A toddler has 40 blocks, of which 12 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?

Answer 1

To use the GCF and the Distributive Property of multiplication over addition, the toddler should find the greatest common factor (GCF) of the number of blue and pink blocks, and then divide this quantity evenly among each group.

The GCF of 12 and 28 is 4.

So, the toddler should sort the blocks into groups such that each group has 4 blue blocks and 4 pink blocks.

To find how many groups the toddler needs to make, we can divide the total number of blocks by the number of blocks per group:

40 blocks / (4 blue blocks + 4 pink blocks) = 40 blocks / 8 blocks = 5 groups.

Therefore, the toddler should sort the blocks into 5 groups, with each group having 4 blue blocks and 4 pink blocks.