Spin is making a school supply display spin has 52 notebooks and 42 binders spin wants to group the supplies in the display so that they are equal number of supplies in each group if we know that spin puts the same number of notebooks and the same number of binders in 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 determine the number of groups Spin can create where there is an equal number of notebooks and binders in each group, we need to find the greatest common divisor (GCD) of 52 (number of notebooks) and 42 (number of binders). The GCD will tell us the largest number by which we can divide both quantities to have equal groups without any leftovers.
Let's find the factors of 52 and 42:
Factors of 52: 1, 2, 4, 13, 26, 52
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The common factors are 1 and 2, and the greatest common factor is 2.
Thus, Spin can make 2 groups, with an equal number of notebooks and binders in each group. To find out how many of each supply he will place in each group, we divide the number of notebooks and the number of binders by 2.
Number of notebooks per group: 52 notebooks / 2 groups = 26 notebooks per group
Number of binders per group: 42 binders / 2 groups = 21 binders per group
Using the distributive property of multiplication over addition, we can represent the total number of supplies per group as:
Number of supplies per group = Number of notebooks per group + Number of binders per group
= 26 notebooks/group + 21 binders/group
= 2 groups * (26 notebooks/group + 21 binders/group)
This equation shows that for each of the two groups, there are 26 notebooks and 21 binders, and it demonstrates the distribution of equal numbers of notebooks and binders across the two separate groups.