Which of the following statements is CORRECT ?

Options

A. The product of two negative integers is always less than both the integers
B. The additive inverse of a negative integer is negative .
C. Multiplicative inverse of 5 is `(1)/(5)`.
D. The difference between an integer and its additive inverse is always odd.

Answer

To determine which of the following statements is correct, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Evaluate Statement 1**: "The product of two negative integers is always less than both the integers."
- Let’s take two negative integers, for example, -2 and -3.
- The product of -2 and -3 is:
\[ (-2) \times (-3) = 6 \]
- Here, 6 is greater than both -2 and -3.
- Therefore, Statement 1 is **incorrect**.

2. **Evaluate Statement 2**: "The additive inverse of a negative integer is negative."
- The additive inverse of a number \( x \) is defined as the number that, when added to \( x \), results in 0.
- If we take a negative integer, say -4, its additive inverse is:
\[ -(-4) = 4 \]
- Since 4 is positive, Statement 2 is **incorrect**.

3. **Evaluate Statement 3**: "The multiplicative inverse of 5 is 1 by 5."
- The multiplicative inverse of a number \( x \) is defined as the number that, when multiplied by \( x \), gives 1.
- For 5, the multiplicative inverse is:
\[ \frac{1}{5} \]
- Therefore, Statement 3 is **correct**.

4. **Evaluate Statement 4**: "The difference between an integer and its additive inverse is always odd."
- Let’s take an integer, say 3. Its additive inverse is -3.
- The difference is:
\[ 3 - (-3) = 3 + 3 = 6 \]
- Since 6 is even, Statement 4 is **incorrect**.

### Conclusion:
After evaluating all statements, we find that the only correct statement is:
- **Statement 3**: "The multiplicative inverse of 5 is 1 by 5."

### Final Answer:
The correct statement is **Option 3**.

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