Simplify the following `:`
75.3-104.645+178.96-47.9

Options

A. 95.715
B. 86.475
C. 101.715
D. 100.475

Answer

To simplify the expression \( 75.3 - 104.645 + 178.96 - 47.9 \), we will follow these steps:

### Step 1: Group the terms
We can rearrange the expression for easier calculation:
\[ (75.3 + 178.96) - (104.645 + 47.9) \]

### Step 2: Add the first group
Now, let's calculate \( 75.3 + 178.96 \):
- Align the decimals:
```
75.300
+178.960
---------
```
- Add the numbers:
- \( 0 + 0 = 0 \)
- \( 0 + 6 = 6 \)
- \( 3 + 9 = 12 \) (write down 2, carry over 1)
- \( 5 + 8 + 1 = 14 \) (write down 4, carry over 1)
- \( 7 + 1 = 8 \) (plus the carry over 1 gives 9)

So, \( 75.3 + 178.96 = 254.26 \).

### Step 3: Add the second group
Next, calculate \( 104.645 + 47.9 \):
- Align the decimals:
```
104.645
+ 47.900
----------
```
- Add the numbers:
- \( 5 + 0 = 5 \)
- \( 4 + 0 = 4 \)
- \( 6 + 9 = 15 \) (write down 5, carry over 1)
- \( 0 + 7 + 1 = 8 \)
- \( 1 + 0 = 1 \)

So, \( 104.645 + 47.9 = 152.545 \).

### Step 4: Subtract the second group from the first group
Now, we subtract:
\[ 254.26 - 152.545 \]
- Align the decimals:
```
254.260
- 152.545
----------
```
- Subtract the numbers:
- \( 0 - 5 \) (we need to borrow, so it becomes \( 10 - 5 = 5 \))
- \( 5 - 4 = 1 \)
- \( 2 - 5 \) (we need to borrow again, so it becomes \( 12 - 5 = 7 \))
- \( 4 - 2 = 2 \)
- \( 2 - 1 = 1 \)

So, \( 254.26 - 152.545 = 101.715 \).

### Final Answer
Thus, the simplified result is:
\[ \boxed{101.715} \]