A toddler has 36 blocks of which 16 are blue and 20 are pink. They want yo 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 shows how the toddler should sort the blocks using the GCF and the distributive property of multiplication over addition?

Question

A toddler has 36 blocks of which 16 are blue and 20 are pink. They want yo 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 shows how the toddler should sort the blocks using the GCF and the distributive property of multiplication over addition?

A 4(4x5)
B 2(8+10)
C. 1(16+20)
D. 4(4+5)

Answer 1

The answer that shows how the toddler should sort the blocks using the GCF and the distributive property of multiplication over addition is:

D. 4(4+5)

Answer 2

To solve this problem, we need to find the greatest common factor (GCF) of the number of blue blocks and pink blocks, and then use the distributive property of multiplication over addition.

Step 1: Find the GCF
The GCF of 16 and 20 is 4.

Step 2: Use the distributive property
We can use the distributive property to divide the blocks into equal groups.

Let's use answer choices A, B, C, and D and apply the GCF and distributive property to each one.

A. 4(4x5)
In this case, we have 4 groups, each with 4x5 blocks.

B. 2(8+10)
In this case, we have 2 groups, each with 8+10 blocks.

C. 1(16+20)
In this case, we have 1 group, with 16+20 blocks.

D. 4(4+5)
In this case, we have 4 groups, each with 4+5 blocks.

Based on the requirement that each group should have an equal number of blue and pink blocks, and that the GCF should be used, the correct answer is option A: 4(4x5).

Answer 3

To solve this problem, we need to find the greatest common factor (GCF) of the numbers 16 and 20. The GCF is the largest number that divides evenly into both numbers.

To find the GCF, we can list the factors of each number and find their common factors:

Factors of 16: 1, 2, 4, 8, 16
Factors of 20: 1, 2, 4, 5, 10, 20

The common factors are 1, 2, and 4. The greatest common factor is 4.

Now, let's use the distributive property of multiplication over addition to divide the blocks into equal groups.

In option A, 4(4x5), we can first calculate what's inside the parentheses: 4x5 = 20. Then multiply the result by 4: 4(20) = 80. This means there would be 80 blocks in total, with 20 blue blocks and 60 pink blocks. So, option A doesn't satisfy the conditions.

In option B, 2(8+10), again, calculate what's inside the parentheses: 8+10 = 18. Then multiply the result by 2: 2(18) = 36. This means there would be 36 blocks in total, with 36 blue blocks and no pink blocks. So, option B doesn't satisfy the conditions.

In option C, 1(16+20), calculate what's inside the parentheses: 16+20 = 36. Then multiply the result by 1: 1(36) = 36. This means there would be 36 blocks in total, with 16 blue blocks and 20 pink blocks. So, option C satisfies the conditions.

Lastly, in option D, 4(4+5), again, calculate what's inside the parentheses: 4+5 = 9. Then multiply the result by 4: 4(9) = 36. This means there would be 36 blocks in total, with 9 blue blocks and 27 pink blocks. So, option D doesn't satisfy the conditions.

Therefore, the correct answer is option C, 1(16+20), which shows that the toddler should sort the blocks by having 16 blue blocks and 20 pink blocks in each group.