When two number are added the sum is the same regardless of the order of addends is
commutative law of addition
The property you are referring to is called the commutative property of addition. It states that the order in which numbers are added does not affect the result of their sum.
To understand why this property holds true, let's consider two numbers, a and b. When we add them in a certain order, say a + b, we are taking the value of a and combining it with the value of b. On the other hand, when we add them in reverse order, b + a, we are taking the value of b and combining it with the value of a.
No matter which order we choose, the act of addition itself does not change. Adding a to b is essentially the same as adding b to a. Therefore, the result, which is the sum of a + b, will always be the same regardless of the order of the addends.
For example, if we have the numbers 3 and 5, whether we add 3 + 5 or 5 + 3, we will always get the sum of 8. This is because addition is commutative, and the order of the addends does not matter.
In mathematical notation, the commutative property of addition can be written as:
a + b = b + a
It's important to note that not all mathematical operations are commutative. Subtraction, division, and exponentiation do not follow the commutative property.