Can someone help me with a math (fraction) question?

dowie said:
I'm not confused - I've given an answer back here:

https://forums.overclockers.co.uk/posts/32318409/

for some reason Inogen has quoted me a bunch of times to argue that I shouldn't simplify the fraction I've given as my answer
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I assume this.
Assuming 3/5 is the portion of the goals scored in the first half by the top 6 teams then we can't answer as we need to know what portion of goals were scored in the first half relative to the second half. Answers of 19/40 are nonsense.

If we define x to be the portion of goals scored in the first half relative to the second half then our answer is:

x(3/5) + (1-x)(1-13/20)

If x = 1/2 then that does indeed work out to be 19/40 but there is no reason to assume that it is.

Assuming there were 5 goals scored in the first half and 20 in the second half then of course we can answer: (3 + 7)/(5 + 20) = 2/5
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You appear to have realised you can't just use both initial figures and they have no relation to each other. But then you try to force one in with the use of proportion, there is no proportional relationship between the first half and the second half. The 2nd half's number of goals is completely unrelated to the first half.

Lets take your final example of 5 goals in total in the first half and 20 goals in total in the second half.

So 25 goals in total.

How many goals did the top 6 score? 3/5 of 5 = 3. + 13/20 = 13. So a total of 16 goals.

So 16/25. and this can't be rounded down so the final answer is

16/25.

But as we don't know know how many goals were scored in each half which this is why I had to answer all the probable out comes.
 
dowie said:
nope, you're just making up poor analogies now

it is just simplifying a fraction that is all, quite a common thing to do when presenting an answer as a fraction (which is what was requested if you read carefully)
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It doesn't ask for your answer "as a fraction". It says "what fraction". ie "how many".

Like I keep saying, if you insist on giving your answer as a fraction, it's 10/25. Not 2/5 because 2/5 does not answer "how many".
 
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h4rm0ny said:
No. Because he asked for the fraction of the total goals which is unknown.
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The total goals just means when you have combined both of the fractions, one of the fractions is first half goals and the other is second half goals, after you have combined the two fractions together you have a fraction of the total number of goals and not just for each half in isolation.
 
inogen said:
For the second time. I think you'll find as far as the question goes 10 is a fraction of 25.
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10 is wrong.

25 goals is the minimum total number of goals that could possibly have been scored.
The top 6 already scored at least 13 goals in the second half and at least 3 in the first half.

So 16/25 based on the lowest possible score line.
 
To be fair, I don't think the OP knows fractions, hence why it's in brackets ? And why he's asking the question ! And some of you are looking far too deep in to this.
3 out of 5 goals were scored first half and 7 out of 20 in the second.
 
Sasahara said:
10 is wrong.

25 goals is the minimum total number of goals that could possibly have been scored.
The top 6 already scored at least 13 goals in the second half and at least 3 in the first half.

So 16/25 based on the lowest possible score line.
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Read the question again.
 
Sasahara said:
10 is wrong.

25 goals is the minimum total number of goals that could possibly have been scored.
The top 6 already scored at least 13 goals in the second half and at least 3 in the first half.

So 16/25 based on the lowest possible score line.
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13 goals scored in the 2nd half by teams outside the top 6. Not in the top 6. Only 7 scored by top half teams totalling 10 out of the 25 goals.
 
Sasahara said:
You appear to have realised you can't just use both initial figures and they have no relation to each other. But then you try to force one in with the use of proportion, there is no proportional relationship between the first half and the second half. The 2nd half's number of goals is completely unrelated to the first half.
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Eh? I've not forced anything - there is also no relation between the independent matches but we're given various proportions in the question. I was highlighting that we'd need more information (assuming the information has been presented so far as proportions). We could be given total goals, we could be given a proportion as they seem to have presented so far.

Sasahara said:
Lets take your final example of 5 goals in total in the first half and 20 goals in total in the second half.

So 25 goals in total.

How many goals did the top 6 score? 3/5 of 5 = 3. + 13/20 = 13. So a total of 16 goals.

So 16/25. and this can't be rounded down so the final answer is

16/25.
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Nope, 13/20 is the number of goals scored by teams outside the top 6

it is 7/20 for the top 6

so combine the total goals and your answer would be 10/25 = 2/5

this is assuming the information presented isn't proportion of goals but rather the actual number of goals, so literally 3 out of 5 goals

Sasahara said:
But as we don't know know how many goals were scored in each half which this is why I had to answer all the probable out comes.
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Yup, you wrote out various combinations of possible answers, you highlighted the same thing I was highlighting int he first part of my answer.

The point is the question is a bit ambiguous and could be read in a couple of different ways. You could read it to mean a proportion of goals, in which case you can't give a definite answer without further information (like what portion of the goals were scored in the first half or what the tootles are) or you could read it to mean there were literally 5 goals scored in total the first half.

inogen said:
It doesn't say "as a fraction". It says "what fraction".
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So what? The question is asking for a fraction.
 
inogen said:
Yes and the fraction of the total goals is 10.

At no point does the question say "expressed as a fraction".
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10 isn't a fraction, that is the total goals scored by the top 6 teams (based on previous assumptions)

the question is:

"What fraction of the total goals did the top 6 teams score?"

That is asking you to give a fraction.

so 10/25 which can be simplified to 2/5
 
dowie said:
10 isn't a fraction, that is the total goals scored by the top 6 teams (based on previous assumptions)

the question is:

"What fraction of the total goals did the top 6 teams score?"

That is asking you to give a fraction.

so 10/25 which can be simplified to 2/5
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No, that's not asking you to give a fraction there's no fractions in the question. That's asking how many goals did the top 6 score.
 
inogen said:
No, that's not asking you to give a fraction there's no fractions in the question.
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There are fractions in the question - what do you think 3/5 is? and 13/20?

That's asking how many goals did the top 6 score.
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nope, giving the answer "10" as you seem to want to do would be doing that

the question literally just asks you for a fraction, your insistence that the answer has to be 10/25 not 2/5 is just based on conditions you've added yourself
 
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