Find the GCF of the two numbers, and rewrite the sum of the two numbers using the distributive property.
14 + 24
Responses
A 4(10 × 20)4(10 × 20)
B 4(10 + 20)4(10 + 20)
C 2(7 + 12)2(7 + 12)
D 2(7 × 12)
The GCF of 14 and 24 is 2.
Using the distributive property:
14 + 24 = 2*7 + 2*12
= 2(7 + 12)
Therefore, the answer is C: 2(7 + 12)
Choose all that are correct.
Responses
A 45 + 54 = 9(7 + 6)45 + 54 = 9(7 + 6)
B 64 + 24 = 8(8 + 3)64 + 24 = 8(8 + 3)
C 40 + 28 = 4(10 + 7)40 + 28 = 4(10 + 7)
D 24 + 18 = 6(4 + 9)
A: 45 + 54 = 9(7 + 6) is correct.
B: 64 + 24 = 8(8 + 3) is correct.
C: 40 + 28 = 4(10 + 7) is correct.
D: 24 + 18 = 6(4 + 9) is not correct.
The correct way to factor 24 + 18 is:
24 + 18 = 6(4) + 6(3)
= 6(4 + 3)
= 6(7)
So the correct response would be:
D: 24 + 18 = 6(7)
To find the GCF (Greatest Common Factor) of two numbers, you need to determine the largest number that divides evenly into both numbers. In this case, the two numbers are 14 and 24.
Step 1: Find the factors of each number.
- The factors of 14 are 1, 2, 7, and 14.
- The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Step 2: Identify the common factors.
The common factors of 14 and 24 are 1 and 2.
Step 3: Determine the GCF.
Since the GCF is the largest common factor, the GCF of 14 and 24 is 2.
Now, let's rewrite the sum of the two numbers (14 + 24) using the distributive property.
The distributive property states that a(b + c) = ab + ac.
Option A: 4(10 × 20)
This does not represent the sum of 14 and 24 using the distributive property.
Option B: 4(10 + 20)
This does not represent the sum of 14 and 24 using the distributive property.
Option C: 2(7 + 12)
This represents the sum of 14 and 24 using the distributive property: 2(7 + 12) = 2(19) = 38.
Option D: 2(7 × 12)
This does not represent the sum of 14 and 24 using the distributive property.
Therefore, the correct answer is option C: 2(7 + 12).