Identity of an Operation
Elementary School
Definition
A number where if you combine it with another quantity via an operation allows that quanity to remain the same. For addition, you have the additive identity of 0 since adding 0 to anything does not alter it. In multiplication, it is 1 since multiplying anything by 1 allows it to remain the same.
Worked examples
\(5 + 0 = 5\)
Adding 0 leaves 5 unchanged; 0 is the additive identity.
\(7 \times 1 = 7\)
Multiplying by 1 leaves 7 unchanged; 1 is the multiplicative identity.
Common mistakes
- \(0\) is the identity for multiplication → \(1\) is the identity for multiplication Multiplying by 0 gives 0, not the original number. Only 1 preserves the value.
- \(1\) is the identity for addition → \(0\) is the identity for addition Adding 1 changes the number. Only adding 0 keeps it the same.
- \(x \cdot 0 = x\) uses the multiplicative identity → \(x \cdot 1 = x\) uses the multiplicative identity The identity must leave the value unchanged; multiplying by 0 gives 0, not x.
Where you'll use it next
You'll use identity properties to simplify algebraic expressions, solve equations, verify matrix identities in linear algebra, and understand inverse operations in abstract algebra.
Found in 1 StudyPug lesson
Understanding the Identity Property in Mathematics
5th Grade5thGrade 5 Math placeholder
Discover the power of the identity property in arithmetic. Learn how it simplifies calculations, solves equations, and forms the foundation for advanced math concepts. Boost your problem-solving skills today!
See also
Identity MatrixAdditive inverse of a numberIdentity FunctionZeroIdentity (Equation)Additive Inverse of a matrix
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026