Which identity is represented when adding 0 to any number?

Which identity is represented when adding 0 to any number?

• A. Additive identity
• B. Multiplicative identity
• C. Numerical identity
• D. Commutative identity

Answer: (A)

The identity represented when adding 0 to any number is known as the additive identity. This principle states that for any number \( x \), the equation \( x + 0 = x \) holds true. This means that when you add zero to any number, the value of that number remains unchanged. The additive identity is fundamental in arithmetic and helps establish the properties of numbers in mathematical operations. This property is particularly important because it shows that zero does not affect the outcome of an addition operation, thus allowing for simpler calculations and a solid foundational understanding of numbers. The other identities listed do not apply in this context. The multiplicative identity refers to multiplying by 1, where the number remains unchanged (e.g., \( x \times 1 = x \)). Numerical identity is not a term that typically describes a mathematical property, and the commutative identity pertains to how the order of addition or multiplication does not affect the result, meaning that \( x + y = y + x \). Thus, the additive identity is specifically connected to the operation of addition and the effect of adding zero to any number.

The identity represented when adding 0 to any number is known as the additive identity. This principle states that for any number ( x ), the equation ( x + 0 = x ) holds true. This means that when you add zero to any number, the value of that number remains unchanged.

The additive identity is fundamental in arithmetic and helps establish the properties of numbers in mathematical operations. This property is particularly important because it shows that zero does not affect the outcome of an addition operation, thus allowing for simpler calculations and a solid foundational understanding of numbers.

The other identities listed do not apply in this context. The multiplicative identity refers to multiplying by 1, where the number remains unchanged (e.g., ( x \times 1 = x )). Numerical identity is not a term that typically describes a mathematical property, and the commutative identity pertains to how the order of addition or multiplication does not affect the result, meaning that ( x + y = y + x ).

Thus, the additive identity is specifically connected to the operation of addition and the effect of adding zero to any number.