A toddler has 36 blocks, of which 16 are blue and 20 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)

To determine how the toddler should sort the blocks 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 blocks (16) and the number of pink blocks (20).

1. Finding the GCF:

   • The factors of 16 are: 1, 2, 4, 8, 16
   • The factors of 20 are: 1, 2, 4, 5, 10, 20
   • The greatest common factor of 16 and 20 is 4.

2. Dividing the blocks:

   • If the toddler wants to create groups with an equal number of blue blocks and pink blocks, and has determined that the GCF is 4, we can determine how many blocks of each color would be in each group:
     • For blue blocks: 16 / 4 = 4 blue blocks per group.
     • For pink blocks: 20 / 4 = 5 pink blocks per group.

3. Using the Distributive Property:

   • The toddler can express the grouping using the distributive property, where each group will consist of 4 blue blocks and 5 pink blocks. This can be represented as: \[ 4 \times (4 + 5) \] This represents 4 groups, each containing (4 blue blocks + 5 pink blocks).

Thus, the best answer that shows how the toddler should sort the blocks is:

4(4 + 5).