If crepresents a number, which of the following statements uses the multiplicative identity?
c.O=0
C. 1 = 0
c+ 0 = 0
The Correct Answer and Explanation is:
The correct answer is:
C × 1 = C
Explanation:
The multiplicative identity is a fundamental concept in mathematics. It refers to the number that, when multiplied by any number, does not change the value of that number. In the set of real numbers, the multiplicative identity is 1.
Why “C × 1 = C” is correct:
This statement adheres to the definition of the multiplicative identity. When any number ( C ) is multiplied by 1, the result is the number itself. For example:
- If ( C = 5 ), then ( 5 × 1 = 5 ).
- If ( C = -3 ), then ( -3 × 1 = -3 ).
- If ( C = 0 ), then ( 0 × 1 = 0 ).
This property is true for all real numbers and demonstrates the essence of the multiplicative identity.
Why the other options are incorrect:
- ( C × 0 = 0 ):
This equation represents the zero property of multiplication, not the multiplicative identity. The zero property states that any number multiplied by 0 is always 0. - ( C + 0 = 0 ):
This equation represents the additive identity, not the multiplicative identity. The additive identity is 0 because adding 0 to any number does not change its value.
The multiplicative identity is specific to multiplication, and the defining characteristic is that multiplying by 1 leaves the number unchanged. This property is critical in algebra, allowing for the simplification and manipulation of equations without altering their values.
In conclusion, ( C × 1 = C ) demonstrates the use of the multiplicative identity, which is a cornerstone of mathematical operations and foundational to various mathematical principles.