Part A
The number of members in the equal-size groups will be the Greatest Common Divisor of the numbers 20 and 25. That number is 5. There are several ways to find this number. One way is to look at the prime factors of 20 and 25:
20 = 2*2*5
25 = 5*5
The largest factor common to both is 5.
There will be 5 students in each group.
Part B
The number of groups is the number of students divided by the size of the group.
There will be 20/5 = 4 groups of sixth graders.
There will be 25/5 = 5 groups of seventh graders.
Partitioning means to find the dividing point between two points.
This is done by prorating the difference in x- and y-coordinates, and adding to the first.
We will take the first point (from A to B) as A(16,8).
The difference is B-A, i.e.
(1,3)-(16,8) = (-15,-5)
2/5 of the difference is (2/5)*(-15,-5) = (-6,-2)
Add the difference to the first coordinates (point A) gives
Point of division = (16,8)+(-6,-2) = (16-6, 8-2) = (10,6)
Ok
the sets are
natural numbers (or counting numbers), this is like 1,2,3,4,5 etc
whole numbers, this is including 0, so 0,1,2,3,4,5,6 etc
integers, this includes the previoius set and negatives, so -3,-2,-1,0,1,2,3,4,5 etc
rational numbers, this is the set of numbers that can be written in form a/b where b≠0, so all integers can be written like this, like example -3=-3/1, so -7/9 belongs here
-7/9 goes in the rational set
240 miles/ 8 miles is not a rate if im not mistaken if im wrong someone correct me
Given the equation -4x+y=16, we can solve for y with the following operation:
Since -4x has negative sing, it passes to the other side with the sign changed. Therefore, y=4x+16