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 and the number of each item in each group, we need to find the greatest common divisor (GCD) of 52 and 42. The GCD of 52 and 42 is 14.
Using the distributive property of multiplication over addition, we can express the total number of notebooks and binders as a product of the number of groups and the number of each item in each group:
52 notebooks = 14 notebooks/group * number of groups
42 binders = 14 binders/group * number of groups
Since the number of notebooks and binders in each group is the same (14), we can find the number of groups by dividing the total number of notebooks or binders by the number of each item in each group:
52 notebooks / 14 notebooks/group = 4 groups
42 binders / 14 binders/group = 3 groups
Therefore, Sven displayed 4 groups and there were 14 notebooks and 14 binders in each group.