Which of the following expressions could you rewrite using the Associative Property?(1 point)

Question

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 plus 8 plus 3

(9⋅5)⋅(8⋅3)

Answer 1

The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. This property can only be applied to expressions where numbers are either all being added or all being multiplied.

Let's analyze each of the expressions you've provided:

1. (5⋅8) + 3: This involves multiplication and addition. You cannot apply the Associative Property here because there are different operations involved.

2. (5+8)⋅3: This expression is a multiplication of a sum. You cannot apply the Associative Property to this expression as it involves both addition and multiplication.

3. (9⋅5) + 8 + 3: This expression consists of a multiplication followed by additions. The Associative Property can be applied here to regroup the additions, for example: (9⋅5) + (8 + 3). However, it is not applicable to the multiplication part since it's intermixed with addition.

4. (9⋅5)⋅(8⋅3): This involves only multiplication. You can apply the Associative Property here. For example, you could regroup it as ((9⋅5)⋅8)⋅3 or (9⋅(5⋅8))⋅3, or any other combination.

The expression that could be rewritten using the Associative Property is:

(9⋅5)⋅(8⋅3)

Answer 2

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

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

Answer 3

To correctly demonstrate the Associative Property of Addition, the expression must show that when you group numbers differently in addition, the result remains the same. The Associative Property of Addition is expressed as:

\[ (a + b) + c = a + (b + c) \]

Now, let’s evaluate the options provided:

1. (x + y) + z + r = x + (y + z) + r: This expression illustrates the Associative Property of Addition correctly because it shows how the grouping of x, y, and z changes while keeping r outside the grouping, but doesn't specify any changes that affect r.

2. x⋅(y + z) = (x⋅y) + z: This expression does not apply to the Associative Property of Addition, but refers to multiplication and addition, making it incorrect.

3. y − (x + 1) = (y − x) + 1: This expression does not demonstrate the Associative Property of Addition. Instead, it involves subtraction, so it is incorrect.

4. m⋅(x⋅y) = (m⋅x)⋅y: This expression demonstrates the Associative Property of Multiplication, not Addition, which makes it incorrect.

The option that correctly demonstrates the Associative Property of Addition is:

(x + y) + z + r = x + (y + z) + r.

Answer 4

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 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

Answer 5

To demonstrate the Associative Property of Multiplication, we must show that the grouping of numbers being multiplied can change without affecting the product. The Associative Property of Multiplication can be expressed as:

\[ (a \cdot b) \cdot c = a \cdot (b \cdot c) \]

Now, let's evaluate the options provided:

1. (3 + 5) ⋅ 2 = 3 + (5 ⋅ 2): This expression involves both addition and multiplication but does not illustrate the Associative Property of Multiplication. It’s incorrect.

2. (3 ⋅ 5) ⋅ 2 = 3 ⋅ (5 ⋅ 2): This expression correctly demonstrates the Associative Property of Multiplication by showing that when multiplying (3 ⋅ 5) by 2 or multiplying 3 by (5 ⋅ 2), the result remains the same.

3. (3 ⋅ 5) + 2 = (3 + 5) ⋅ 2: This expression mixes multiplication and addition, so it does not demonstrate the Associative Property of Multiplication. It’s incorrect.

4. (3 ⋅ 5) ⋅ 2 = (3 ⋅ 5) ⋅ 2: This is simply a repetition and does not demonstrate any property, so it is also incorrect.

The option that correctly demonstrates the Associative Property of Multiplication is:

(3 ⋅ 5) ⋅ 2 = 3 ⋅ (5 ⋅ 2).