Identity property of multiplication

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

1. The identity element for multiplication is 1.
2. This property holds true for all real numbers, including positive, negative, and zero.
3. It helps simplify expressions and solve equations in algebra.
4. In proofs, this property is often used to justify steps where multiplying by 1 does not alter the value.
5. This property is fundamental in understanding and working with multiplicative inverses.

Review Questions

• What is the identity element in multiplication?
• If $a$ is a real number, what is $a \times 1$ equal to?
• How does the identity property of multiplication help simplify algebraic expressions?

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 $b$, $a \times b = b \times a$.