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. 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 times open paren 52 plus 42 close paren. - no response given 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 times open paren 52 times 42 close paren. - no response given 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 times open paren 26 plus 21 close paren. - no response given 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 solve the problem of how Sven can group his notebooks and binders evenly, we first need to determine the greatest common divisor (GCD) of the numbers of notebooks (52) and binders (42). The GCD will tell us the greatest number of groups Sven can create such that each group contains the same number of notebooks and the same number of binders.

1. Calculate the GCD of 52 and 42:

   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 greatest common factor is 2.

2. Determine the number of notebooks and binders in each group:

   If Sven makes 2 groups, then:

   • The number of notebooks in each group would be \( \frac{52}{2} = 26 \)
   • The number of binders in each group would be \( \frac{42}{2} = 21 \)

3. Represent using the Distributive Property of Multiplication over Addition:

   Sven made 2 groups. He put 26 notebooks and 21 binders into each group. Using the Distributive Property, the answer can be shown as:

   \[ 2(26 + 21) \]

So, the correct response is that Sven made 2 groups with 26 notebooks and 21 binders in each group, represented as \( 2(26 + 21) \).