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The commutative property allows for the order of the numbers to be changed in an operation without affecting the answer.
The commutative property applies to both addition and multiplication.
When adding 18 + 2, the sum is 20.
18 + 2 = 20
Even when the terms are reversed, the sum remains 20.
2 + 18 = 20
When multiplying 3 × 5, the product is 15.
3 × 5 = 15
Even when the factors are reversed, the product remains 15.
5 × 3 = 15
The commutative property also applies to the addition of decimals.
Example:
3,2 + 4,39 = 7,59
4,39 + 3,2 = 7,59
The associative property allows for the numbers in an operation to be grouped in different ways using brackets, without changing the final result.
The operation that is placed inside the brackets must be done first.
The associative property applies to both addition and multiplication.
When adding 4 + 2 + 3, the sum is 9.
4 + 2 + 3 = 9
When grouping the first 2 terms of this addition, the sum remains 9.
(4 + 2) + 3 = ?
6 + 3 = ?
6 + 3 = 9
Again, the sum remains the same when grouping the last 2 terms.
4 + (2 + 3) = ?
4 + 5 = ?
4 + 5 = 9
When multiplying 2 × 5 × 4, the product is 40.
2 × 5 × 4 = 40
When grouping the first 2 factors, the product remains 40.
(2 × 5) × 4 = ?
10 × 4 = ?
10 × 4 = 40
Again, the product remains the same when grouping the last 2 factors.
2 × (5 × 4) = ?
2 × 20 = ?
2 × 20 = 40
The associative property also applies to the addition of decimals.
Example:
3,45 + 2,7 + 9,12 = 15,27
(3,45 + 2,7) + 9,12 = 15,27
3,45 + (2,7 + 9,12) = 15,27