Question
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?
Simone did not use the correct factors for 24 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 correct operations in the equation.
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?
Simone did not use the correct factors for 24 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 correct operations in the equation.
Answers
GPT-4o mini
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 8, but when she factored the expression, she incorrectly used the factors of 24 and 56 to represent them as 8(4 + 7) instead of correctly distributing based on their actual GCF. The correct equation based on GCF would be to factor out 8 and represent both 24 and 56 correctly. The correct expression should be \( 8(3 + 7) \) instead of \( 8(4 + 7) \).
The greatest common factor (GCF) of 24 and 56 is 8, but when she factored the expression, she incorrectly used the factors of 24 and 56 to represent them as 8(4 + 7) instead of correctly distributing based on their actual GCF. The correct equation based on GCF would be to factor out 8 and represent both 24 and 56 correctly. The correct expression should be \( 8(3 + 7) \) instead of \( 8(4 + 7) \).