n+5=5+n? commutative, associative, and identity properties

In mathematics, commutativity is the property that changing the order of something does not change the end result

The equation you provided, n+5=5+n, demonstrates the commutative property of addition.

To explain, the commutative property of addition states that changing the order of numbers being added does not affect the sum. In this case, n+5 is equivalent to 5+n, meaning that regardless of whether n is added to 5 or 5 is added to n, the result will always be the same.

To understand why this is the case, we can break it down step-by-step:

1. Start with the equation: n+5=5+n.

2. By the commutative property, we can switch the order of n and 5: 5+n=5+n.

3. Since we have the same numbers on both sides of the equation, they are equal: 5+n=5+n.

Overall, the commutative property of addition allows us to interchange the order of numbers being added and still obtain the same result.

Now, let's move on to the associative and identity properties.

The associative property of addition states that changing the grouping of three or more numbers being added does not affect the sum. However, in the equation you provided, we only have two numbers (n and 5) being added, so the associative property is not applicable here.

The identity property of addition states that adding zero (0) to any number does not change its value. Again, looking at the equation n+5=5+n, we don't see any addition of zero, so the identity property is also not applicable in this case.

In summary, the equation n+5=5+n demonstrates the commutative property of addition, where the order of the numbers being added can be interchanged without affecting the final sum. The associative and identity properties are not applicable in this context.