Evaluate:
`13.6725 div 75`

Answer

To evaluate \( 13.6725 \div 75 \), we will follow these steps:

### Step 1: Set up the division
We start with the division of \( 13.6725 \) by \( 75 \). Since \( 13.6725 \) is a decimal number, we will treat it as \( 136.725 \) for the purpose of division. We will place the decimal point in the quotient after we finish the division.

### Step 2: Determine how many times \( 75 \) fits into \( 136 \)
Next, we see how many times \( 75 \) fits into \( 136 \).

- \( 75 \times 1 = 75 \)
- \( 75 \times 2 = 150 \) (too much)

So, \( 75 \) fits into \( 136 \) **1 time**.

### Step 3: Subtract and bring down the next digit
Now, we subtract \( 75 \) from \( 136 \):
\[ 136 - 75 = 61 \]
Next, we bring down the next digit, which is \( 7 \), making it \( 617 \).

### Step 4: Determine how many times \( 75 \) fits into \( 617 \)
Now, we check how many times \( 75 \) fits into \( 617 \).

- \( 75 \times 8 = 600 \)
- \( 75 \times 9 = 675 \) (too much)

So, \( 75 \) fits into \( 617 \) **8 times**.

### Step 5: Subtract and bring down the next digit
Now, we subtract \( 600 \) from \( 617 \):
\[ 617 - 600 = 17 \]
Next, we bring down the next digit, which is \( 2 \), making it \( 172 \).

### Step 6: Determine how many times \( 75 \) fits into \( 172 \)
Next, we check how many times \( 75 \) fits into \( 172 \).

- \( 75 \times 2 = 150 \)
- \( 75 \times 3 = 225 \) (too much)

So, \( 75 \) fits into \( 172 \) **2 times**.

### Step 7: Subtract and bring down the next digit
Now, we subtract \( 150 \) from \( 172 \):
\[ 172 - 150 = 22 \]
Next, we bring down the last digit, which is \( 5 \), making it \( 225 \).

### Step 8: Determine how many times \( 75 \) fits into \( 225 \)
Now, we check how many times \( 75 \) fits into \( 225 \).

- \( 75 \times 3 = 225 \)

So, \( 75 \) fits into \( 225 \) **3 times**.

### Step 9: Subtract to find the remainder
Now, we subtract \( 225 \) from \( 225 \):
\[ 225 - 225 = 0 \]

### Step 10: Place the decimal point in the quotient
Now, we have completed the division. The quotient is \( 0.1823 \) (since we initially moved the decimal point two places to the right).

### Final Answer
Thus, the result of \( 13.6725 \div 75 \) is:
\[ \boxed{0.1823} \]