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An operation is commutative if a change in the order of the numbers does not change the results. This means the numbers can be swapped. Numbers can be added in any order. For example: 4 + 5 = 5 + 4 x + y = y + x Numbers can be multiplied in any order. For example: 5 × 3 = 3 × 5 a × b = b × a Numbers that are subtracted are NOT commutative. For example: 4 - 5 ≠ 5 - 4 x - y ≠ y -x Numbers that are divided are NOT commutative. For example: 4 ÷ 5 ≠ 5 ÷ 4 x ÷ y ≠ y ÷ x An operation is associative if a change in grouping does not change the results. This means the parenthesis (or brackets) can be moved. Numbers that are added can be grouped in any order. For example: (4 + 5) + 6 = 5 + (4 + 6) (x + y) + z = x+ (y + z) Numbers that are multiplied can be grouped in any order. For example: (4 × 5) × 6 = 5 × (4 × 6) (x × y) × z = x × (y × z) Numbers that are subtracted are NOT associative. For example: (4 - 5) - 6 ≠ 4 - (5- 6) (x - y) - z ≠ x - (y- z) Numbers that are divided are NOT associative. For example: (4 ÷ 5) ÷ 6 ≠ 4 ÷ (5÷ 6) (x ÷ y ) ÷ z ≠ x ÷ ( y ÷ z)

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15y ago
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10y ago

Commutative Property

Identity Property

Zero Property

Associative Property

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13y ago

commutative, distributive, associative

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Q: What are the propeties in math?
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