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)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the number of groups, we need to find the greatest common factor of 52 and 42.

The prime factors of 52 are 2, 2, 13.
The prime factors of 42 are 2, 3, 7.

The common factors between the two numbers are 2.

Therefore, Sven made 2 groups.

To find the number of items in each group, we need to divide the total number of items by the number of groups.

For notebooks: 52 / 2 = 26 notebooks per group.
For binders: 42 / 2 = 21 binders per group.

Using the Distributive Property of Multiplication over Addition, we can write the answer as:

Number of groups: 2
Number of notebooks per group: 26 (2 x 13)
Number of binders per group: 21 (2 x 7)

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find out how many groups Sven displayed, we need to determine the common factor of the number of notebooks and binders he has.

The factors of 52 are: 1, 2, 4, 13, 26, 52.
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.

From the factors listed above, the common factor is 2.

Using the Distributive Property of Multiplication over Addition, we can represent the number of groups as:
52 notebooks + 42 binders = (2 notebooks + 2 binders) * x groups.

Since the common factor is 2, Sven displayed 2 groups, with each group containing 2 notebooks and 2 binders.