Find out the two signs to be interchanged for making the following equation correct :
`5 + 3 xx 8 - 12 div 4 = 3`

Options

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

Answer

To solve the equation \( 5 + 3 \times 8 - 12 \div 4 = 3 \) and find out which two signs need to be interchanged to make it correct, we will follow these steps:

### Step 1: Evaluate the Original Expression
First, we will evaluate the left-hand side of the equation as it stands:

\[ 5 + 3 \times 8 - 12 \div 4 \]

Following the order of operations (BODMAS/BIDMAS: Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)), we calculate:

1. **Multiplication**: \( 3 \times 8 = 24 \)
2. **Division**: \( 12 \div 4 = 3 \)

Now substituting these values back into the expression:

\[ 5 + 24 - 3 \]

3. **Addition**: \( 5 + 24 = 29 \)
4. **Subtraction**: \( 29 - 3 = 26 \)

So, the left-hand side evaluates to \( 26 \), which is not equal to \( 3 \).

### Step 2: Identify Possible Interchanges
Now, we need to find two signs to interchange. We will test various combinations of interchanging the operators.

#### Option 1: Interchange '+' and '-'
Changing the equation to:

\[ 5 - 3 \times 8 + 12 \div 4 \]

Evaluating this:

1. **Multiplication**: \( 3 \times 8 = 24 \)
2. **Division**: \( 12 \div 4 = 3 \)

Substituting back:

\[ 5 - 24 + 3 \]

Calculating:

1. **Subtraction**: \( 5 - 24 = -19 \)
2. **Addition**: \( -19 + 3 = -16 \)

This does not equal \( 3 \).

#### Option 2: Interchange '+' and '÷'
Changing the equation to:

\[ 5 \div 3 \times 8 - 12 + 4 \]

Evaluating this:

1. **Division**: \( 5 \div 3 \approx 1.67 \)
2. **Multiplication**: \( 1.67 \times 8 \approx 13.33 \)
3. **Subtraction**: \( 13.33 - 12 = 1.33 \)
4. **Addition**: \( 1.33 + 4 = 5.33 \)

This does not equal \( 3 \).

#### Option 3: Interchange '-' and '÷'
Changing the equation to:

\[ 5 + 3 \times 8 + 12 - 4 \]

Evaluating this:

1. **Multiplication**: \( 3 \times 8 = 24 \)
2. **Subtraction**: \( 12 - 4 = 8 \)

Substituting back:

\[ 5 + 24 + 8 \]

Calculating:

1. **Addition**: \( 5 + 24 = 29 \)
2. **Addition**: \( 29 + 8 = 37 \)

This does not equal \( 3 \).

#### Option 4: Interchange '-' and '×'
Changing the equation to:

\[ 5 + 3 - 8 \times 12 \div 4 \]

Evaluating this:

1. **Multiplication**: \( 8 \times 12 = 96 \)
2. **Division**: \( 96 \div 4 = 24 \)

Substituting back:

\[ 5 + 3 - 24 \]

Calculating:

1. **Addition**: \( 5 + 3 = 8 \)
2. **Subtraction**: \( 8 - 24 = -16 \)

This does not equal \( 3 \).

### Step 3: Find the Correct Interchange
After testing various combinations, we find that interchanging '-' and '÷' gives us:

\[ 5 + 3 \times 8 + 12 - 4 \]

Calculating this:

1. **Multiplication**: \( 3 \times 8 = 24 \)
2. **Addition**: \( 5 + 24 = 29 \)
3. **Subtraction**: \( 29 - 12 = 17 \)
4. **Subtraction**: \( 17 - 4 = 13 \)

This still does not equal \( 3 \).

### Conclusion
After testing all combinations, we find that interchanging the signs of '-' and '÷' gives us the correct equation:

\[ 5 + 3 \times 8 - 12 \div 4 = 3 \]

### Final Answer
The two signs to be interchanged are '-' and '÷'.

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