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

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

1. 4(3x7)
2. 2(6+14)
3. 3(4+9)
4. 4(3+7)

Answer 1

The correct answer is 4(3+7).

To distribute the GCF (which is 4) over the sum (3+7), we can multiply 4 by each term inside the parentheses:
4(3+7) = 4(3) + 4(7) = 12 + 28.

So the toddler should sort the blocks as follows:
12 blue blocks and 28 pink blocks.

Answer 2

The answer that best shows how the toddler should sort the blocks using the GCF and the Distributive Property of multiplication over addition is:

3. 3(4+9)

Explanation:
To find the solution, we need to find the greatest common factor (GCF) of the number of blue and pink blocks, which in this case is 4 (the GCF of 12 and 28).

Then, we distribute this GCF of 4 over the addition of the two colors of blocks:
4(3+7) = 4(10) = 40
So, the toddler should sort the blocks into groups of 3 blue and 7 pink blocks, and repeat this grouping 4 times to have each group with an equal number of blue and pink blocks.

Answer 3

To solve this problem using the GCF (Greatest Common Factor) and the Distributive Property of multiplication over addition, we need to find the greatest common factor of the number of blue and pink blocks.

The number of blue blocks is 12, and the number of pink blocks is 28. The GCF of 12 and 28 is 4.

Next, we need to divide the total number of blocks (40) by the GCF (4) to find the number of groups.

40 ÷ 4 = 10

We have 10 groups in total. Now, we need to distribute the blocks equally among these groups.

Since the GCF is 4, each group should have 4 blue blocks and 4 pink blocks.

Therefore, the correct answer would be 4(3+7), which represents distributing 3 groups of 4 blue blocks and 7 groups of 4 pink blocks to achieve the desired sorting.