Which of the following expressions could you rewrite using the Associative Property?(1 point)
Responses
(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
(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 times 8 right parenthesis plus 3
Which of the following correctly demonstrates the Associative Property of Addition?(1 point)
Responses
(x+y)+z+r=x+(y+z)+r
left parenthesis x plus y right parenthesis plus z plus r equals x plus left parenthesis y plus z right parenthesis plus r
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
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
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
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 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
(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
The expression that can be rewritten using the Associative Property is (9⋅5)⋅(8⋅3).
To rewrite an expression using the Associative Property, you need to rearrange the grouping of numbers. The Associative Property states that for addition or multiplication, the grouping of numbers can be changed without changing the result.
Let's examine the given expressions:
1. (5+8)⋅3: This expression does not involve any multiplication operations inside parentheses, so the Associative Property does not directly apply. No rewriting is needed.
2. (9⋅5)+8+3: Here, we have addition operations, but no multiplication inside parentheses. So, the Associative Property does not apply here either. No rewriting is needed.
3. (9⋅5)⋅(8⋅3): In this expression, we have multiplication operations inside parentheses. According to the Associative Property, we can rearrange the grouping of numbers, so let's rewrite it using the property:
(9⋅5)⋅(8⋅3) = 9⋅(5⋅8)⋅3
We can group the numbers 5 and 8 together since they are multiplied, and then multiply the result by 9.
4. (5⋅8)+3: Similar to the first expression, this one does not have any multiplication inside parentheses. Therefore, no rewriting is needed using the Associative Property.
So, the only expression that could be rewritten using the Associative Property is (9⋅5)⋅(8⋅3).