Question

which of the following demonstrates the zero property of multiplication?

select one:
a. \\(3 + 0 = 0\\)
b. \\(-10 \cdot 0 = 0\\)
c. \\(5 + 0 = 0 + 5\\)
d. \\(25 + (-25) = 0\\)

which of the following demonstrates the associative property of multiplication?

Explanation:

Define the Zero Property of Multiplication

The property states that any number multiplied by zero equals zero.

$$ a \cdot 0 = 0 $$

Analyze the given options

We evaluate each choice to find the multiplication by zero.

• Option a: \(3 + 0 = 0\) is mathematically incorrect and represents addition.
• Option b: \(-10 \cdot 0 = 0\) shows a number multiplied by zero resulting in zero.
• Option c: \(5 + 0 = 0 + 5\) demonstrates the commutative property of addition.
• Option d: \(25 + (-25) = 0\) demonstrates the additive inverse property.

Identify the correct choice

Option b correctly demonstrates the Zero Property of Multiplication.

Answer:

• a. \(3 + 0 = 0\)
• b. \(-10 \cdot 0 = 0\) (Correct answer)
• c. \(5 + 0 = 0 + 5\)
• d. \(25 + (-25) = 0\)