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Associative Property

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Q: What is the grouping of factors is changed the product remains the same?
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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.


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***


What is the definition associative property of multipilication?

The associative property of multiplication states that when multiplying three or more numbers, the grouping of the numbers does not affect the result. In other words, you can change the order in which the numbers are multiplied, and the product will remain the same. For example, (2 × 3) × 4 is equal to 2 × (3 × 4), both resulting in 24.


When the order of numbers being added is changed the sum?

remains the same


What does the graph do when the line y-intercepts is changed?

The lines become parallel to each other providing that the slope remains the same.

Related questions

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.


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***


What does the word associative property of multiplication mean?

It means that if you change the grouping (parentheses) of a multiplication problem, you will still get the same answer. Ex. (3 x 2) x 4 = 24 and 3 x (2 x 4) = 24. You changed the location of the parentheses, but the product always remains 12.


When the total product remains constant the marginal product will be?

Zero


When total product remains constant the marginal product will be?

Zero


If supply shifts to the right and demand remains constant?

When supply shifts to the right and demand remains constant then there will be an excess of product. Prices for the product will fall as well.


What do you call the remains of organisms that are actually changed to rock?

Fossils.


What is the definition associative property of multipilication?

The associative property of multiplication states that when multiplying three or more numbers, the grouping of the numbers does not affect the result. In other words, you can change the order in which the numbers are multiplied, and the product will remain the same. For example, (2 × 3) × 4 is equal to 2 × (3 × 4), both resulting in 24.


When the order of numbers being added is changed the sum?

remains the same


How has love changed over time?

"Love remains the same." ~Gavin Rosdale


If you changed the water to water vapor in a pressure cooker what volume would the water vapor occupy?

If it remains sealed the volume remains the same.


Which physical quantity remains constant when the state is changed?

The melting point and boiling point remain constant when the physical state is changed.