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 1(16+20) 1 left parenthesis 16 plus 20 right parenthesis 4(4+5) 4 left parenthesis 4 plus 5 right parenthesis 2(8+10) 2 left parenthesis 8 plus 10 right parenthesis 4(4×5)

Answer 1

To solve this problem, we need to determine how the toddler can sort the blocks into groups that contain both colors in equal numbers, using the GCF (Greatest Common Factor) and the Distributive Property of multiplication over addition.

First, we should find the GCF of the number of blue blocks (16) and pink blocks (20).

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 is 4.

So, the toddler can group the blocks into 4 groups. Now we can distribute the blue and pink blocks into these groups.

• Each group should receive an equal number of blue and pink blocks.
• Since there are 16 blue blocks total, dividing by 4 groups gives us 4 blue blocks per group.
• Since there are 20 pink blocks total, dividing by 4 groups gives us 5 pink blocks per group.

We can express this using the distributive property as follows:

Total blocks sorted would be represented as: \[ 4(4 + 5) \]

This indicates that there are 4 groups, with each group containing 4 blue blocks and 5 pink blocks.

Therefore, the best response is: 4(4 + 5).