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
To find the number of groups, we can use the Distributive Property of Multiplication over Addition.
First, let's find the greatest common divisor (GCD) of 52 and 42 to determine the maximum number of supplies that can be grouped together. The GCD of 52 and 42 is 2.
Next, let's divide both the number of notebooks and binders by the GCD to find the number of groups we can make.
Number of notebooks = 52 ÷ 2 = 26
Number of binders = 42 ÷ 2 = 21
So, Sven can make 26 groups, with each group containing 26 notebooks and 21 binders.
huh I don't get it.
To find out how many groups Sven displayed and how many of each item went into each group, we need to find the greatest common divisor (GCD) of 52 and 42.
Step 1: Find the prime factorization of 52: 2 x 2 x 13.
Step 2: Find the prime factorization of 42: 2 x 3 x 7.
Step 3: Find the common prime factors: 2.
Step 4: Multiply the common prime factors: 2.
So, the GCD of 52 and 42 is 2.
Next, we divide the total number of each item by the GCD to determine how many items will go into each group.
Number of notebooks in each group = 52 / 2 = 26.
Number of binders in each group = 42 / 2 = 21.
Therefore, Sven displayed 2 groups, and each group had 26 notebooks and 21 binders.