Mathematics Properties: Associative and Commutative, Lecture notes of Mathematics

The associative and commutative properties in mathematics, applicable to both addition and multiplication. The associative property ensures that the order of adding or multiplying numbers does not change the result, while the commutative property allows for interchanging the order of addends or factors without affecting the sum or product. Examples and general rules are provided for each property.

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ASSOCIATIVE PROPERTY:
In mathematics, the associative property holds true for both addition and
multiplication.
Associative property of addition-when adding three numbers, if the order
of the addends remains the same and the addends are regrouped, the sum
of the numbers will remain the same.
Examples: (2 + 4) + 8 = 2 + (4 + 8)
6 + 8 = 2 + 12
14 = 14
General Rule: (a + b) + c = a + (b+ c)
Associative property of multiplication-when multiplying three numbers, if
the order of the factors remains the same and the factors are regrouped,
the product of the number will remain the same.
Examples: 5 (3 * 9) = (5 * 3) * 9
5 * 27 = 15 * 9
135 = 135
General Rule: a (b * c) = (a*b) c
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ASSOCIATIVE PROPERTY:

In mathematics, the associative property holds true for both addition and multiplication.

Associative property of addition-when adding three numbers, if the order of the addends remains the same and the addends are regrouped, the sum of the numbers will remain the same. Examples: (2 + 4) + 8 = 2 + (4 + 8) 6 + 8 = 2 + 12 14 = 14 General Rule: (a + b) + c = a + (b+ c) Associative property of multiplication-when multiplying three numbers, if the order of the factors remains the same and the factors are regrouped, the product of the number will remain the same. Examples: 5 (3 * 9) = (5 * 3) * 9 5 * 27 = 15 * 9 135 = 135 General Rule: a (b * c) = (a*b) c

COMMUTATIVE PROPERTY:

In mathematics, the commutative property holds true for both addition and multiplication.

Commutative property of addition-changing the order of the addends in an addition problem will not affect the sum. Examples: 3 + 4 = 4 + 3 7 = 7 General Rule : a + b = b + a Commutative property of multiplication-changing the order of the factors in a multiplication problem will not affect the product. Examples: (9)(6) = (6)(9) 54 = 54 General Rule: (a)(b) = (b)(a)