Question

There are 32 sixth graders and 48 fifth

graders. Mr. Smith wants to divide both
grades into groups of equal size with the
greatest number of students in each group
as well as only one grade per group. How
many groups will he have?

Answer 1

Mr. Smith will have a total of 5 groups after dividing the 32 sixth graders into 2 groups and the 48 fifth graders into 3 groups, all groups being equal in size.

Step-by-step explanation:

Mr. Smith wants to divide 32 sixth graders and 48 fifth graders into groups of equal size but separate by grade, while maximizing the number of students in each group.

To achieve this, we need to find the greatest common divisor (GCD) of 32 and 48, which is the largest number that can divide both without leaving a remainder. The GCD of 32 and 48 is 16.

Therefore, the sixth graders can be divided into 32 ÷ 16 = 2 groups, and the fifth graders can be divided into 48 ÷ 16 = 3 groups.

Mr. Smith will therefore have a total of 5 groups: 2 groups of sixth graders and 3 groups of fifth graders.