Which signs should be interchanged if the equation below needs to be true?

`2 div 16-2 + 6 xx 1 = 0`

A. x and -

B. - and +

C. - and `div`

D. + and `xx`

Options

A. D
B. C
C. B
D. A

Answer

To determine which signs should be interchanged in the equation `2 div 16 - 2 + 6 xx 1 = 0` to make it true, we will analyze each option step by step.

### Step 1: Write down the original equation
The original equation is:
\[ 2 \div 16 - 2 + 6 \times 1 = 0 \]

### Step 2: Evaluate the original equation
Let's calculate the left-hand side of the equation:
1. Calculate \( 2 \div 16 \):
\[ 2 \div 16 = 0.125 \]
2. Now substitute this value into the equation:
\[ 0.125 - 2 + 6 \times 1 \]
3. Calculate \( 6 \times 1 \):
\[ 6 \times 1 = 6 \]
4. Now substitute this value:
\[ 0.125 - 2 + 6 = 0.125 - 2 + 6 \]
5. Combine the terms:
\[ 0.125 - 2 = -1.875 \]
\[ -1.875 + 6 = 4.125 \]

The left-hand side evaluates to \( 4.125 \), which does not equal \( 0 \).

### Step 3: Test the options
Now, we will test each option to see which one makes the equation true.

#### Option A: Interchange `x` and `-`
This means the equation becomes:
\[ 2 \div 16 + 2 + 6 \times 1 \]
Calculating:
1. \( 2 \div 16 = 0.125 \)
2. Substitute:
\[ 0.125 + 2 + 6 = 0.125 + 2 + 6 = 8.125 \]
This does not equal \( 0 \).

#### Option B: Interchange `-` and `+`
This means the equation becomes:
\[ 2 \div 16 + 2 - 6 \times 1 \]
Calculating:
1. \( 2 \div 16 = 0.125 \)
2. Substitute:
\[ 0.125 + 2 - 6 = 0.125 + 2 - 6 = -3.875 \]
This does not equal \( 0 \).

#### Option C: Interchange `-` and `div`
This means the equation becomes:
\[ 2 - 16 \div 2 + 6 \times 1 \]
Calculating:
1. \( 16 \div 2 = 8 \)
2. Substitute:
\[ 2 - 8 + 6 = 2 - 8 + 6 = 0 \]
This equals \( 0 \).

#### Option D: Interchange `+` and `xx`
This means the equation becomes:
\[ 2 \div 16 - 2 + 6 \div 1 \]
Calculating:
1. \( 6 \div 1 = 6 \)
2. Substitute:
\[ 2 \div 16 - 2 + 6 = 0.125 - 2 + 6 = 4.125 \]
This does not equal \( 0 \).

### Conclusion
The correct option is **C**: Interchange `-` and `div`.