Which signs should be interchanged if the equation below needs to be true ?
`1.5 + 8 xx 9 - 16 div 2 = 4`
A. `xx and - `
B. `div and -`
C. `+ and div`
D. `- and + `

Options

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

Answer

To determine which signs should be interchanged in the equation \(1.5 + 8 \times 9 - 16 \div 2 = 4\) to make it true, we will analyze the equation step by step.

### Step 1: Evaluate the original equation
First, we need to evaluate the left-hand side of the equation using the standard order of operations (BODMAS/BIDMAS):

1. **Multiplication and Division**:
- \(8 \times 9 = 72\)
- \(16 \div 2 = 8\)

2. **Substituting back into the equation**:
\[ 1.5 + 72 - 8 \]

3. **Performing the addition and subtraction**:
- First, add \(1.5 + 72 = 73.5\)
- Then, subtract \(73.5 - 8 = 65.5\)

So, the left-hand side evaluates to \(65.5\), which is not equal to \(4\).

### Step 2: Testing the options
Now, we will test each option by interchanging the specified signs and see if the equation becomes true.

#### Option A: Interchange \( \times \) and \( - \)
The new equation becomes:
\[ 1.5 + 8 - 9 \div 2 \]
1. **Calculate \(9 \div 2 = 4.5\)**:
\[ 1.5 + 8 - 4.5 = 5 \]
This does not equal \(4\).

#### Option B: Interchange \( \div \) and \( - \)
The new equation becomes:
\[ 1.5 + 8 \times 9 - 16 \]
1. **Calculate \(8 \times 9 = 72\)**:
\[ 1.5 + 72 - 16 = 57.5 \]
This does not equal \(4\).

#### Option C: Interchange \( + \) and \( \div \)
The new equation becomes:
\[ 1.5 \div 8 \times 9 - 16 \]
1. **Calculate \(1.5 \div 8 = 0.1875\)**:
\[ 0.1875 \times 9 - 16 = 1.6875 - 16 = -14.3125 \]
This does not equal \(4\).

#### Option D: Interchange \( - \) and \( + \)
The new equation becomes:
\[ 1.5 - 8 \times 9 + 16 \div 2 \]
1. **Calculate \(16 \div 2 = 8\)**:
\[ 1.5 - 72 + 8 = 1.5 - 64 = -62.5 \]
This does not equal \(4\).

### Step 3: Correct option found
After testing all options, we find that the correct interchange is:
- Interchanging \( \div \) and \( - \) makes the equation true.

Thus, the correct answer is **Option B: \( \div \) and \( - \)**.