Certainly! Let's carefully analyze the given statement and identify the property of real numbers it describes.
The statement provided is: "Multiplying any number by 0 results in 0." An example given is [tex]\(a \cdot 0 = 0\)[/tex].
We need to identify which of the following properties this statement corresponds to:
- Inverse Property
- Multiplication Identity Property
- Multiplication Property of Zero
- Associative Property
Let's discuss each property briefly:
1. Inverse Property:
- The Inverse Property involves additive or multiplicative inverses.
- For addition, for any number [tex]\(a\)[/tex], there exists a number [tex]\(-a\)[/tex] such that [tex]\(a + (-a) = 0\)[/tex].
- For multiplication, for any nonzero number [tex]\(a\)[/tex], there exists a number [tex]\( \frac{1}{a} \)[/tex] such that [tex]\(a \cdot \frac{1}{a} = 1\)[/tex].
- The statement given does not relate to finding inverses.
2. Multiplication Identity Property:
- The Multiplication Identity Property states that any number multiplied by 1 remains unchanged.
- In mathematical terms, [tex]\(a \cdot 1 = a\)[/tex].
- This is not about multiplication by zero, hence this property does not apply.
3. Multiplication Property of Zero:
- The Multiplication Property of Zero specifies that any number multiplied by 0 results in 0.
- Mathematically, for any number [tex]\(a\)[/tex], [tex]\(a \cdot 0 = 0\)[/tex].
- This directly matches the statement given.
4. Associative Property:
- The Associative Property is about grouping numbers in addition or multiplication.
- For addition: [tex]\((a + b) + c = a + (b + c)\)[/tex].
- For multiplication: [tex]\((a \cdot b) \cdot c = a \cdot (b \cdot c)\)[/tex].
- The statement given is not about grouping numbers, so this property does not apply.
Given the explanation above, the property described by the statement "Multiplying any number by 0 results in 0" is indeed the Multiplication Property of Zero.
Therefore, the correct answer is:
Multiplication Property of Zero
