Which property states that any number divided by itself equals 1?

The property that states any number divided by itself equals 1 is the identity property of division. This property highlights the fundamental relationship between division and the concept of identity in mathematics. When you take a non-zero number and divide it by itself, the result is always 1. This indicates that the original number retains its identity in that operation, as dividing by itself effectively neutralizes the value, returning the identity element for multiplication, which is 1.

In this context, it's essential to understand the significance of identity elements in mathematical operations. In addition to division, there are identity properties for addition and multiplication, which are similarly foundational in arithmetic. The identity property of division emphasizes that we can simplify calculations and understand the behavior of numbers in division using this concept.

This property stands distinct from others like the properties of zero, which concerns the results of operations involving zero, or the inverse property of multiplication, which deals with multiplication and its corresponding divisions. The division property of equality pertains to the rules that govern equations but doesn’t specifically address the outcome of dividing a number by itself. Each of these concepts is important but serves different purposes in understanding arithmetic and algebraic principles.