Definition
Multiplicative identity
The multiplicative identity is one, because multiplying by one leaves a number unchanged.
What it means
Multiplying by one means taking one copy of a number. One copy of a number is still that number. It works whether the one is written first or second.
Remember it
One copy stays the same.
Example
One group of 36 contains 36, so 1 × 36 = 36. Thirty-six groups of one also contain 36 altogether, so 36 × 1 = 36.
Watch for
One is the identity for multiplication, but adding one changes the number: 36 + 1 = 37.
Common mix-up
Do not swap the two identity numbers: one is the multiplicative identity, while zero is the additive identity.
Exact meaning
The multiplicative identity is the number one: for any number a for which multiplication is defined, a × 1 = 1 × a = a.