Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
The identity property of multiplication states that any number multiplied by 1 remains unchanged. Mathematically, for any real number $a$, $a \times 1 = a$.
5 Must Know Facts For Your Next Test
The identity element for multiplication is 1.
This property holds true for all real numbers, including positive, negative, and zero.
It helps simplify expressions and solve equations in algebra.
In proofs, this property is often used to justify steps where multiplying by 1 does not alter the value.
This property is fundamental in understanding and working with multiplicative inverses.
Review Questions
Related terms
Identity Property of Addition: Any number plus zero remains unchanged. Mathematically, for any real number $a$, $a + 0 = a$.
Multiplicative Inverse: For any nonzero real number $a$, there exists another real number $b$ such that $a \times b = 1$. The number $b$ is called the multiplicative inverse or reciprocal of $a$.
Commutative Property of Multiplication: The order in which two numbers are multiplied does not change the product. Mathematically, for any real numbers $a$ and $b$, $a \times b = b \times a$.