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 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 . 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 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) .

Answer 1

To find out how many groups Sven can make with an equal number of notebooks and binders in each group, we first need to determine the greatest common divisor (GCD) of the amount of notebooks (52) and binders (42).

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

This means Sven can create 2 groups.

2. Distributing the items:
   • For notebooks: \( \frac{52}{2} = 26 \)
   • For binders: \( \frac{42}{2} = 21 \)

Thus, Sven puts 26 notebooks and 21 binders into each group.

3. Using the Distributive Property: To represent the situation using the Distributive Property of Multiplication over Addition, we can express the total items in each group as follows:

\[ 2(26 + 21) \]

This means that in each of the 2 groups, 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).