Simplify `: 53.5-34.68+64.75-28.9`

Answer

To simplify the expression \( 53.5 - 34.68 + 64.75 - 28.9 \), we can follow these steps:

### Step 1: Rearrange the Expression
First, we can rearrange the expression to group the addition and subtraction together:
\[ (53.5 + 64.75) - (34.68 + 28.9) \]

### Step 2: Convert to Like Decimal Places
To make the addition and subtraction easier, we can convert all numbers to have the same number of decimal places. Here, we can convert them to two decimal places:
- \( 53.5 \) becomes \( 53.50 \)
- \( 64.75 \) remains \( 64.75 \)
- \( 34.68 \) remains \( 34.68 \)
- \( 28.9 \) becomes \( 28.90 \)

Now, the expression looks like this:
\[ (53.50 + 64.75) - (34.68 + 28.90) \]

### Step 3: Perform the Addition
Now, we will add the numbers in the first parentheses:
\[ 53.50 + 64.75 \]
Aligning the decimal points:
```
53.50
+ 64.75
--------
```
Adding:
- \( 0 + 5 = 5 \)
- \( 5 + 7 = 12 \) (write down 2, carry over 1)
- \( 3 + 4 + 1 = 8 \)
- \( 5 + 6 = 11 \)

So, \( 53.50 + 64.75 = 118.25 \).

### Step 4: Perform the Addition in the Second Parentheses
Next, we will add the numbers in the second parentheses:
\[ 34.68 + 28.90 \]
Aligning the decimal points:
```
34.68
+ 28.90
--------
```
Adding:
- \( 8 + 0 = 8 \)
- \( 6 + 9 = 15 \) (write down 5, carry over 1)
- \( 4 + 8 + 1 = 13 \) (write down 3, carry over 1)
- \( 3 + 2 = 5 \)

So, \( 34.68 + 28.90 = 63.58 \).

### Step 5: Subtract the Results
Now we subtract the results from Step 3 and Step 4:
\[ 118.25 - 63.58 \]
Aligning the decimal points:
```
118.25
- 63.58
--------
```
Subtracting:
- \( 5 - 8 \) (we need to borrow, so it becomes \( 15 - 8 = 7 \))
- \( 2 - 5 \) (we need to borrow, so it becomes \( 12 - 5 = 7 \))
- \( 7 - 3 = 4 \)
- \( 1 - 6 \) (we need to borrow, so it becomes \( 11 - 6 = 5 \))

So, \( 118.25 - 63.58 = 54.67 \).

### Final Answer
Thus, the simplified result is:
\[ \boxed{54.67} \]