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What is the difference between a commutative property and an associative property in math?
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 are the associative and commutative properties alike and different?
The associative and commutative are properties of operations defined on mathematical structures. Both properties are concerned with the order - of operators or operands. According to the ASSOCIATIVE property, the order in which the operation is carried out does not matter. Symbolically, (a + b) + c = a + (b + c) and so, without ambiguity, either can be written as a + b + c. According to the COMMUTATIVE property the order in which the addition is carried out does not matter. In symbolic terms, a + b = b + a For real numbers, both addition and multiplication are associative and commutative while subtraction and division are not. There are many mathematical structures in which a binary operation is not commutative - for example matrix multiplication.
Does order matter in multiplication?
No. Multiplication is commutative so the order of the multiplicands does not matter. Multiplication is associative so the order in which the operations are carried out does not matter.
What is the commutative property and What is the associative property?
Binary operations can have commutative and associative properties. Binary operations are essentially rules that tell you how to combine two elements to make a third (they need not all be different). Addition, subtraction, multiplication and division are the more common ones. Exponentiation, taking logarithms, etc are less well known. Commmutativity implies that a * b = b * a Associativity implies that (a * b) * c = a * (b * c) and so either can be written as a * b * c Addition and multiplication of numbers are associative as well as commutative whereas division is neither. However, multiplication of matrices is not commutative.
What is the properties under multiplication?
commutative, associative, distributive
