Which of the following demonstrates the Associative Property of Multiplication?(1 point)
Responses
(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)
left parenthesis 3 times 5 right parenthesis times 2 equals 3 times left parenthesis 5 times 2 right parenthesis
(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 times 5 right parenthesis times 2 equals 3 times left parenthesis 5 times 2 right parenthesis
Use the Associative Property to determine which expression is correctly simplified.(1 point)
Responses
−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
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 times negative 2 minus 6 y
−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)
−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
According to the Associative Property, which expression is equivalent to 30m+(21m−53)+(18−2m)?(1 point)
Responses
(49m−53)+16
left parenthesis 49 m minus 53 right parenthesis plus 16
(30m+21m)+(18−2m)
left parenthesis 30 m plus 21 m right parenthesis plus left parenthesis 18 minus 2 m right parenthesis
53m−35
53 m minus 35
51m+(−53+18)−2m
(30m+21m)+(18−2m)
left parenthesis 30 m plus 21 m right parenthesis plus left parenthesis 18 minus 2 m right parenthesis
The expression (3⋅5)⋅2=3⋅(5⋅2) demonstrates the Associative Property of Multiplication.
The demonstration of the Associative Property of Multiplication can be found by examining the options given.
In the Associative Property of Multiplication, the grouping of numbers does not change the final result. This property allows us to change the grouping of numbers without affecting the product.
Let's analyze the options:
1. (3+5)⋅2=3+(5⋅2)
This is an example of the Distributive Property, not the Associative Property. It involves multiplying a sum by a number.
2. (3⋅5)⋅2=(3⋅5)⋅2
This equation states that a product of two numbers, (3⋅5), multiplied by 2 is equal to the same product, (3⋅5), multiplied by 2. This is an example of the Reflexive Property, not the Associative Property.
3. (3⋅5)⋅2=3⋅(5⋅2)
This option shows that the grouping of multiplication can be changed without affecting the final result. The product of 3⋅5 (15) is multiplied by 2 in the first expression, while in the second expression, the product of 5⋅2 (10) is multiplied by 3. As the order of multiplication can be changed while keeping the final result the same, this is an example of the Associative Property of Multiplication.
4. (3⋅5)+2=(3+5)⋅2
This is an example of the Distributive Property, not the Associative Property. It involves multiplying a sum by a number.
Therefore, the correct answer that demonstrates the Associative Property of Multiplication is option 3: (3⋅5)⋅2=3⋅(5⋅2).