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# Explain the commutative and associative properties of addition and multiplication of integers.

__Solution:__

**Commutative Property of Addition and Multiplication of Integers**

$A + B = B + A$ for any two integers A, B

$A \times B = B \times A $ for any two integers A, B

According to the commutative property...

The sum of any two integers is the same irrespective of the order in which they are added.

The product of any two integers is the same irrespective of the order in which they are multiplied.

__Example:__

$5 + (-2) = (-2) + 5; 5 \times 2 = 2 \times 5$

Associative Property of Addition and Multiplication of Integers

$(A + B )+ C = A + (B + C)$ for any three integers A, B, and C

$(A \times B) \times C = A \times (B \times C) $ for any three integers A, B, and C

According to the associative property...

The sum of any three integers is the same irrespective of the grouping in which they are added.

The product of any three integers is the same irrespective of the grouping in which they are multiplied.

__Example:__

$(5 + 2 )+ 4 = 5 + (2 + 4); (5 \times 2) \times 4 = 5 \times (2 \times 4)$