What is Identity Property?
The mathematical property that for every operation (addition, subtraction, multiplication, division) there is an operator (the identity element) that leaves the operand unchanged
The identity property is a mathematical rule that says there are certain special numbers, called identity elements, that don’t change the value of another number when used in an operation.
Identity property for addition and subtraction is 0 because adding or subtracting 0 from any number does not change its value. Let’s give it a try:
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Addition: 7 + 0 = 7
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Subtraction: 7 - 0 = 7
Identity property for multiplication and division is 1 because multiplying or dividing by 1 doesn’t change the value of the multiplicand or dividend. Let’s check:
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Multiplication: 7 × 1 = 7
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Division: 7 ÷ 1 = 7
These identity elements, 0 for addition and 1 for multiplication, are called “identities” because they keep the number’s identity the same.
When Do Students Learn About the Identity Property?
Students first encounter the concept of the identity property in early childhood and elementary school math, as they develop an understanding of basic addition and subtraction.
Grades 1–2 – Basic Addition and Multiplication Identities
Students learn that adding 0 or multiplying by 1 doesn’t change a number.
Grades 3–5 – Applying Identity in Operations
Students use the identity property to simplify problems and understand its role in arithmetic and algebra.
Grades 6+ – Identity Property in Algebra
Students apply identity properties when simplifying algebraic expressions and solving equations.
