Question

Question

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)
Responses

4(4+5)
4 left parenthesis 4 plus 5 right parenthesis

4(4×5)
4 left parenthesis 4 times 5 right parenthesis

2(8+10)
2 left parenthesis 8 plus 10 right parenthesis

1(16+20)

Answer 1

To determine how the toddler should sort the blocks, we first need to find the greatest common factor (GCF) of the number of blue blocks (16) and pink blocks (20).

The GCF of 16 and 20 is 4. This means the toddler can create groups with a certain number of blue and pink blocks such that each group has both colors and the same number of each.

If we divide the total number of blue blocks (16) by the GCF (4), we can tell that each group will have 4 blue blocks. Similarly, dividing the total number of pink blocks (20) by the GCF (4) shows that each group will have 5 pink blocks.

Thus, the toddler can form groups of 4 blue and 5 pink blocks.

Given the options, we can express the number of groups in terms of the GCF and the total number of blocks in each group as follows:

• The number of groups will be 4 (since 16 blue blocks / 4 = 4 groups of blue and 20 pink blocks / 5 = 4 groups of pink).
• Therefore, you can express the total number of blocks in each group as 4 blue blocks and 5 pink blocks.

This corresponds to the expression: \[ 4(4 + 5) \]

Thus, the best answer is:

4(4 + 5)