Simone applied the distributive property using the greatest common factor to determine the expression that is equivalent to 24+56

Question

. Her work is shown below.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56

24+56=8(4+7)

What statement best describes Simone's error?

(1 point)
Responses

Simone did not use the correct factors for 56 in the equation.
Simone did not use the correct factors for 56 in the equation.

Simone did not use the greatest common factor in the equation.
Simone did not use the greatest common factor in the equation.

Simone did not use the correct operations in the equation.
Simone did not use the correct operations in the equation.

Simone did not use the correct factors for 24 in the equation.

Answer 1

The correct response is:

Simone did not use the greatest common factor in the equation.

Simone's error lies in her choice of the factor (8) that she used to simplify the expression. The greatest common factor (GCF) of 24 and 56 is actually 8 (since both numbers can be divided by 8 evenly), but her reasoning presents an incorrect interpretation of applying the distributive property related to the factors involved. Therefore, while she correctly uses the GCF in the sense that any common factor could potentially work to factor the expression, her breakdown of the original equation in conjunction with the addition doesn't convincingly demonstrate a proper application of the distributive property.

Answer 2

wrong

Answer 3

I apologize for the error in my previous response. Let's analyze the situation again carefully.

Simone has the expression \( 24 + 56 \) and factored it as \( 8(4 + 7) \).

The greatest common factor of 24 and 56 is indeed 8, but let's break down how Simone reached her equation:

• She factored \( 24 \) as \( 8 \times 3 \) and \( 56 \) as \( 8 \times 7 \).
• Therefore, she could correctly rewrite the expression as \( 8(3 + 7) \), which would yield \( 8(10) = 80 \).
• However, she incorrectly used the factors of 24 and 56 in the equation by saying \( 8(4 + 7) \), which doesn't reflect their proper relationship.

Given this understanding, the better response is:

Simone did not use the correct factors for 24 in the equation.

This reflects that while she started with the right idea, the addition of \( 4 + 7 \) does not correspond correctly to how those numbers factor back to 24 and 56. Thank you for your patience, and I'm sorry for the confusion!