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)
To rewrite the addition problem so that the numbers left in the parentheses have no common factor except 1, we need to factor out the greatest common factor from the numbers 48 and 36. The GCF of 48 and 36 is 12.
So, by applying the distributive property, we can rewrite (48 + 36) as 12(4 + 3).
Therefore, the equivalent expression that has numbers in the parentheses whose only common factor is 1 is C. 12(4 + 3).
To rewrite the addition problem using the distributive property, we need to find an equivalent expression where the numbers in the parentheses have no common factor except 1.
Let's examine the options:
A. 4(12 + 9): In this case, the numbers 12 and 9 have a common factor of 3, so this option is not correct.
B. 2(24 + 18): The numbers 24 and 18 have a common factor of 6, so this option is not correct.
C. 12(4 + 3): The numbers 4 and 3 have no common factor except 1, so this option is correct.
D. 36(12 + 1): The numbers 12 and 1 have a common factor of 1, so this option is not correct.
Therefore, the correct equivalent expression that has numbers in the parentheses whose only common factor is 1 is C. 12(4 + 3).
To rewrite the addition problem shown using the distributive property, we need to factor out the greatest common factor (GCF) of the numbers inside the parentheses.
In this case, the GCF of 48 and 36 is 12. We can rewrite the original expression as:
(48 + 36) = 12 * (4 + 3)
Now, let's check each option to find the equivalent expression with numbers in the parentheses whose only common factor is 1.
A. 4(12 + 9)
The numbers inside the parentheses have a common factor of 3 (12 and 9 are both divisible by 3), which means this option is not correct.
B. 2(24 + 18)
The numbers inside the parentheses have a common factor of 6 (24 and 18 are both divisible by 6), so this option is not correct either.
C. 12(4 + 3)
The numbers inside the parentheses have no common factor except 1, so this option is a possible answer.
D. 36(12 + 1)
The numbers inside the parentheses have a common factor of 12 (12 and 1 are both divisible by 12), so this option is not correct.
Therefore, the correct answer is:
C. 12(4 + 3)