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)
The answer that best shows how the toddler should sort the blocks using the GCF and the Distributive Property of multiplication over addition is 2(6+14).
To sort the blocks so that each group has both colors of blocks and an equal number of blue and pink blocks, the toddler can use the Greatest Common Factor (GCF) and the Distributive Property of multiplication over addition.
The GCF of 12 and 28 is 4. This means that the toddler needs to make groups of 4 blocks with an equal number of blue and pink blocks.
Using the Distributive Property of multiplication over addition, the toddler can express the number of blue blocks as 3x4 and the number of pink blocks as 7x4. This means there are 3 groups of 4 blue blocks and 7 groups of 4 pink blocks.
Therefore, the answer that best shows how the toddler should sort the blocks is 4(3x7).
To find the best way to sort the blocks, we need to find the greatest common factor (GCF) of the number of blue and pink blocks.
The GCF of 12 and 28 is 4. This means that the toddler should sort the blocks into groups of 4, as each group will have an equal number of blue and pink blocks.
Next, we can use the distributive property of multiplication over addition to represent the number of blue and pink blocks in each group.
For each group of 4 blocks, there will be 3 blue blocks and 1 pink block. This can be represented as 4(3 + 1).
Therefore, the correct answer is 4(3+1).