Which of the following expressions could you rewrite using the Associative Property?(1 point)
Responses
(9⋅5)⋅(8⋅3)
left parenthesis 9 times 5 right parenthesis times left parenthesis 8 times 3 right parenthesis
(5+8)⋅3
left parenthesis 5 plus 8 right parenthesis times 3
(9⋅5)+8+3
left parenthesis 9 times 5 right parenthesis plus 8 plus 3
(5⋅8)+3
left parenthesis 5 times 8 right parenthesis plus 3
Which of the following correctly demonstrates the Associative Property of Addition?
x⋅(y+z)=(x⋅y)+z
m⋅(x⋅y)=(m⋅x)⋅y
(x+y)+z+r=x+(y+z)+r
y−(x+1)=(y−x)+1
The correct expression that demonstrates the Associative Property of Addition is:
(x+y)+z+r=x+(y+z)+r
Which of the following demonstrates the Associative Property of Multiplication?(1 point)
Responses
(3⋅5)+2=(3+5)⋅2
left parenthesis 3 times 5 right parenthesis plus 2 equals left parenthesis 3 plus 5 right parenthesis times 2
(3+5)⋅2=3+(5⋅2)
left parenthesis 3 plus 5 right parenthesis times 2 equals 3 plus left parenthesis 5 times 2 right parenthesis
(3⋅5)⋅2=(3⋅5)⋅2
left parenthesis 3 times 5 right parenthesis times 2 equals left parenthesis 3 times 5 right parenthesis times 2
(3⋅5)⋅2=3⋅(5⋅2)
The correct expression that demonstrates the Associative Property of Multiplication is:
(3⋅5)⋅2=3⋅(5⋅2)
Use the Associative Property to determine which expression is correctly simplified.(1 point)
Responses
−3⋅(4x⋅−2)⋅−6y=18−8x
negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals 18 minus 8 x
−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)(−2⋅−6y)
negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals left parenthesis negative 3 times 4 x right parenthesis left parenthesis negative 2 times negative 6 y right parenthesis
−3⋅(4x⋅−2)⋅−6y=−7xy
negative 3 times left parenthesis 4 x times negative 2 right parenthesis times negative 6 y equals negative 7 x y
−3⋅(4x⋅−2)⋅−6y=(−3⋅4x)⋅−2−6y
The correct simplified expression using the Associative Property is:
−3⋅(4x⋅−2)⋅−6y=−7xy
According to the Associative Property, which expression is equivalent to 30m+(21m−53)+(18−2m)?(1 point)
Responses
51m+(−53+18)−2m
51 m plus left parenthesis negative 53 plus 18 right parenthesis minus 2 m
53m−35
53 m minus 35
(30m+21m)+(18−2m)
left parenthesis 30 m plus 21 m right parenthesis plus left parenthesis 18 minus 2 m right parenthesis
(49m−53)+16
According to the Associative Property, the expression that is equivalent to 30m+(21m−53)+(18−2m) is:
(30m+21m)+(18−2m)
To determine which of the expressions can be rewritten using the Associative Property, we need to understand what the Associative Property is.
The Associative Property states that for addition or multiplication, the grouping of numbers can be rearranged without changing the result.
Let's consider the expressions:
1. (9⋅5)⋅(8⋅3)
To rewrite this using the Associative Property, we can rearrange the grouping of numbers:
(9⋅5)⋅(8⋅3) = 9⋅(5⋅8)⋅3
2. (5+8)⋅3
The expression is already in a form where parentheses are used to group numbers, so there is no need to rearrange it. Hence, it can't be rewritten using the Associative Property.
3. (9⋅5)+8+3
This expression has addition operations, but the Associative Property only applies to addition or multiplication operations. Thus, we can't rewrite it using the Associative Property.
4. (5⋅8)+3
The expression is also already in a form where parentheses are used to group numbers, so there is no need to rearrange it. Hence, it can't be rewritten using the Associative Property.
In conclusion, the expression that can be rewritten using the Associative Property is (9⋅5)⋅(8⋅3).