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?
To solve this problem, we need to find the greatest common factor (GCF) of the number of blue blocks and the number of pink blocks. The GCF of 16 and 20 is 4.
Next, we need to divide the total number of blocks by the GCF to find the number of groups. The total number of blocks is 36, and the GCF is 4. Therefore, the number of groups is 36 / 4 = 9.
Now, we need to divide the number of blue blocks and pink blocks by the number of groups to find the number of blocks in each group. The number of blue blocks is 16, and the number of pink blocks is 20. Dividing by 9, we get:
Number of blue blocks in each group = 16 / 9 = 1.77 (rounded to 2)
Number of pink blocks in each group = 20 / 9 = 2.22 (rounded to 2)
Since we cannot have fractions of blocks, we will round the numbers down to the nearest whole number. Therefore, each group should have 2 blue blocks and 2 pink blocks.
To sort the blocks using the GCF and the Distributive Property of multiplication over addition, we can represent each group as a multiplication of the GCF with the sum of the number of blue and pink blocks. Since each group has 2 blue blocks and 2 pink blocks, we can say:
Group 1: 4 blocks (2 blue + 2 pink)
Group 2: 4 blocks (2 blue + 2 pink)
Group 3: 4 blocks (2 blue + 2 pink)
Group 4: 4 blocks (2 blue + 2 pink)
Group 5: 4 blocks (2 blue + 2 pink)
Group 6: 4 blocks (2 blue + 2 pink)
Group 7: 4 blocks (2 blue + 2 pink)
Group 8: 4 blocks (2 blue + 2 pink)
Group 9: 4 blocks (2 blue + 2 pink)
So, the toddler should sort the blocks into 9 groups, with each group having 2 blue blocks and 2 pink blocks.