A toddler has 48 blocks, of which 20 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?

To determine how the toddler can sort the blocks into groups that have an equal number of both blue and pink blocks, we need to find a common number of blocks in each group that allows both colors to be evenly distributed.

The toddler has:

• 20 blue blocks
• 28 pink blocks

To find the largest equal grouping of blue and pink blocks, we need to find the greatest common factor (GCF) of 20 and 28.

The factors of each number are:

• Factors of 20: 1, 2, 4, 5, 10, 20
• Factors of 28: 1, 2, 4, 7, 14, 28

The GCF of 20 and 28 is 4. This means that we can create groups where each group consists of an equal number of blue and pink blocks that can be 4.

Now, we can distribute the blocks:

• For blue blocks: 20 blue blocks / 4 groups = 5 blue blocks per group
• For pink blocks: 28 pink blocks / 4 groups = 7 pink blocks per group

Now we check the options given through the Distributive Property:

1. 3(7+8) = 3 × 15 = 45 (not valid)
2. 4(5+7) = 4 × 12 = 48 (valid, as it matches the total number of blocks)
3. 9(2+3) = 9 × 5 = 45 (not valid)

Based on this analysis, the answer that best shows how the toddler can sort the blocks such that each group has both colors with equal numbers is 4(5+7).

This means that if the toddler makes 4 groups, each group will have 5 blue blocks and 7 pink blocks, achieving the desired sorting of the blocks.