The commutative property is a fundamental concept in mathematics that applies to various mathematical operations, including addition and multiplication. In the context of integers, the commutative property refers to the ability to change the order of the numbers being added or multiplied without changing the result. In simpler terms, it means that the order in which you add or multiply integers does not matter.

**Commutative Property of Addition:**
The commutative property of addition states that for any two integers a and b, the sum of a and b will be the same regardless of the order in which they are added. In other words, a + b = b + a.

For example:
- 2 + 3 = 3 + 2 = 5
- (-5) + 7 = 7 + (-5) = 2

**Commutative Property of Multiplication:**
Similarly, the commutative property of multiplication states that for any two integers a and b, the product of a and b will be the same regardless of the order in which they are multiplied. In other words, a × b = b × a.

For example:
- 2 × 3 = 3 × 2 = 6
- (-5) × 7 = 7 × (-5) = -35

**Importance and Application:**
The commutative property is important because it allows us to simplify calculations and manipulate expressions without changing their overall value. It provides flexibility in rearranging terms in equations and expressions, which can be particularly useful in algebraic manipulations.

The commutative property is not limited to addition and multiplication of integers. It also holds true for other mathematical operations, such as addition and multiplication of fractions, as well as addition and multiplication of real numbers.

**Conclusion:**
In summary, the commutative property of integers states that the order in which integers are added or multiplied does not affect the final result. It provides a foundational concept in mathematics and is applicable to various operations beyond just integers. Understanding and applying the commutative property allows for simplification and manipulation of mathematical expressions, leading to more efficient calculations and problem-solving.

Commutative property= a+b = b+a.
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