Simplify `:`
23.667-2.55-19.205+80.432

Answer

To simplify the expression \( 23.667 - 2.55 - 19.205 + 80.432 \), we will follow these steps:

### Step 1: Group the terms with the same sign
We can group the positive and negative terms together:
- Positive terms: \( 23.667 + 80.432 \)
- Negative terms: \( -2.55 - 19.205 \)

### Step 2: Add the positive terms
Now, we will add the positive terms:
\[ 23.667 + 80.432 \]
Aligning the decimal points:
```
23.667
+ 80.432
---------
```
Now, we add:
- \( 7 + 2 = 9 \)
- \( 6 + 3 = 9 \)
- \( 6 + 4 = 10 \) (write down 0 and carry over 1)
- \( 2 + 0 + 1 = 3 \)
- \( 8 + 0 = 8 \)

So,
\[ 23.667 + 80.432 = 104.099 \]

### Step 3: Add the negative terms
Next, we will add the negative terms:
\[ -2.55 - 19.205 \]
Aligning the decimal points:
```
19.205
+ 2.550
---------
```
Now, we add:
- \( 5 + 0 = 5 \)
- \( 0 + 5 = 5 \)
- \( 2 + 2 = 4 \)
- \( 9 + 0 = 9 \)
- \( 1 + 0 = 1 \)

So,
\[ -2.55 - 19.205 = -21.755 \]

### Step 4: Combine the results
Now we combine the results from Step 2 and Step 3:
\[ 104.099 - 21.755 \]
Aligning the decimal points:
```
104.099
- 21.755
---------
```
Now, we subtract:
- From the rightmost column: \( 9 - 5 = 4 \)
- Next column: \( 0 - 5 \) (we can't do this, so we borrow 1, making it 10): \( 10 - 5 = 5 \) (and we reduce the next column by 1)
- Next column: \( 0 - 7 \) (again, we can't do this, so we borrow 1, making it 10): \( 10 - 7 = 3 \) (and we reduce the next column by 1)
- Next column: \( 3 - 1 = 2 \)
- Finally: \( 1 - 0 = 1 \)

So,
\[ 104.099 - 21.755 = 82.344 \]

### Final Answer
The simplified result is:
\[ \boxed{82.344} \]

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