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 toddle should sort the blocks using gcf and the distributive property of multiplication over addition.
4(3x7)
2(6+14)
3(4+9)
4(3+7)
The answer that best shows how the toddler should sort the blocks using the GCF (Greatest Common Factor) and the distributive property of multiplication over addition is 4(3 + 7).
The GCF of 12 and 28 is 4. This means that both 12 and 28 are divisible by 4. By dividing both numbers by 4, we can determine that the toddler should make groups of 4 blocks.
So, for the blue blocks, the toddler should make 12/4 = 3 groups, with 3 blue blocks in each group. For the pink blocks, the toddler should make 28/4 = 7 groups, with 7 pink blocks in each group.
Therefore, the toddler should sort the blocks into groups of 3 blue blocks and 7 pink blocks.
To sort the blocks according to the given conditions, the toddler can use the distributive property of multiplication over addition with the greatest common factor (GCF) to determine the equal number of blocks in each group.
The GCF of 12 and 28 is 4.
To distribute the blocks equally, the toddler can use the equation:
GCF (number of groups) x (number of blocks in each group)
Therefore, the correct answer would be:
4(3+7)
This means that the toddler would create 4 groups, with each group having 3 blue blocks and 7 pink blocks. This arrangement would satisfy both the toddler's desire for each group to have both colors of blocks and for each group to have an equal number of blue and pink blocks.
To solve this problem using the greatest common factor (GCF) and the distributive property of multiplication over addition, we need to find the GCF of the number of blue blocks and the number of pink blocks.
First, we determine the GCF of 12 (the number of blue blocks) and 28 (the number of pink blocks). The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 28 are 1, 2, 4, 7, 14, and 28. The highest common factor among these numbers is 4.
Now, we can distribute the 4 to create equal groups. Each group should have an equal number of blue blocks and pink blocks. By dividing the blue and pink blocks by 4, we get:
Blue blocks: 12 ÷ 4 = 3
Pink blocks: 28 ÷ 4 = 7
Therefore, the toddler should sort the blocks using the expression 4(3 + 7), which means multiplying 4 by the sum of 3 and 7. This will result in the toddler having four groups, each having an equal number of blue blocks (3) and an equal number of pink blocks (7).