If you are adding up a group of numbers, and you break them up into smaller groups and add these up separately getting sub-totals, and then you add up the sub-totals, you will get exactly the same answer (assuming that you haven't made an error) as if you just added the numbers up all at once. In other words, you can associate any numbers on the list with any other numbers by putting them together, and the addition still works and still gives the same answer. Here's an example:
1+2+3+4+5 = 15. That's all at once. Now in sub-groups: 1+2+3 = 6. And 4+5 = 9. And 6+9 = 15. We still get 15, in either case.
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The associative law of addition refers to the fact that numbers can be grouped in different combinations and the answer will still be the same.
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Commutative Law: a + b = b + a Associative Law: (a + b) + c = a + (b + c)
The associative law holds for all numbers. There are operations that it may not hold for, but that is an entirely different matter.
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there are 3 laws of arithmetic. These are Associative law, Distributive Law and Cummutative law.
For any three numbers a, b, and c:a + b = b + a (commutative law)(a + b) + c = a + (b + c) (associative law)Both the commutative and associative laws are also valid for multiplication.a x (b + c) = (a x b) + (a x c) (distributive law)For any three numbers a, b, and c:a + b = b + a (commutative law)(a + b) + c = a + (b + c) (associative law)Both the commutative and associative laws are also valid for multiplication.a x (b + c) = (a x b) + (a x c) (distributive law)For any three numbers a, b, and c:a + b = b + a (commutative law)(a + b) + c = a + (b + c) (associative law)Both the commutative and associative laws are also valid for multiplication.a x (b + c) = (a x b) + (a x c) (distributive law)For any three numbers a, b, and c:a + b = b + a (commutative law)(a + b) + c = a + (b + c) (associative law)Both the commutative and associative laws are also valid for multiplication.a x (b + c) = (a x b) + (a x c) (distributive law)
The associative law states that the order in which elements are grouped does not affect the outcome of an operation. In mathematics, this law is commonly used in addition and multiplication. For example, (a + b) + c is equal to a + (b + c), and (a * b) * c is equal to a * (b * c).
Any pair can added first (Only applies for addition)
(1 + 2) + 3 = 1 + (2 + 3)
Both union and intersection are commutative, as well as associative.
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