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what is the difference between commutative and symmetric properties

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Q: What is the difference between the commutative and symmetric properties?
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What is the difference between the commutative property and associative property?

In the case of addition: Commutative property: a + b = b + a Associative property: (a + b) + c = a + (b + c) Note that (1) the commutative property involves two numbers; the associative property involves three; and (2) the commutative property changes the order of the operands; the associative property doesn't. Repeatedly applying the two properties allow you to rearrange an addition that involves several numbers in any order.


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What is the difference between the commutative property and the associative property?

Commutative: a + b = b + a a × b = b × a Associative: (a + b) + c = a + (b + c) (a × b) × c = a × (b × c) Commutative states that the sum or product remains the same no matter the order of the factors. Associative states that the sum or product remains the same no matter the grouping of the factors.


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Commutative means that the order can be changed without affecting the answer. For example, multiplication is commutative but division is not. 2 x 4 = 8 and 4 x 2 = 8 (commutative) 2 / 4 = 1/2 but 4 / 2 = 2 (not commutative) Associative means that the order that two operations is completed can be changed without affecting the answer. (2 x 4) x 3 = 2 x (4 x 3) - (associative)


How can you tell the difference between the associative commutative distributive and the identity properties?

The associative property refers to grouping numbers, which allows you to regroup numbers without changing the answer. 2(1x) = (2x1)xThe commutative property refers to changing the order of numbers without changing the answer. 4+1 = 1+4The distributive property refers to distribution of multiplication over addition. a x (b + c) = a x b + a x c