If crepresents a number, which of the following statements uses the multiplicative identity?
c.O=0
C. 1 = 0
c+ 0 =
The Correct Answer and Explanation is:
The correct answer is: c * 1 = c
This statement uses the multiplicative identity.
Explanation:
The multiplicative identity is a fundamental concept in arithmetic and algebra. It refers to the number that, when multiplied by any other number, leaves the other number unchanged. In the case of real numbers, the multiplicative identity is 1. This means that for any number x, multiplying x by 1 gives x back:
[
x * 1 = x
]
Now, let’s analyze each of the options in your question:
- c * 0 = 0: This statement uses the multiplicative property of zero, which states that any number multiplied by 0 equals 0. This is not an example of the multiplicative identity, as multiplying by 0 does not leave the number unchanged.
- 1 = 0: This is a false statement in standard arithmetic, and it doesn’t involve the multiplicative identity in any way. The multiplicative identity is 1, and it is never equal to 0.
- c + 0 = c: This statement uses the additive identity, which is 0. The additive identity states that adding 0 to any number c leaves the number unchanged. However, this is an example of addition, not multiplication, so it doesn’t involve the multiplicative identity.
- c * 1 = c: This is the correct statement that uses the multiplicative identity. It shows that multiplying any number c by 1 results in c, which is the definition of the multiplicative identity.
In summary, the multiplicative identity refers to the number 1, which has the property that multiplying it by any number does not change that number. Therefore, the statement c * 1 = c is the one that uses the multiplicative identity.