One times any number
The Identity Property of Multiplication — one times any number equals that number — is a Grade 4 concept in Saxon Math Intermediate 4 (Chapter 3). The number 1 acts as a multiplicative identity: 1 x 9 = 9, 123 x 1 = 123, 1 x 15 = 15. This works both ways since multiplication is commutative. A common error is confusing this with addition: 45 + 1 = 46, but 45 x 1 = 45. The identity property also underpins creating equivalent fractions by multiplying by forms of 1 like 3/3.
Key Concepts
Property One times any number equals the number.
Examples $1 \times 9 = 9$ $123 \times 1 = 123$ $1 \times 15 = 15$.
Explanation Multiplying by one is like a number looking in a mirror. It sees itself and stays exactly the same. One group of seven is just seven. That’s why it’s called the identity property, because the number always keeps its original identity! How cool is that?
Common Questions
What is the Identity Property of Multiplication?
Any number multiplied by 1 equals itself. Written as a x 1 = a. Examples: 1 x 9 = 9, 123 x 1 = 123. The number 1 is the multiplicative identity because it preserves a number's identity.
A library has 45 shelves, each holding 1 dictionary. How many dictionaries?
45 x 1 = 45. The Identity Property says any number times 1 equals itself. The library has 45 dictionaries total.
What is the difference between adding 0 and multiplying by 1?
Both preserve the number's value, but through different operations. 45 + 0 = 45 (additive identity). 45 x 1 = 45 (multiplicative identity). Never add the identity numbers together.
How does multiplying by 1 relate to equivalent fractions?
Multiplying a fraction by 3/3, 5/5, or any n/n (which all equal 1) creates equivalent fractions without changing the value. This is a direct application of the Identity Property.
What is 243 x 1?
243. The Identity Property states any number multiplied by 1 equals itself. The multiplication does not change the value.