Question
Simone applied the distributive property using the greastest common factor to determine the expression that is quicalen to 28+60. Her work is shown below.
Factors of 24: 1,2,4,7,14,28
Factors of 56: 1,2,3,4,5,6,10,15,20,30,60
28+60=4(7+20)
What statement best describes Simone's error?
A. Simone did not use the correct operations in the equation.
B. Simone did not use the greatest common factor in the equation.
C. Simone did not use the correct factors for 60 in the equation.
D. Simone did not use the correct factors for 28 in the equation.
Factors of 24: 1,2,4,7,14,28
Factors of 56: 1,2,3,4,5,6,10,15,20,30,60
28+60=4(7+20)
What statement best describes Simone's error?
A. Simone did not use the correct operations in the equation.
B. Simone did not use the greatest common factor in the equation.
C. Simone did not use the correct factors for 60 in the equation.
D. Simone did not use the correct factors for 28 in the equation.
Answers
GPT-4o mini
The correct answer is **C. Simone did not use the correct factors for 60 in the equation.**
In her expression, Simone factored out 4 from 28 and 60. The correct way to express 28 + 60 using the distributive property with the greatest common factor would involve the actual greatest common factor of both numbers, which is not 4. The correct GCF is actually 4, but when factoring out terms, the way she structured 7 + 20 is incorrect because she didn't correctly represent the sum of the original numbers (28 + 60) relative to their factors.
If we correctly calculate it:
- The greatest common factor (GCF) of 28 and 60 is 4.
- Factoring out 4 gives us: 28 + 60 = 4(7 + 15).
So the factors for 60 are not correct in Simone's work (she mistakenly used 20 instead of 15). Thus, the best statement that describes her error is option C.
In her expression, Simone factored out 4 from 28 and 60. The correct way to express 28 + 60 using the distributive property with the greatest common factor would involve the actual greatest common factor of both numbers, which is not 4. The correct GCF is actually 4, but when factoring out terms, the way she structured 7 + 20 is incorrect because she didn't correctly represent the sum of the original numbers (28 + 60) relative to their factors.
If we correctly calculate it:
- The greatest common factor (GCF) of 28 and 60 is 4.
- Factoring out 4 gives us: 28 + 60 = 4(7 + 15).
So the factors for 60 are not correct in Simone's work (she mistakenly used 20 instead of 15). Thus, the best statement that describes her error is option C.