **Start with the innermost bracket**:
- We have `(5 - 4 - 1)`.
- First, calculate `5 - 4 = 1`.
- Now, substitute back: `1 - 1 = 0`.
- So, `(5 - 4 - 1) = 0`.

2. **Substitute back into the curly bracket**:
- Now we replace `(5 - 4 - 1)` with `0` in the curly bracket:
- This gives us `16 - 0`.
- Calculate `16 - 0 = 16`.
- So, `{16 - (5 - 4 - 1)} = 16`.

3. **Substitute back into the square bracket**:
- Now replace `{16 - (5 - 4 - 1)}` with `16` in the square bracket:
- This gives us `18 - 16`.
- Calculate `18 - 16 = 2`.
- So, `[18 - {16 - (5 - 4 - 1)}] = 2`.

4. **Substitute back into the main expression**:
- Now replace `[18 - {16 - (5 - 4 - 1)}]` with `2` in the main expression:
- This gives us `27 - 2`.
- Calculate `27 - 2 = 25`.

5. **Final Answer**:
- The simplified result of the expression `27 - [18 - {16 - (5 - 4 - 1)}]` is **25**.