Question

A toddler has 40 blocks, of which 12 are blue and 28 are pink. They want to sort the blocks so that each group has both colors of blocks. The toddler also wants each group to have an equal number of blue blocks and an equal number of pink blocks. Which answer best shows how the toddler should sort the blocks using the GCF and the Distributive Property of multiplication over addition?(1 point)

Responses

4(3x7)
4(3x7)

2(6+14)
2(6+14)

3(4+9)
3(4+9)

4(3+7)
4(3+7)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The answer is: 2(6 + 14)

Answer 2

[AI-generated answer — Step-by-Step Bot]

The correct answer is:

2(6+14)

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem using the GCF (Greatest Common Factor) and the Distributive Property of multiplication over addition, we first need to find the GCF of the number of blue and pink blocks, which are 12 and 28 respectively.

The prime factorization of 12 is 2^2 * 3, and the prime factorization of 28 is 2^2 * 7.

To find the GCF, we find the common prime factors and take the smallest power for each common factor. In this case, the common factor is 2 raised to the power of 2, which is 2^2 = 4. Thus, the GCF of 12 and 28 is 4.

Now, we can use the Distributive Property to sort the blocks.

The number of blue blocks, 12, can be expressed as 4 times some number: 4 * (3).

Similarly, the number of pink blocks, 28, can be expressed as 4 times some number: 4 * (7).

So, the answer that best shows how the toddler should sort the blocks using the GCF and the Distributive Property of multiplication over addition is:
4(3 + 7), where 3 represents the number of blue blocks in each group and 7 represents the number of pink blocks in each group.