Which of the following expressions could you rewrite using the Associative Property?
Responses
(5⋅8)+3
(9⋅5)⋅(8⋅3)
(9⋅5)+8+3
(5+8)⋅3
(9⋅5)⋅(8⋅3)
Which of the following expressions could you rewrite using the Associative Property?
The expression (9⋅5)⋅(8⋅3) can be rewritten using the Associative Property.
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
(5⋅8)+3
left parenthesis 5 times 8 right parenthesis plus 3
(9⋅5)⋅(8⋅3)
You can rewrite the expression (5+8)⋅3 using the Associative Property.
Which of the following correctly demonstrates the Associative Property of Addition?(1 point)
Responses
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
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+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
x⋅(y+z)=(x⋅y)+z
a b or c or d
The correct option that demonstrates the Associative Property of Addition is:
(x+y)+z+r = x+(y+z)+r
This equation shows that the grouping of the numbers (x+y), (y+z), and (x+(y+z)) doesn't affect the sum.
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
The correct option that demonstrates the Associative Property of Multiplication is:
(3⋅5)⋅2 = 3⋅(5⋅2)
This equation shows that the grouping of the numbers (3⋅5), (5⋅2), and (3⋅(5⋅2)) doesn't affect the product.
To determine which of the following expressions can be rewritten using the Associative Property, let's first understand what the Associative Property is.
The Associative Property states that the way in which numbers are grouped in an addition or multiplication expression does not affect the final result. In other words, we can change the grouping of the numbers without changing the sum or product.
Now let's examine the given expressions and determine which ones can be rewritten using the Associative Property:
1. (5⋅8)+3
In this expression, the numbers 5 and 8 are multiplied first, and then the result is added to 3. The expression cannot be rewritten using the Associative Property because the original grouping is necessary to determine the correct answer.
2. (9⋅5)⋅(8⋅3)
In this expression, the numbers 9 and 5 are multiplied first, and then the product is multiplied by 8 and 3. The expression can be rewritten using the Associative Property by changing the grouping of the numbers. We can group 5 and 8 together, and 9 and 3 together:
((9⋅5)⋅8)⋅3
By doing this, we are changing the grouping of the numbers without changing the final product.
3. (9⋅5)+8+3
In this expression, the numbers 9 and 5 are multiplied first, and then the product is added to 8 and 3. The expression cannot be rewritten using the Associative Property because the original grouping is necessary to determine the correct sum.
4. (5+8)⋅3
In this expression, the numbers 5 and 8 are added first, and then the sum is multiplied by 3. The expression can be rewritten using the Associative Property by changing the grouping of the numbers. We can group 5 and 3 together, and 8 and 3 together:
(5+(8⋅3))
By doing this, we are changing the grouping of the numbers without changing the final product.
Therefore, the expressions that can be rewritten using the Associative Property are:
- (9⋅5)⋅(8⋅3)
- (5+8)⋅3