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

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

Simone did not use the correct factors for 24 in the equation.
Simone did not use the correct factors for 24 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 56 in the equation.
Simone did not use the correct factors for 56 in the equation.

3 answers

The correct statement that best describes Simone's error is:

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

The greatest common factor (GCF) of 24 and 56 is actually 8, which she correctly identified and used in factoring the expression. However, when she wrote the equation as \(24 + 56 = 8(4 + 7)\), she separated 24 into \(8 \times 3\) (which is correct) and 56 into \(8 \times 7\) (also correct), but did not actually calculate the left-hand side correctly.

If she had used the GCF properly, she would have factored both 24 and 56 accurately into terms that would lead to the correct equivalent expression. The left side should be clearly shown as \(8(3 + 7)\). So while she initially used the GCF correctly, the way she presented the factoring was misleading regarding her application of the distributive property. Therefore, the answer still points towards her not applying the greatest common factor correctly in the equation.

wrong

I apologize for the confusion in my previous response. Let's re-evaluate the situation.

Simone calculated \(24 + 56\) and factored it as \(8(4 + 7)\). The numbers within the parentheses \(4\) and \(7\) are not the correct terms that correlate to the original numbers \(24\) and \(56\) when factored by their GCF (which is \(8\)). Instead, the correct factoring should yield \(8(3 + 7)\) for \(24\) and \(56\).

The best statement that describes Simone's error is:

Simone did not use the correct operations in the equation.

This is because she incorrectly added the two results of the division by 8 (which should have been the result of factoring out 8 from both expressions). Thank you for your patience, and I appreciate the opportunity to clarify.