The Distributive Property Quick Check
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Question
Philip is sorting acorns he collected. He has 92 acorns: 66 still have their tops, 26 do not. Philip wants to sort the acorns into groups with the same number of acorns, including some with and without tops. He wants each group to have an equal number of acorns with tops and an equal number of acorns without tops. Which answer best shows how Philip can represent how he should sort the acorns?(1 point)
Responses
1(66+26)
1 left parenthesis 66 plus 26 right parenthesis
24(3+1)
24 left parenthesis 3 plus 1 right parenthesis
2(33+13)
2 left parenthesis 33 plus 13 right parenthesis
6(11+4)
6 left parenthesis 11 plus 4 right parenthesis
To represent how Philip should sort the acorns, we need to find a multiplication expression that represents the number of groups and the number of acorns in each group.
Looking at the options:
1. 1(66+26)
2. 24(3+1)
3. 2(33+13)
4. 6(11+4)
We can eliminate options 1, 2, and 4 because they do not represent equal numbers of acorns with tops and without tops.
Option 3, 2(33+13), represents 2 groups, where each group has 33 acorns with tops and 13 acorns without tops. Therefore, option 3 best shows how Philip should sort the acorns.
To answer this question, we need to determine the number of acorns with tops and the number of acorns without tops.
Given that Philip has a total of 92 acorns, we know that the number of acorns with tops plus the number of acorns without tops should be equal to 92.
The possible combinations we can consider are as follows:
1. Option 1: 1(66+26)
This represents 1 group where the number of acorns with tops is 66 and the number of acorns without tops is 26.
2. Option 2: 24(3+1)
This represents 24 groups where the number of acorns with tops is 3 and the number of acorns without tops is 1.
3. Option 3: 2(33+13)
This represents 2 groups where the number of acorns with tops is 33 and the number of acorns without tops is 13.
4. Option 4: 6(11+4)
This represents 6 groups where the number of acorns with tops is 11 and the number of acorns without tops is 4.
Now, we need to determine which option satisfies Philip's requirement of having each group with an equal number of acorns with tops and an equal number of acorns without tops.
Looking at the options, only Option 1 represents a group with equal numbers of acorns with tops and without tops (66 and 26 respectively).
Therefore, the correct answer is Option 1: 1(66+26).