Question

There are 12 girls and 15 boys in a class. The teacher wants to make reading groups with the same number of girls and the same number of boys in each group. What is the greatest number of reading groups that can be made?

Answer 1

3 groups of 4 girls and 5 boys

Explanation:

What this question is asking of you is what is the greatest common divisor of 12 and 15. Or, what is the biggest number that divides both 12 and 15.

in order to find this we have to split each number into it's prime components.

for 12 they are 2,2 and 3 (`2*2*3 =12`)
and for 15 they are 3 and 5 (`3*5=15`)

Out of those two groups (2,2,3) and (3,5) the only thing in common is 3, so 3 is the greatest common divisor. That tells us that the greatest number of groups that can exist and have the same number of girls and the same number of boys for each group is 3.

Now to find out how many girls and boys there are going to be in each group we divide the totals by 3, so:
`12/3=4` girls per group, and

`15/3=5` boys per group.

(just as a thought exercise, if there were 16 boys, the divisors would have been (2,2,3) and (2,2,2,2), leaving us with 4 groups [`2*2`] of 3 girls [12/4] and 4 boys [16/4] )

Answer 2

3

Explanation:

Consider the ratio in the format `("girls")/("boys") ->12/15`

You can not have parts of a person so we need the least number of pupils that we can have in this ratio.

`("girls")/("boys") ->(12-:3)/(15-:3) = 4/5`

As 5 is a prime number we can not go any smaller.

If we have 4 girls and 5 boys it gives a total of `4+5=9` in the smallest possible group.

It is known that 3 groups of 9 gives 27 pupils. 27 pupils is all the class.

So the greatest number of groups is 3