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Properties of Whole Numbers - Associativity Property of Whole Numbers

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Associative Property of Whole Numbers:

The two whole numbers are said to be associative if the result remains the same even if we change the grouping of the numbers.

1. Associative Property of Addition:

The addition is associative for whole numbers as their sum remains the same even if we change the grouping of the numbers.

(2 + 3) + 4 = 5 + 4 = 9
2 + (3 + 4) = 2 + 7 = 9

i.e., (2 + 3) + 4 = 2 + (3 + 4)
In both cases, we get 9.

The addition is associative for whole numbers.

2. Associative Property of multiplication:

Multiplication is associative for whole numbers as their product remains the same even if we change the grouping of the numbers.

(6 × 5) × 3 = 30 × 3 = 90
6 × (5 × 3) = 6 × 15 = 90.

i.e., (6 × 5) × 3 = 6 × (5 × 3)
In both cases, we get 90.

Multiplication is associative for whole numbers.

3. Associative Property of Subtraction:

Subtraction is not associative for whole numbers as their difference may change if we change the grouping of the numbers.

8 – (6 – 2) ≠ (8 – 6) – 2

8 - (4) ≠ (2) – 2

4 ≠ 0

Subtraction is not associative for whole numbers.

4. Associative Property of Division:

The division is not associative for whole numbers as their result may change if we change the grouping of the numbers.

81 ÷ 3 ≠ 8 ÷ 1

27 ≠ 8

The division is not associative for whole numbers.

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