Multiple Choice Question
Byron wants to use the distributive property to rewrite the addition problem shown so that the numbers left in the parentheses have no common factor except 1.
(48 + 36)
Which is an equivalent expression that has numbers in the parentheses whose only common factor is 1?
A.
4(12 + 9)
B.
2(24 + 18)
C.
12(4 + 3)
D.
36(12 + 1)
A. 4(12 + 9)
To rewrite the addition problem using the distributive property, we need to find a factor that both 48 and 36 have in common, and remove it from the parentheses.
Let's examine the options:
A. 4(12 + 9)
The common factor of 48 and 36 is 4. However, in this expression, both 12 and 9 have a common factor of 3, so it is not the correct choice.
B. 2(24 + 18)
The common factor of 48 and 36 is 12. In this expression, there are no common factors between 24 and 18, so it is a potential candidate.
C. 12(4 + 3)
The common factor of 48 and 36 is 12. In this expression, both 4 and 3 have a common factor of 1, so it is a potential candidate.
D. 36(12 + 1)
The common factor of 48 and 36 is 12. However, in this expression, both 12 and 1 have a common factor of 1, so it is not the correct choice.
Therefore, the correct answer is either option B or option C. Both options have numbers in the parentheses whose only common factor is 1.
To rewrite the expression (48 + 36) using the distributive property so that the numbers in the parentheses have no common factor except 1, we need to find the greatest common factor (GCF) of 48 and 36.
The GCF of 48 and 36 is 12.
Now let's go through each answer choice and see which one satisfies the condition.
A. 4(12 + 9)
The GCF of 12 and 9 is 3, which is not equal to 1. Therefore, option A is incorrect.
B. 2(24 + 18)
The GCF of 24 and 18 is 6, which is not equal to 1. Therefore, option B is incorrect.
C. 12(4 + 3)
The GCF of 4 and 3 is 1, which satisfies the condition. Therefore, option C is correct.
D. 36(12 + 1)
The GCF of 12 and 1 is 1, which satisfies the condition. Therefore, option D is correct.
So, the equivalent expression that has numbers in the parentheses whose only common factor is 1 is either option C or option D.