Which of the following demonstrates the zero property?
A. [tex]$0 \times x=x \times 0$[/tex]
B. [tex]$0=x \times 0$[/tex]
C. [tex]$0=x+0$[/tex]
D. [tex]$0+x=x+0$[/tex]
Answer (2)
The zero property states that any number multiplied by zero is zero.
Option A demonstrates the commutative property of multiplication.
Option B correctly demonstrates the zero property: 0 = x × 0 .
Options C and D demonstrate properties of addition, not the zero property.
The correct answer is B .
Explanation
Understanding the Zero Property The zero property of multiplication states that any number multiplied by zero equals zero. We need to identify which of the given options correctly demonstrates this property.
Analyzing Each Option Let's examine each option:
Option A: 0 × x = x × 0 . This shows that multiplying 0 by x is the same as multiplying x by 0, which is the commutative property of multiplication. It doesn't explicitly state that the result is zero.
Option B: 0 = x × 0 . This option states that any number x multiplied by 0 equals 0, which is exactly the zero property of multiplication.
Option C: 0 = x + 0 . This demonstrates the identity property of addition, where adding 0 to any number x results in x. It is not related to the zero property of multiplication.
Option D: 0 + x = x + 0 . This demonstrates the commutative property of addition, where adding 0 to x is the same as adding x to 0. It is not related to the zero property of multiplication.
Identifying the Correct Option Based on the analysis, option B, 0 = x × 0 , correctly demonstrates the zero property of multiplication.
Examples
The zero property is fundamental in many areas of mathematics and real-life applications. For instance, if you are calculating the total cost of items and one of the items has a quantity of zero, the zero property tells you that the cost contribution of that item is zero, regardless of its price. This principle simplifies calculations and helps in understanding the impact of zero values in various scenarios, from budgeting to inventory management.
The zero property states that any number multiplied by zero equals zero, which is correctly illustrated in Option B: 0 = x × 0 . The other options either demonstrate properties of addition or do not accurately reflect the zero property. Thus, the correct answer is B.
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