2006-10-02 10:23:59 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The cummutative law says that you can change the order of the operands without changing the result. So 2 + 4 = 4 + 2 and 3*7 = 7*3, because addition and multiplication are commutative.
The associative law says that you can change the grouping of the operands without changing the result. So (2 + 4) + 6 = 2 + (4 + 6) and (3*7)*4 = 3*(7*4), because addition and multiplication are associative.
2006-10-02 10:28:24 · answer #1 · answered by DavidK93 7 · 0⤊ 0⤋
The Associative Law: a + ( b + c ) = ( a + b ) + c When an operation is defined, it is at once clear how two objects are to be combined. But what if we have three objects? If we call these objects a, b, c, and we wish to combine them in the given order, then there are two possibilities: We can first operate on a and b and combine the result with c, or we can combine a with the result of operating first on b and c. Let us take, for example, the operation of addition and the numbers 4, 17, and 2. We may then interpret the expression 4 + 17 + 2 either as (4 + 17) + 2 or as 4 + (17 + 2). In the first case, we get 21 + 2, and in the second case we get 4 + 19. It turns out that in both cases we get the final result 23. The Commutative Law: a + b = b + a The commutative law states that the order in which two objects appear does not affect the result of the operation: operating on a and b always leads to the same result as operating on b and a. Well-known elementary examples of commutative operations are addition and multiplication of numbers. In other domains, we have the examples of logical AND and OR for propositions as well as the union and intersection operations in set theory. But not all operations have this nice property. If the operation is the quotient of two natural numbers m and n, it is certainly not the case that in general, n/m = m/n, so this operation is not commutative. The Distributive Law a • ( b + c ) = a • b + a • c In contrast to the associative and commutative laws, with the distributive law there are always two operations involved. If the two operations are addition “+” and multiplication “•”, then the distributive law of multiplication with respect to addition states that we always have the relationship a • (b + c) = a • b + a • c.
2016-03-17 03:52:22 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Associative Law
2016-10-03 09:22:55 · answer #3 · answered by Anonymous · 0⤊ 0⤋
http://www.britannica.com/eb/article-9361274
2006-10-02 10:34:37 · answer #4 · answered by whatthe 3 · 0⤊ 0⤋