Interchanging which two signs will make the following equation correct ?
`15 + 3 xx 9 - 4 div 16 = 57`
A. - and +
B. - and `div`
C. - and `xx`
D. + and `div`

Options

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

Answer

To solve the equation `15 + 3 xx 9 - 4 div 16 = 57` by interchanging two signs, we will evaluate each option step by step.

1. **Original Equation**:
We start with the equation:
\[ 15 + 3 \times 9 - 4 \div 16 = 57 \]

2. **Evaluate the Left-Hand Side (LHS)**:
Let's calculate the LHS using the original signs:
- First, calculate \(3 \times 9 = 27\).
- Then, calculate \(4 \div 16 = 0.25\).
- Now substitute these values back into the equation:
\[ 15 + 27 - 0.25 = 15 + 27 - 0.25 = 41 - 0.25 = 40.75 \]
The LHS evaluates to \(40.75\), which is not equal to \(57\).

3. **Testing Option A (- and +)**:
Change the signs to:
\[ 15 - 3 \times 9 + 4 \div 16 \]
- Calculate \(15 - 27 + 0.25 = -12 + 0.25 = -11.75\) (not equal to \(57\)).

4. **Testing Option B (- and div)**:
Change the signs to:
\[ 15 + 3 \times 9 + 4 \div 16 \]
- Calculate \(15 + 27 + 0.25 = 42.25\) (not equal to \(57\)).

5. **Testing Option C (- and xx)**:
Change the signs to:
\[ 15 + 3 - 4 \times 16 \]
- Calculate \(15 + 3 - 64 = 18 - 64 = -46\) (not equal to \(57\)).

6. **Testing Option D (+ and div)**:
Change the signs to:
\[ 15 \div 3 \times 9 - 4 + 16 \]
- Calculate \(5 \times 9 - 4 + 16 = 45 - 4 + 16 = 41 + 16 = 57\) (this is equal to \(57\)).

7. **Conclusion**:
The correct option is D, where we interchange the + and div signs, making the equation valid.