Question

Sven is making a school supply display. Sven has 52 notebooks and 42 binders. Sven wants to group the supplies in the display so that there are an equal number of supplies in each group. If we know that Sven puts the same number of notebooks and the same number of binders into each group, how many groups did he display and how many of each item went into each group? Represent your answer using the Distributive Property of Multiplication over Addition.(1 point)
Responses

Sven made 2 groups. He put 26 notebooks and 21 binders into each group. Using the Distributive Property, the answer can be shown as 2(26×21)
.
Sven made 2 groups. He put 26 notebooks and 21 binders into each group. Using the Distributive Property, the answer can be shown as 2 left parenthesis 26 times 21 right parenthesis .

Sven made 2 groups. He put 26 notebooks and 21 binders into each group. Using the Distributive Property, the answer can be shown as 2(26+21)
.
Sven made 2 groups. He put 26 notebooks and 21 binders into each group. Using the Distributive Property, the answer can be shown as 2 left parenthesis 26 plus 21 right parenthesis .

Sven made 1 group. He put all 52 notebooks and all 42 binders into that one group. Using the Distributive Property, the answer can be shown as 1(52×42)
.
Sven made 1 group. He put all 52 notebooks and all 42 binders into that one group. Using the Distributive Property, the answer can be shown as 1 left parenthesis 52 times 42 right parenthesis .

Sven made 1 group. He put all 52 notebooks and all 42 binders into that one group. Using the Distributive Property, the answer can be shown as 1(52+42)
.
Sven made 1 group. He put all 52 notebooks and all 42 binders into that one group. Using the Distributive Property, the answer can be shown as 1 left parenthesis 52 plus 42 right parenthesis .
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Answer 1

To determine how Sven can group his notebooks and binders evenly, we first need to find the greatest common divisor (GCD) of 52 and 42.

1. **Finding the GCD:**
- The factors of 52 are: 1, 2, 4, 13, 26, 52
- The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42
- The common factors are: 1, 2
- The greatest common divisor is 2.

2. **Calculating the number of groups and items per group:**
- Since the GCD is 2, Sven can make 2 groups.
- Each group will have:
- Notebooks per group: 52 notebooks ÷ 2 groups = 26 notebooks
- Binders per group: 42 binders ÷ 2 groups = 21 binders

3. **Using the Distributive Property:**
- The total supplies in each group can be represented as:
\[
2(26 + 21)
\]
This shows that there are 2 groups, and in each group, there are 26 notebooks and 21 binders.

Therefore, the correct response is:
**Sven made 2 groups. He put 26 notebooks and 21 binders into each group. Using the Distributive Property, the answer can be shown as 2(26 + 21).**