Identity Property of Addition
The Identity Property of Addition states that adding zero to any number leaves that number unchanged: a + 0 = a and 0 + a = a. In Grade 6 Saxon Math Course 1, this property is formalized as one of the foundational arithmetic properties. Zero is called the additive identity because it preserves a number's identity under addition. For example, a video game character with 1,250 gold coins who collects an empty chest (0 coins) still has exactly 1,250 coins.
Key Concepts
Property If one of two addends is zero, the sum of the addends is identical to the nonzero addend. $$ 5 + 0 = 5 $$.
Examples 1. You have 23 gummy bears and your friend gives you 0 more. You still have 23: $23 + 0 = 23$. 2. Your bank account has 500 dollars. You add 0 dollars. The balance remains 500 dollars: $500 + 0 = 500$. 3. This property works both ways, so $0 + 1999 = 1999$.
Explanation Zero is the 'chillest' number in addition. Adding it is like giving another number a high five—it's friendly, but it doesn't change anything. The number keeps its original 'identity' and value, which is why this property is so cool!
Common Questions
What does the Identity Property of Addition state?
Adding zero to any number does not change its value: a + 0 = a and 0 + a = a.
Why is zero called the additive identity?
Because adding zero leaves a number's identity (value) completely unchanged — zero is the unique number with this property.
Write an equation showing 1,250 + 0.
1,250 + 0 = 1,250, illustrating the Identity Property of Addition.
Does this property work in the reverse order (0 + a)?
Yes. By the Commutative Property, 0 + 1,250 = 1,250 + 0 = 1,250.
Is there a similar identity property for multiplication?
Yes. The Identity Property of Multiplication states a × 1 = a — multiplying by 1 leaves a number unchanged; 1 is the multiplicative identity.