Evaluate:
`3.765 div 25`

Answer

To evaluate \( 3.765 \div 25 \), we will follow these steps:

### Step 1: Set up the division
We start by setting up the division of \( 3.765 \) by \( 25 \). Since \( 3.765 \) is a decimal, we will treat it as \( 3.765 \) divided by \( 25 \).

### Step 2: Handle the decimal point
Since \( 3.765 \) is less than \( 25 \), we cannot divide it directly. We write \( 0 \) as the quotient and place a decimal point in the answer. We then consider \( 37.65 \) (the next two digits after the decimal) for division.

### Step 3: Divide 37 by 25
Now we look at \( 37 \). The largest multiple of \( 25 \) that fits into \( 37 \) is \( 25 \) (which is \( 25 \times 1 \)).

- Write \( 1 \) above the division line.
- Subtract \( 25 \) from \( 37 \):
\[ 37 - 25 = 12 \]

### Step 4: Bring down the next digit
Next, we bring down the next digit, which is \( 6 \), making it \( 126 \).

### Step 5: Divide 126 by 25
Now, we divide \( 126 \) by \( 25 \). The largest multiple of \( 25 \) that fits into \( 126 \) is \( 125 \) (which is \( 25 \times 5 \)).

- Write \( 5 \) above the division line.
- Subtract \( 125 \) from \( 126 \):
\[ 126 - 125 = 1 \]

### Step 6: Bring down the next digit
Now we bring down the next digit, which is \( 5 \), making it \( 15 \).

### Step 7: Divide 15 by 25
Now, we divide \( 15 \) by \( 25 \). Since \( 15 \) is less than \( 25 \), we write \( 0 \) above the division line.

### Step 8: Bring down a zero
We bring down a zero, making it \( 150 \).

### Step 9: Divide 150 by 25
Now, we divide \( 150 \) by \( 25 \). The largest multiple of \( 25 \) that fits into \( 150 \) is \( 150 \) (which is \( 25 \times 6 \)).

- Write \( 6 \) above the division line.
- Subtract \( 150 \) from \( 150 \):
\[ 150 - 150 = 0 \]

### Step 10: Final answer
Since we have no remainder left, we can conclude that:
\[ 3.765 \div 25 = 0.1506 \]

### Final Answer:
\[ \boxed{0.1506} \]

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