Simplify: 63.7-28.89 + 76.4-37.66.

Answer

To simplify the expression \(63.7 - 28.89 + 76.4 - 37.66\), we will follow these steps:

### Step 1: Rewrite the Expression
First, we rewrite the expression clearly:
\[ 63.7 - 28.89 + 76.4 - 37.66 \]

### Step 2: Group the Positive and Negative Terms
We can group the positive and negative terms together:
\[ (63.7 + 76.4) - (28.89 + 37.66) \]

### Step 3: Calculate the Sum of Positive Terms
Now, let's calculate \(63.7 + 76.4\):
- Align the decimal points:
\[ \begin{array}{r} 63.7 \\ +76.4 \\ \hline \end{array} \]
- Add the numbers:
- \(3 + 4 = 7\)
- \(6 + 7 = 13\) (write down 3 and carry over 1)
- \(1 + 6 + 1 = 8\)

So, \(63.7 + 76.4 = 140.1\).

### Step 4: Calculate the Sum of Negative Terms
Next, we calculate \(28.89 + 37.66\):
- Align the decimal points:
\[ \begin{array}{r} 28.89 \\ +37.66 \\ \hline \end{array} \]
- Add the numbers:
- \(9 + 6 = 15\) (write down 5 and carry over 1)
- \(8 + 6 + 1 = 15\) (write down 5 and carry over 1)
- \(2 + 3 + 1 = 6\)

So, \(28.89 + 37.66 = 66.55\).

### Step 5: Subtract the Sums
Now we subtract the sum of the negative terms from the sum of the positive terms:
\[ 140.1 - 66.55 \]
- Align the decimal points:
\[ \begin{array}{r} 140.10 \\ -66.55 \\ \hline \end{array} \]
- Subtract the numbers:
- Start from the right: \(0 - 5\) (we need to borrow, making it \(10 - 5 = 5\))
- Next column: \(0 - 5\) (again we need to borrow, making it \(10 - 5 = 5\))
- Next column: \(3 - 6\) (we need to borrow, making it \(13 - 6 = 7\))
- Last column: \(1 - 0 = 1\)

So, \(140.10 - 66.55 = 73.55\).

### Final Answer
Thus, the simplified result of the expression \(63.7 - 28.89 + 76.4 - 37.66\) is:
\[ \boxed{73.55} \]