Definition
Identity property
The identity property uses a special number that leaves another number unchanged.
Continue from this idea into connected AXIO math.
Defining relationship
Identity means “same value comes out”: + 0 and × 1 leave a number as it was.
For an operation, an identity is a number that leaves every allowed number unchanged. For addition, 0 is the identity: a + 0 = 0 + a = a. For multiplication, 1 is the identity: a × 1 = 1 × a = a.
- 1
additive identity: + 0
- 2
multiplicative identity: × 1
- The original value stays 7
- Identity is about no change
What it means
An identity number is an operation’s “do-nothing” number. Add zero and the number stays put. Multiply by one and the number stays put. The identity changes with the operation, but the result keeps its original value.
Remember it
Identity means “same value comes out”: + 0 and × 1 leave a number as it was.
Example
Start with 37. The addition identity gives 37 + 0 = 37. The multiplication identity gives 37 × 1 = 37. In both equations, 37 is unchanged.
Watch for
Zero is not the multiplication identity: 8 × 0 = 0, not 8. One is not the addition identity: 8 + 1 = 9.
Common mix-up
The identity property keeps a number unchanged. The zero property of multiplication changes every product with a zero factor to 0.
Exact meaning
For an operation, an identity is a number that leaves every allowed number unchanged. For addition, 0 is the identity: a + 0 = 0 + a = a. For multiplication, 1 is the identity: a × 1 = 1 × a = a.