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

Avenged7Fold · 29 Nov 2018 at 14:01

mmj_uk said:
How are people reading the OP's question as numbers of goals? he has written them as fractions not "3 out of 5" and "13 out of 20".

If you didn't interpret them as actual goal numbers, then you couldn't answer the question as you don't know how many goals were scored in the first half compared to the second.

Minusorange · 29 Nov 2018 at 14:01

Avenged7Fold said:
For those saying that the answer is 19/40, can you tell me how many total goals were scored and how many total goals did the top 6 score?

Total goals scored doesn't matter when it's asking for the fraction of the total goals

I see it as 3/5 of total goals scored in first half and 7/20 of total goals scored in second half and it wants the total fraction of total goals scored in both halves which results in 19/40

Tuppy_Glossop · 29 Nov 2018 at 14:03

mmj_uk said:
How are people reading the OP's question as numbers of goals? he has written them as fractions not "3 out of 5" and "13 out of 20".

They look like fractions but could easily be a shorthand version of the latter. OP may be a lazy transcriber/typist. Or the original question may have been bobbins.

Avenged7Fold · 29 Nov 2018 at 14:03

Minusorange said:
Total goals scored doesn't matter when it's asking for the fraction of the total goals

I see it as 3/5 of total goals scored in first half and 7/20 of total goals scored in second half and it wants the total fraction of total goals scored in both halves which results in 19/40

It does because if less goals were scored in the first compared to the second, you can't treat the fractions as equal because it is asking you for a fraction for the TOTAL.

If you do it your way you are assuming the same number of goals were scored for the first half as the second.

Try and put some context to your working out and see if it works.

mmj_uk · 29 Nov 2018 at 14:04

Avenged7Fold said:
If you didn't interpret them as actual goal numbers, then you couldn't answer the question as you don't know how many goals were scored in the first half compared to the second.

You're given 2 fractions and are being asked to give the answer as a fraction, you don't need to know the numbers of goals involved.

Avenged7Fold · 29 Nov 2018 at 14:05

mmj_uk said:
You're given 2 fractions and are being asked to give the answer as a fraction, you don't need to know the numbers involved.

It is not asking you to add the fractions, it is asking you for the percentage scored in total by the top 6

dl8860 · 29 Nov 2018 at 14:05

Minusorange said:
Total goals scored doesn't matter when it's asking for the fraction of the total goals

I see it as 3/5 of total goals scored in first half and 7/20 of total goals scored in second half and it wants the total fraction of total goals scored in both halves which results in 19/40

19/40 (0.475) will be the correct answer if and only if the same number of goals are scored in each half, so in your own way you are right. But you aren't accounting for the fact that the number of goals scored in each half is undefined. Check the maths

adolf hamster · 29 Nov 2018 at 14:07

Avenged7Fold said:
Oh god, this thread haha

3 goals out of 5

7 goals out of 20

That makes 10 goals scored by the top 6 out of 25 goals.

10/25 = 40%

For those saying that the answer is 19/40, can you tell me how many total goals were scored and how many total goals did the top 6 score?

except say the numbers were first half they got 12 goals out of 20 (or 3/5 of the goals if you simplify it down), second half they get 7 goals out of 20, that gives you 19 goals out of 40 (47.5%)

but then if you have 24 goals out of 40 in the first half, and still 7 out of 20 in the second that gives 31 out of 60 goals (52%)

or to go even further, lets say it's 48 goals out of 80 in the first and same old 7 out of 20 in the second that's 55 out of 100 (55%)

as mentioned without knowing how many total goals were scored in the first and second halves it's unsolvable, all the fractions tell you is a percentage of goal scoring in the first and second halves but it doesn't translate to overall success unless we can assume the denominator is an empirical number of goals scored.

mmj_uk · 29 Nov 2018 at 14:14

Avenged7Fold said:
It is not asking you to add the fractions, it is asking you for the percentage scored in total by the top 6

Where does it ask for a percentage? you can work out the percentage from the fraction but that's not what it's asking for.

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

It's like saying if I own 1/2 (half) of a car park and someone else owns 1/4 (quarter) of the same car park then what fraction of the car park is owned by the both of us. It doesn't matter how many car parking spaces are involved.

