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What is the grouping of factors is changed the product remains the same?

Associative Property


Definition of associative property?

Changing the grouping of the factors. The product stays the same.


When the grouping of factors is changed the product stays the same what is this called?

The commutative property of multiplication


What are the propertys of multiplycation?

The properties of multiplication include commutative property (changing the order of factors does not change the product), associative property (changing the grouping of factors does not change the product), distributive property (multiplication distributes over addition), and identity property (multiplying a number by 1 gives the same number).


The property that states that for three or more numbers their sum or product is always the same regardless of their grouping?

The associative property.


What is subtraction commutative or associative?

Subtraction is neither commutative property or association property because commutative property of multiplication is when you change the order of the factors the product stays the same and it isn't associated property because you can change the grouping of the factors the product stays the same you can't do that first attraction it wouldn't work it would be a negative zero.


Is this true or false In arithmetic the grouping of the addends or factors does not affect the sum or product?

True.


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.


Does changing the grouping of factors change the sum?

No, but if you're talking about factors, the result is a product. (a × b) × c = a × (b × c)


What is the associative property for multiplication?

An observation that grouping or associating numbers in differing orders results in the same product during a multiplication operation....


Changing the orders of factors does not change the product?

The Commutative Property of Multiplication states that changing the order of the factors does not change the product


What is a definition for the associative property of multiplication and how you would use it to compute 4 times 25 times 27 mentally?

The addition or multiplication of a set of numbers is the same regardless of how the numbers are grouped. The associative property will involve 3 or more numbers. The parenthesis indicates the terms that are considered one unit.The groupings (Associative Property) are within the parenthesis. Hence, the numbers are 'associated' together. In multiplication, the product is always the same regardless of their grouping. The Associative Property is pretty basic to computational strategies. Remember, the groupings in the brackets are always done first, this is part of the order of operations.When we change the groupings of addends, the sum does not change:(2 + 5) + 4 = 11 or 2 + (5 + 4) = 11(9 + 3) + 4 = 16 or 9 + (3 + 4) = 16Just remember that when the grouping of addends changes, the sum remains the same.Multiplication ExampleWhen we change the groupings of factors, the product does not change:(3 x 2) x 4 = 24 or 3 x (2 x 4) = 24.Just remember that when the grouping of factors changes, the product remains the same.Think Grouping! Changing the grouping of addends does not change the sum, changing the groupings of factors, does not change the product.*** 4x(25x27) = (4x25)x27***