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Which of the following correctly demonstrates the use of the Commutative Property of Multiplication?(1 point)

Responses

11(b+z)=11b+11z
11 left parenthesis b plus z right parenthesis equals 11 b plus 11 z

3(b10+4)=3(4+b10)3
3 left parenthesis b superscript 10 baseline plus 4 right parenthesis equals 3 left parenthesis 4 plus b superscript 10 baseline right parenthesis 3

2(b10+z11)=(b10+z11)⋅2
2 left parenthesis b superscript 10 baseline plus z superscript 11 baseline right parenthesis equals left parenthesis b superscript 10 baseline plus z superscript 11 baseline right parenthesis times 2

z^11⋅2=z^11+2

3 answers

The correct demonstration of the Commutative Property of Multiplication is:

z^11⋅2=z^11+2

However, this statement is actually incorrect because it states that the multiplication of \( z^{11} \) and \( 2 \) equals the addition of \( z^{11} \) and \( 2 \), which is not true.

None of the provided options correctly showcase the Commutative Property of Multiplication in its true form. The Commutative Property states that \( a \cdot b = b \cdot a \). A correct example would illustrate something like \( 2 \cdot 3 = 3 \cdot 2 \).

If you need further clarification or adjustments, please provide more context or additional options.

Use the Commutative Property to determine the missing step in proving the equivalence of 12a+10+a=10+a+12a .

Step 1: [missing]

Step 2: 10+13a=10+13a

Step 3: The expressions are equivalent because they both equal the same value.

(1 point)
Responses

12a+10+a−10=10+a+12a−10
d plus 10 plus a equals 10 plus a plus d

12a+10=10+12a
d plus 10 plus a equals 10 plus a plus d

12a+10+a−a=10+a+12a−a
d plus 10 plus a equals 10 plus a plus d

10+12a+a=10+13a

To use the Commutative Property in this context, we are rearranging the terms of the expression. The Commutative Property states that the order in which two numbers are added (or multiplied) does not affect their sum (or product).

Given that the goal is to show \( 12a + 10 + a = 10 + a + 12a \), the missing step involves rearranging the terms on the left side of the equation.

The correct missing step would be:

10 + 12a + a = 10 + a + 12a

Here's a breakdown of how it fits into the overall proof:

  • Step 1: Rearranging the terms using the Commutative Property: \( 12a + 10 + a \) becomes \( 10 + a + 12a \).
  • Step 2: Combine like terms: \( 10 + 13a = 10 + 13a \).
  • Step 3: Conclude that the expressions are equivalent because they both equal the same value.

So the correct response that fits as the missing step is:

10 + 12a + a = 10 + a + 12a.

Please ensure to select a suitable response from the provided options that matches this explanation.