Simplify : 8.349 - 2.57 + 6.28 - 9.6

Answer

To simplify the expression \( 8.349 - 2.57 + 6.28 - 9.6 \), we can follow these steps:

### Step 1: Rearrange the expression
We can rearrange the expression to group the addition and subtraction:
\[ 8.349 + 6.28 - 2.57 - 9.6 \]

### Step 2: Add the first two numbers
Now, we will add \( 8.349 \) and \( 6.28 \). To do this, we can align the decimal points:
```
8.349
+ 6.280
--------
```
Now, we add column by column:
- In the thousandths place: \( 9 + 0 = 9 \)
- In the hundredths place: \( 4 + 8 = 12 \) (write down 2 and carry over 1)
- In the tenths place: \( 3 + 2 + 1 = 6 \)
- In the units place: \( 8 + 6 = 14 \)

So, we have:
\[ 8.349 + 6.28 = 14.629 \]

### Step 3: Add the last two numbers
Next, we will add \( 2.57 \) and \( 9.6 \):
```
2.570
+ 9.600
--------
```
Now, we add column by column:
- In the thousandths place: \( 0 + 0 = 0 \)
- In the hundredths place: \( 7 + 0 = 7 \)
- In the tenths place: \( 5 + 6 = 11 \) (write down 1 and carry over 1)
- In the units place: \( 2 + 9 + 1 = 12 \)

So, we have:
\[ 2.57 + 9.6 = 12.17 \]

### Step 4: Subtract the two results
Now, we need to subtract \( 12.17 \) from \( 14.629 \):
```
14.629
- 12.170
--------
```
Now, we subtract column by column:
- In the thousandths place: \( 9 - 0 = 9 \)
- In the hundredths place: \( 2 - 7 \) (we need to borrow, so it becomes \( 12 - 7 = 5 \))
- In the tenths place: \( 5 - 1 = 4 \)
- In the units place: \( 4 - 2 = 2 \)

So, we have:
\[ 14.629 - 12.17 = 2.459 \]

### Final Answer
Thus, the simplified result is:
\[ \boxed{2.459} \]