Minusorange · 29 Nov 2018 at 14:15

dl8860 said:
19/40 (0.475) will be the correct answer if and only if the same number of goals are scored in each half, so in your own way you are right. But you aren't accounting for the fact that the number of goals scored in each half is undefined. Check the maths

How can I be both right & wrong at the same time :cool:

Avenged7Fold · 29 Nov 2018 at 14:16

mmj_uk said:
Where does it ask for a percentage? you can work out the percentage from the fraction but that's not what it's asking for.

It's like saying if I own 1/2 (half) of a car park and someone else owns 1/4 (quarter) of the same car park then what fraction of the car park is own by the both of us. It doesn't matter how many car parking spaces are involved.

Fact is that it does not say that the number of goals in the first half is the same as the second. So it isn't the case of they own a quarter of the same carpark

If you own half a car park and the other owns a quarter of another car park which is twice the size of your small carpark, then what is the total space owned by both of you out of the total carpark space?

The point made is that you cannot add fractions without knowing the value of the denomination. The question only really makes sense if you take it as goal values. There are a few posts here proving you can get a variety of answers using your logic of addition.

Put it this way, the way i worked it out originally assumes them to be the actual goal values but they still work as fractions.

Tuppy_Glossop · 29 Nov 2018 at 14:16

Double post, exsqueeze me.

touch · 29 Nov 2018 at 14:17

Minusorange said:
How can I be both right & wrong at the same time

He didn't say you were right. He said you were right "in your own way". (You're wrong.)

Minusorange · 29 Nov 2018 at 14:19

Tuppy_Glossop said:
Fuzzy sets.

I still think I'm 1/1 right because it's asking for fraction of total goals and not ratio of total goals for top 6 vs bottom 14

touch said:
He didn't say you were right. He said you were right "in your own way". (You're wrong.)

But the math is right - https://www.varsitytutors.com/hotmath/hotmath_help/topics/adding-fractions-unlike-denominators I'm just following the rules

dowie · 29 Nov 2018 at 14:20

Amleto said:
Jesus H Christ this thread is sad.

Some people here must think that 1/2 + 1/2 = 2/4. What's 2/4? Oh yeah, it's 1/2. People here are literally saying 1/2 + 1/2 = 1/2 without realising.

Yup that is painful.

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

touch · 29 Nov 2018 at 14:21

Minusorange said:
But the math is right - https://www.varsitytutors.com/hotmath/hotmath_help/topics/adding-fractions-unlike-denominators I'm just following the rules

Yep, you have added the fractions together correctly. However, that's not the way to solve the question.

Minusorange · 29 Nov 2018 at 14:24

touch said:
Yep, you have added the fractions together correctly. However, that's not the way to solve the question.

It's the ONLY way to solve the question as it is posed otherwise it is unsolvable without knowing the ratio of goals 1st to 2nd half so you have to assume both halves are equal to each other

Avenged7Fold · 29 Nov 2018 at 14:24

Minusorange said:
I still think I'm 1/1 right because it's asking for fraction of total goals and not ratio of total goals for top 6 vs bottom 14

But the math is right - https://www.varsitytutors.com/hotmath/hotmath_help/topics/adding-fractions-unlike-denominators I'm just following the rules

You are assuming the answer is obtained by adding the fractions together.

dowie · 29 Nov 2018 at 14:28

Minusorange said:
It's the ONLY way to solve the question as it is posed otherwise it is unsolvable without knowing the ratio of goals 1st to 2nd half so you have to assume both halves are equal to each other

Nope, there is no reason to make the assumption that an equal number of goals were scored in each half.

If we read 3/5 as meaning there were literally 5 goals in the first half and 13/20 as meaning there were literally 20 goals in the second half then we can solve it directly and get 2/5.

Otherwise we can only solve it as far as stating what I provided above: x(3/5) + (1-x)(1-13/20) where x = the portion of goals scored in the first half relative to the second.

There is no reason to assume that portion is 1/2.

inogen · 29 Nov 2018 at 14:33

To be fair the question is formed in such a way to make you think you should be looking at the 3/5 and 13/20 as fractions.

This is more of problem solving analysis question than a maths one. The maths is easy. Easier than using the right maths.

You literally cannot answer the question by treating them as fractions.

Also, as I said earlier. Although giving the answer of 2/5 is technically correct, it is less precise than 10/25. It's 10 out of the 25 goals. not 2 out of 5 goals. Though it is 2 out of every 5 goals scored.

The question asks for the fraction of the total goals. Which is 10 out of 25. Not 2 out of 5.