Yes, addition is commutative for integers.
This means that when you add two integers, the order in which you add them does not affect the result. According to the provided reference, "Integers are commutative under addition when any two integers are added irrespective of their order, the sum remains the same."
Understanding Commutativity
The commutative property of addition states that for any two integers, a and b, the following equation holds true:
a + b = b + a
Examples
Here are some examples demonstrating the commutative property with integers:
- Example 1: 3 + 5 = 8 and 5 + 3 = 8
- Example 2: -2 + 7 = 5 and 7 + (-2) = 5
- Example 3: -4 + (-1) = -5 and -1 + (-4) = -5
Table Illustrating Commutative Property
| Integer a | Integer b | a + b | b + a |
|---|---|---|---|
| 10 | 2 | 12 | 12 |
| -5 | 8 | 3 | 3 |
| -3 | -6 | -9 | -9 |
| 0 | 4 | 4 | 4 |
| -7 | 0 | -7 | -7 |
Why is this important?
The commutative property is a fundamental property in mathematics that simplifies calculations and provides a foundation for more advanced concepts. Understanding this property helps in solving algebraic equations and performing arithmetic operations with ease.
