Question

which of the following is true about the additive identity? the additive identity of a number is the distance from 0 to that number on the number line. it is neither positive nor negative. if x is the additive identity, then x + y = x. the additive identity works with decimals, but not fractions.

Explanation:

Step1: Recall additive identity definition

The additive identity of any number (including decimals, fractions, integers etc.) is 0. For any number \(x\), \(x + 0=x\).

Step2: Analyze each option

• Option 1: The additive - identity works for all real numbers (including decimals and fractions), so this is false.
• Option 2: If \(x\) is the additive identity (\(x = 0\)), then \(x + y=y\) (not \(x + y=x\)), so this is false.
• Option 3: The additive identity \(0\) is neither positive nor negative, which is a correct property of the additive identity.
• Option 4: The additive identity of a number is 0, not the distance from 0 to the number on the number - line. The distance from 0 to a number on the number - line is the absolute value of the number. So this is false.

Answer:

It is neither positive nor negative.