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?

Question

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.

Answer 2

To find the best way for the toddler to sort the blocks, we can start by finding the greatest common factor (GCF) of 12 and 28.

Step 1: Find the GCF of 12 and 28
- The factors of 12 are 1, 2, 3, 4, 6, and 12.
- The factors of 28 are 1, 2, 4, 7, 14, and 28.
- The greatest common factor of 12 and 28 is 4.

Step 2: Divide the total number of blocks by the GCF
- Since the toddler has a total of 40 blocks, divide 40 by 4.
- 40 ÷ 4 = 10

Step 3: Distribute the blocks evenly among the groups
- Since the GCF is 4, we will create 4 equal groups.
- Each group will have an equal number of blue and pink blocks.

Sorting the blocks using the GCF and the Distributive Property of multiplication over addition:
- There are 12 blue blocks and 28 pink blocks.
- The GCF of 12 and 28 is 4.
- Divide the total number of blocks by the GCF: 40 ÷ 4 = 10.
- Create 4 equal groups: 10 blocks in each group.
- Each group will have 2 blue blocks and 2 pink blocks.

Therefore, the toddler should sort the blocks into 4 equal groups, with each group having 2 blue blocks and 2 pink blocks.

Answer 3

To sort the blocks so that each group has both colors of blocks and an equal number of blue and pink blocks, we can use the Greatest Common Factor (GCF) and the Distributive Property of multiplication over addition.

First, let's find the GCF of 12 and 28, which is 4.

Now, we can imagine dividing each set of blocks into groups of 4, which ensures each group will have an equal number of blue and pink blocks.

For the blue blocks:
12 blocks ÷ 4 (GCF) = 3 groups

For the pink blocks:
28 blocks ÷ 4 (GCF) = 7 groups

So, we have a total of 3 groups of blue blocks and 7 groups of pink blocks.

Next, we use the Distributive Property of multiplication over addition to determine the total number of blocks in each group.

For the blue blocks:
3 groups × 4 (GCF) = 12 blocks per group
So, each group should have 12 blue blocks.

For the pink blocks:
7 groups × 4 (GCF) = 28 blocks per group
Each group should have 28 pink blocks.

Therefore, the toddler should sort the blocks into groups where each group has 12 blue blocks and 28 pink blocks by using the GCF and the Distributive Property of multiplication over addition.