A toddler has 36 blocks of which 16 are blue and 20 are pink they want to sort the block 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 toddlers should sort the blocks using the GCF and the distributive property of multiplication over addition A 2(8 + 10) B 1(16 + 20) C 4(4 + 5) D 4(4 x 5)

To solve this problem, we first need to figure out how many groups we can make with equal numbers of blue and pink blocks, according to the given restrictions.

There are 16 blue blocks and 20 pink blocks. To create groups with an equal number of blue and pink blocks, we need to find the greatest common factor (GCF) of these two numbers.

1. The factors of 16 (blue blocks) are: 1, 2, 4, 8, 16
2. The factors of 20 (pink blocks) are: 1, 2, 4, 5, 10, 20

The GCF of 16 and 20 is **4**.

Next, we will divide the total number of each colored block by the GCF to determine how many blocks of each color would be in each group:
- Blue blocks per group: \( \frac{16}{4} = 4 \)
- Pink blocks per group: \( \frac{20}{4} = 5 \)

Thus, we can arrange the blocks into 4 groups, each containing 4 blue blocks and 5 pink blocks.

Now, we can express this using the distributive property:
- The total number of blocks in each group is \( 4 \) blue blocks + \( 5 \) pink blocks = \( 4 + 5 \).
- Since there are 4 groups, this can be expressed as \( 4(4 + 5) \).

Thus, the correct answer that best shows how the toddler should sort the blocks is **C**: \( 4(4 + 5) \).