51 `div` 3 + 17 `xx` 2 – 12 = 10

Options

A. `+` and `div`
B. `-` and `xx`
C. `div` and `xx`
D. `xx` and +

Explanation

To solve the equation \( 51 \div 3 + 17 \times 2 - 12 = 10 \) and determine which operation needs to be changed to make the equation true, we will follow these steps:

### Step 1: Solve the original equation
1. **Perform the division**:
\[ 51 \div 3 = 17 \]
2. **Perform the multiplication**:
\[ 17 \times 2 = 34 \]
3. **Combine the results**:
\[ 17 + 34 - 12 \]
4. **Add 17 and 34**:
\[ 17 + 34 = 51 \]
5. **Subtract 12 from 51**:
\[ 51 - 12 = 39 \]

### Step 2: Analyze the result
The result of the original equation is \( 39 \), which is not equal to \( 10 \). Therefore, we need to change one of the operations.

### Step 3: Change the operations
Let's try changing the multiplication to subtraction and the subtraction to multiplication.

1. **Change \( + \) to \( - \)** and \( - \) to \( \times \):
\[ 51 \div 3 - 17 \times 2 + 12 \]

### Step 4: Solve the modified equation
1. **Perform the division**:
\[ 51 \div 3 = 17 \]
2. **Perform the multiplication**:
\[ 17 \times 2 = 34 \]
3. **Combine the results**:
\[ 17 - 34 + 12 \]
4. **Subtract 34 from 17**:
\[ 17 - 34 = -17 \]
5. **Add 12 to -17**:
\[ -17 + 12 = -5 \]

### Step 5: Try another combination
Now let's change the multiplication to subtraction and keep the subtraction as is.

1. **Change \( \times \) to \( - \)**:
\[ 51 \div 3 + 17 - 12 \times 2 \]

### Step 6: Solve this modified equation
1. **Perform the division**:
\[ 51 \div 3 = 17 \]
2. **Perform the multiplication**:
\[ 12 \times 2 = 24 \]
3. **Combine the results**:
\[ 17 + 17 - 24 \]
4. **Add 17 and 17**:
\[ 17 + 17 = 34 \]
5. **Subtract 24 from 34**:
\[ 34 - 24 = 10 \]

### Conclusion
By changing the multiplication operation to subtraction and keeping the subtraction operation as multiplication, we get the desired result of \( 10 \). Thus, the correct operation to change is the multiplication to subtraction.