The identity property of addition is a property of real numbers that states that the sum of 0 and any number is equal to that number. The term "identity" is used in many other areas of mathematics to represent the same concept: an equation that, given certain constraints, is true regardless of what number is plugged into the equation. This can be written in the form of an addition sentence as:

a + 0 = 0 + a = a

where a is a number. The equation says that no matter what a is, if we add 0 to a, the solution will still be a. Also, the order in which we add 0 does not affect the outcome based on the commutative property of addition). This is because 0 has no quantity, so adding no quantity to any quantity will still result in the same original quantity. Because of this, 0 is also referred to as the "additive identity."

One way to visualize this is to use a set of objects. Generally, when adding more objects to an existing number of objects, the result is an increase in the number of objects. However, if we add (or remove) 0 objects from a set of objects, it makes sense that the number of objects we have stays the same.

Examples

Add 0 to 27, ⅓, and 1056.38.

27 + 0 = 0 + 27 = 27

⅓ + 0 = 0 + ⅓ = ⅓

1056.38 + 0 = 0 + 1056.38 = 1056.38

It doesn't matter what a is, adding 0 will always result in the original value, a.

The identity property of addition is just one property of real numbers. There is also an identity property of multiplication, as well as other properties such as the commutative and associative properties of addition. Together, they form some of the building blocks of algebra. Using identities can make algebraic equations significantly easier to manipulate and solve, and algebra is used to some degree in most areas of mathematics.