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Fractions: Approach to solving THIS type of question
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Author:  g00d_dad [ Mon Jun 03, 2019 10:07 am ]
Post subject:  Fractions: Approach to solving THIS type of question

Please, can someone help me find an approach to solving the below question:

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X has 6 numbers: 1, 2, 4, 5, 6, 7.

Arrange the numbers to make a true fractions statement as shown below:

Image

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Many thanks

Author:  Surferfish [ Mon Jun 03, 2019 11:05 am ]
Post subject:  Re: Fractions: Approach to solving THIS type of question

Just by trying out different variations I got:

52/4 = 7 6/1

I don't know if there's a more systematic way to get the correct answer though.

Author:  solimum [ Mon Jun 03, 2019 12:49 pm ]
Post subject:  Re: Fractions: Approach to solving THIS type of question

That doesn't seem to work surferfish - 52/4 is 13, I think the idea is for the RHS to be a mixed number (I can see now that yours could be read as that but it's not very "tidy" )

Can't see a quick route to another solution - will experiment! The two denominators need to be multiples which must mean 2 & 4 if neither of them is 1

Author:  Tinkers [ Mon Jun 03, 2019 12:54 pm ]
Post subject:  Re: Fractions: Approach to solving THIS type of question

Given how fractions work, my first thought is the the demoninator in the both should either be the same or one needs to be a multiple of the other so that would be my starting point, in this case likely to be 2 and 4 (although any of them and 1 could work in theory but I suspect unlikely).

Author:  solimum [ Mon Jun 03, 2019 1:00 pm ]
Post subject:  Re: Fractions: Approach to solving THIS type of question

Got it! 6 is also a multiple of 2, so....

45/6 = 7 1/2

Author:  Surferfish [ Mon Jun 03, 2019 1:16 pm ]
Post subject:  Re: Fractions: Approach to solving THIS type of question

solimum wrote:
Got it! 6 is also a multiple of 2, so....

45/6 = 7 1/2


Yes well done, I think this is the answer they were looking for.

I think my solution is also mathematically correct but agree that "six oneths", or any denominator of "1", is probably not what they were thinking of.

Author:  g00d_dad [ Mon Jun 03, 2019 2:07 pm ]
Post subject:  Re: Fractions: Approach to solving THIS type of question

Quote:
I think this is the answer they were looking for.


Thanks all for the answers so far. It would be great if you could also go through the thought process that you used. I feel that "hit and trial" method could take a long time for some combinations.

May be there is an approach in which you combine the numbers in certain sequences to get to multiples/fractions faster, instead of trying out various combinations randomly.

Author:  ToadMum [ Mon Jun 03, 2019 2:58 pm ]
Post subject:  Re: Fractions: Approach to solving THIS type of question

g00d_dad wrote:
Quote:
I think this is the answer they were looking for.


Thanks all for the answers so far. It would be great if you could also go through the thought process that you used. I feel that "hit and trial" method could take a long time for some combinations.

May be there is an approach in which you combine the numbers in certain sequences to get to multiples/fractions faster, instead of trying out various combinations randomly.


Where does the question come from? Is there no explanation of the solutions there?

Author:  g00d_dad [ Mon Jun 03, 2019 3:20 pm ]
Post subject:  Re: Fractions: Approach to solving THIS type of question

It is from Schofield and Sims Fractions Book #5.
https://www.schofieldandsims.co.uk/prod ... k-5-year-5

This is the only type of question in that book that was puzzling, and I don't want to buy the answer book for 10£ just for this one question. Also, I am not even sure if there is going to be a method in there or just straight forward answer.


Please, can someone (from experience) comment on the quality of questions in S&S books as compared to other books? My daughter finds them a bit on the harder side. She does score consistently around 24-26 out of 28 but takes more time than usual.

Author:  solimum [ Mon Jun 03, 2019 4:43 pm ]
Post subject:  Re: Fractions: Approach to solving THIS type of question

As Tinkers and I both mentioned, the key is to spotting that the denominators (ie the numbers at the "bottom" of the fraction) must be multiples of eachother: the simplest conversion of a top-heavy (or improper) fraction to a mixed number would have the same denominators on both sides, then further simplification to get a new denominator on the RHS

And then it is just a matter of trial and error. Trying the various top-heavy "quarters" and looking at remainders (eg 21/4, 27/4 ...). No magic tricks, but an understanding of how fractions, and simplifying fractions "works" (which eludes many of the pupils I deal with, but I digress)

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