Maths problem on fraction and ratio

[Swt]

Question
In a school 2/3 of the students study a language.
Of those who study a language 2/5 study french.
Find the ratio of those who study french to students who do not study french. Give the answer in its simplest form.

Heres the issue have tried
2/5:2/3
6/15:10/15
6:10
3:5 wont accept no matter 3:5 or 5:3

Tried doing it on a whole school basis taking the 2/5 from the 2/3 and adding the 1/3 on to include the whole school incase that was the issue, but the computer keeps saying answer wrong.
Just want to know if its the computer or im misreading it somehow. Please help

 

[MarkFL]

Hello, and welcome to FMH!

Can you find the fraction of the students who study French, which is 2/5 of 2/3? From there you can obtain the correct ratio.

 

[Swt]

Take french = 2/5 × 2/3= 4/15
Dont take french would therefore be 11/15
So would the ratio be
4/15:11/15
= 4:11?
I did that it still said the answer was wrong

 

[Dr.Peterson]

Your work would be correct if 2/5 of the students studied French, and 2/3 do not (though that would make no sense!).

What it says is that 2/5 of the 2/3 who study a language, study French. That is entirely different. It is your misreading, not the computer, that is the problem.

Once you find the correct fraction who study French, you can use that to find the fraction who do not, and work from there.

 

[HallsofIvy]

One way: imagine that there are 300 students in the school. 2/3 of the students. (2/3)(300)= 200, study a language. Of those, 2/5, so (2/5)(200)= 80, study French. The other 300- 80= 220 students do not study French. The ratio of students who study French to those who do not is 80 to 220 which can be reduced to 8 to 22 and then 4 to 11.

Notice that, because everything is in terms of "ratios", the original number does not matter. though choosing a number that is divisible by both "3" and "5" makes the arithmetic simpler. If we had taken the school to have 15 students (the smallest number divisible by both 3 and 5) we would have said (2/3)(15)= 10 students take a language and that (2/5)(10)= 4 study French. The other 15- 4 = 11 students do not study French. So the ratio of student who study French to those who do not is (Ta Da) 4 to 11. Now whether you machine will expect "4 to 11" or "4:11" or 4/11. I cannot say.

 

[firemath]

Your work would be correct if 2/5 of the students studied French, and 2/3 do not (though that would make no sense!).

What it says is that 2/5 of the 2/3 who study a language, study French. That is entirely different. It is your misreading, not the computer, that is the problem.

Once you find the correct fraction who study French, you can use that to find the fraction who do not, and work from there.

Complex fractions, I presume?

 

[Swt]

Such a silly mistake. Thanks for your help. Is there a way to delete this thread or close it now I have sorted the problem?

 

[Dr.Peterson]

Complex fractions, I presume?

I wouldn't quite call it that; but the OP's method for the last step amounts to that (in the form of ratios of fractions). I'd use a very different-looking method, but it's equivalent.

The first part, of course, is just multiplication of fractions.