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Number Theory and Fractions Unit Test

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?

A. [tex]$2(8+10)$[/tex]
B. [tex]$4(4+5)$[/tex]
C. [tex]$4(4 \times 5)$[/tex]
D. [tex]$1(16+20)$[/tex]



Answer :

GinnyAnswer
To determine the best way to sort the blocks so that each group has an equal number of blue and pink blocks, we need to find the greatest common factor (GCF) of the number of blue blocks (16) and the number of pink blocks (20). This GCF will allow us to divide the blocks into the specified groups.

1. Find the GCF of 16 and 20:

By systematically identifying the greatest common factor, we find that the GCF of 16 and 20 is 4.

2. Dividing each color by the GCF:

To create equal groups:
- For blue blocks: [tex]\( \frac{16}{4} = 4 \)[/tex]
- For pink blocks: [tex]\( \frac{20}{4} = 5 \)[/tex]

3. Using the Distributive Property of multiplication over addition:

After determining how many of each color will be in a group, we can express the total distribution using the Distributive Property:
- We have 4 groups of (4 blue blocks + 5 pink blocks).

Therefore, the correct way to express the sorting is:
[tex]\[ 4(4 + 5) \][/tex]

So, the best answer is:
[tex]\[ 4(4 + 5) \][/tex]

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