Question
Which of the following expressions could you rewrite using the Associative Property?(1 point)
Responses
(5⋅8)+3
left parenthesis 5 times 8 right parenthesis plus 3
(5+8)⋅3
left parenthesis 5 plus 8 right parenthesis times 3
(9⋅5)⋅(8⋅3)
left parenthesis 9 times 5 right parenthesis times left parenthesis 8 times 3 right parenthesis
(9⋅5)+8+3
Responses
(5⋅8)+3
left parenthesis 5 times 8 right parenthesis plus 3
(5+8)⋅3
left parenthesis 5 plus 8 right parenthesis times 3
(9⋅5)⋅(8⋅3)
left parenthesis 9 times 5 right parenthesis times left parenthesis 8 times 3 right parenthesis
(9⋅5)+8+3
Answers
Answer
Which of the following correctly demonstrates the Associative Property of Addition?(1 point)
Responses
x⋅(y+z)=(x⋅y)+z
x times left parenthesis y plus z right parenthesis equals left parenthesis x times y right parenthesis plus z
y−(x+1)=(y−x)+1
y minus left parenthesis x plus 1 right parenthesis equals left parenthesis y minus x right parenthesis plus 1
m⋅(x⋅y)=(m⋅x)⋅y
m times left parenthesis x times y right parenthesis equals left parenthesis m times x right parenthesis times y
(x+y)+z+r=x+(y+z)+r
Responses
x⋅(y+z)=(x⋅y)+z
x times left parenthesis y plus z right parenthesis equals left parenthesis x times y right parenthesis plus z
y−(x+1)=(y−x)+1
y minus left parenthesis x plus 1 right parenthesis equals left parenthesis y minus x right parenthesis plus 1
m⋅(x⋅y)=(m⋅x)⋅y
m times left parenthesis x times y right parenthesis equals left parenthesis m times x right parenthesis times y
(x+y)+z+r=x+(y+z)+r
Answered by
GPT-4o mini
The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. This means that when you have multiple numbers being added or multiplied, you can change the grouping without affecting the outcome.
Out of the given expressions, the one that can be rewritten using the Associative Property is:
**(9⋅5)⋅(8⋅3)**
This expression involves multiplication and can be regrouped (e.g., you could compute (9⋅8)⋅5⋅3, and it would yield the same product).
The other expressions either involve addition separately or are structured in a way (like addition applied to a single number) that does not involve regrouping in a context where the Associative Property applies.
So the correct answer is:
**(9⋅5)⋅(8⋅3)**
Out of the given expressions, the one that can be rewritten using the Associative Property is:
**(9⋅5)⋅(8⋅3)**
This expression involves multiplication and can be regrouped (e.g., you could compute (9⋅8)⋅5⋅3, and it would yield the same product).
The other expressions either involve addition separately or are structured in a way (like addition applied to a single number) that does not involve regrouping in a context where the Associative Property applies.
So the correct answer is:
**(9⋅5)⋅(8⋅3)**
Answered by
GPT-4o mini
The Associative Property of Addition states that when three or more numbers are added, the way in which the numbers are grouped does not affect the sum. In other words, for any numbers \( a \), \( b \), and \( c \):
\[
(a + b) + c = a + (b + c)
\]
Among the provided responses, the expression that correctly demonstrates the Associative Property of Addition is:
**(x+y)+z+r=x+(y+z)+r**
This expression shows that regardless of how we group the terms \( x \), \( y \), \( z \), and \( r \) in addition, the overall sum remains the same.
The other options incorrectly describe properties of addition or multiplication or are unrelated (like subtraction).
So the correct answer is:
**(x+y)+z+r=x+(y+z)+r**
\[
(a + b) + c = a + (b + c)
\]
Among the provided responses, the expression that correctly demonstrates the Associative Property of Addition is:
**(x+y)+z+r=x+(y+z)+r**
This expression shows that regardless of how we group the terms \( x \), \( y \), \( z \), and \( r \) in addition, the overall sum remains the same.
The other options incorrectly describe properties of addition or multiplication or are unrelated (like subtraction).
So the correct answer is:
**(x+y)+z+r=x+(y+z)+r**
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