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Zero (0) is...

Zero (0) is

A

the identity for addition of rational numbers.

B

the identity for subtraction of rational numbers.

C

the identity for multiplication of rational numbers.

D

the identity for division of rational numbers.

Text Solution

AI Generated Solution

The correct Answer is:
**Step-by-Step Solution:** 1. **Understanding Identity Element**: In mathematics, an identity element for a particular operation is a number that, when used in that operation with any other number, does not change the other number. 2. **Identity for Addition**: For addition, the identity element is 0. This means that if you take any rational number (let's denote it as \( \frac{p}{q} \)), and add 0 to it, the result will still be \( \frac{p}{q} \). - Example: \( \frac{3}{4} + 0 = \frac{3}{4} \) 3. **Identity for Subtraction**: The identity element for subtraction is not defined in the same way because subtracting 0 from a number does not change the number, but adding a number to 0 does not affect the number either. However, the term "identity" is not typically used for subtraction. 4. **Identity for Multiplication**: The identity element for multiplication is 1. This means that if you multiply any rational number by 1, the result is the same rational number. - Example: \( \frac{3}{4} \times 1 = \frac{3}{4} \) 5. **Identity for Division**: The identity element for division is also not defined in the same way. Dividing by 1 does not change the number, but dividing by 0 is undefined. 6. **Conclusion**: Therefore, we can conclude that 0 is the identity for addition of rational numbers. **Final Answer**: 0 is the identity for addition of rational numbers. ---
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