Question

Which of the following statements is not true? (A) The product of any number and zero is zero. (B) The order in which two numbers are multiplied does not change the product. (c) The product of any number and \(-1\) is a negative number. (D) The product of any number and \(-1\) is the opposite of the number.

Short answer

The false statement among the provided options is (C) 'The product of any number and -1 is a negative number'. This is not true in case of negative numbers.

Step-by-step solution

Analyse statement (A)

The statement (A) 'The product of any number and zero is zero'. This is a true statement. It's a basic multiplication property, as any number multiplied by zero equals zero.

Analyse statement (B)

The statement (B) 'The order in which two numbers are multiplied does not change the product'. This is known as the commutative property of multiplication and is also true, as changing the order of multiplication does not affect the product. For instance, \(5 \times 3 = 15\) and \(3 \times 5 = 15\).

Analyse statement (C)

The statement (C) 'The product of any number and -1 is a negative number'. On the surface, this statement appears to be true. However, it's crucial to consider all possible numbers, including negative ones. As, when a negative number is multiplied by -1, the result is a positive number, not a negative number. Therefore, this statement is false.

Analyse statement (D)

The statement (D) 'The product of any number and -1 is the opposite of the number'. This is true, as multiplying any number by -1 simply changes its sign.