Simplify: `12 1/2-5.375+8.125-2.9+10-3 4/5+11.08`

Options

A. `26.93`
B. `32.43`
C. `29.63`
D. `36.59`

Answer

To simplify the expression \( 12 \frac{1}{2} - 5.375 + 8.125 - 2.9 + 10 - 3 \frac{4}{5} + 11.08 \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Decimals
1. **Convert \( 12 \frac{1}{2} \)**:
\[ 12 \frac{1}{2} = 12 + \frac{1}{2} = 12 + 0.5 = 12.5 \]

2. **Convert \( 3 \frac{4}{5} \)**:
\[ 3 \frac{4}{5} = 3 + \frac{4}{5} = 3 + 0.8 = 3.8 \]

### Step 2: Rewrite the Expression
Now we can rewrite the expression using the decimal values:
\[ 12.5 - 5.375 + 8.125 - 2.9 + 10 - 3.8 + 11.08 \]

### Step 3: Group Positive and Negative Numbers
**Positive Numbers**:
\[ 12.5 + 8.125 + 10 + 11.08 \]

**Negative Numbers**:
\[ -5.375 - 2.9 - 3.8 \]

### Step 4: Calculate the Sum of Positive Numbers
\[ 12.5 + 8.125 = 20.625 \]
\[ 20.625 + 10 = 30.625 \]
\[ 30.625 + 11.08 = 41.705 \]

### Step 5: Calculate the Sum of Negative Numbers
\[ 5.375 + 2.9 = 8.275 \]
\[ 8.275 + 3.8 = 12.075 \]

### Step 6: Subtract the Sum of Negative Numbers from Positive Numbers
\[ 41.705 - 12.075 \]

### Step 7: Perform the Subtraction
Align the numbers for subtraction:
```
41.705
- 12.075
_________
```
- Start from the rightmost digit:
- 5 - 5 = 0
- 0 - 7 (need to borrow) = 10 - 7 = 3 (borrow 1 from the next column)
- 6 - 0 = 6
- 1 - 2 (need to borrow) = 11 - 2 = 9 (borrow 1 from the next column)
- 3 - 1 = 2

So, \( 41.705 - 12.075 = 29.630 \).

### Final Answer
The simplified value is:
\[ \boxed{29.63} \]