Which of the following is not true?

Options

A. `(2)/(3)+(5)/(4)=(5)/(4)+(2)/(3)`
B. `(2)/(3)-(5)/(4)=(5)/(4)-(2)/(3)`
C. `(2)/(3)xx(5)/(4)=(5)/(4)xx (2)/(3)`
D. `(2)/(3)div (5)/(4) =(2)/(3) xx (4)/(5)`

Answer

To determine which of the following statements is not true, we will analyze each option step by step.

### Given Options:
1. \( a + b = b + a \)
2. \( a - b = b - a \)
3. \( a \times b = b \times a \)
4. \( \frac{a}{b} = a \times \frac{1}{b} \)

### Step 1: Analyze Option 1
- **Statement**: \( a + b = b + a \)
- **Explanation**: This statement represents the commutative property of addition, which states that the order of addition does not affect the sum.
- **Conclusion**: This statement is true.

### Step 2: Analyze Option 2
- **Statement**: \( a - b = b - a \)
- **Explanation**: This statement suggests that subtraction is commutative, which is not true. The order in which you subtract numbers matters.
- **Conclusion**: This statement is not true.

### Step 3: Analyze Option 3
- **Statement**: \( a \times b = b \times a \)
- **Explanation**: This statement represents the commutative property of multiplication, which states that the order of multiplication does not affect the product.
- **Conclusion**: This statement is true.

### Step 4: Analyze Option 4
- **Statement**: \( \frac{a}{b} = a \times \frac{1}{b} \)
- **Explanation**: This statement is a representation of division as multiplication by the reciprocal. It is a valid mathematical identity.
- **Conclusion**: This statement is true.

### Final Conclusion
After analyzing all options, we find that:
- Option 1 is true.
- Option 2 is not true.
- Option 3 is true.
- Option 4 is true.

Thus, the option that is not true is **Option 2**: \( a - b = b - a \).

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