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Fraction Mix Up

Discussion in 'Mathematics' started by ERedman, Nov 3, 2011.

  1. I currently tutor a GSCE student who is very able, but writes his fractions upside down.



    If a fraction is given to him as a/b he can carry out all manipulations in the form of fractions, but will often make the error of switching the numerator and denominator over when converting to and from divisions.



    Tonight we were working on a different topic, but when it came to calculating 5 divided by 4, he wrote 4/5.



    Does anyone have any ideas of how I can help him to remember the link with division?



    Thank you.
     
  2. I currently tutor a GSCE student who is very able, but writes his fractions upside down.



    If a fraction is given to him as a/b he can carry out all manipulations in the form of fractions, but will often make the error of switching the numerator and denominator over when converting to and from divisions.



    Tonight we were working on a different topic, but when it came to calculating 5 divided by 4, he wrote 4/5.



    Does anyone have any ideas of how I can help him to remember the link with division?



    Thank you.
     
  3. afterdark

    afterdark Lead commenter

    write down a simple division [use the division symbol with 2 dots between the dividend and the divisor]
    draw an arrow from the dividend to the top dot
    draw an arrow from the divisor to the bottom dot

    then write equals sign and then the fraction

    ask the student which is bigger than one and which is less than one
    5 divided by 4 or 4 divided by 5
    remind the student that division is not commutative
    he may think that it is commutative as multiplication is
    Good luck
    [​IMG]
     
  4. Nazard

    Nazard New commenter

    Maybe the problem is with the traditional (bus shelter) division method. In this method the divisor goes on the page first. If you use this method to convert 5/4 to a decimal then you write:
    4 ) 5 (with a line on top of the 5) - which always feels unhelpfully like it is the wrong way around.
     
  5. Thank you. I have tried this with him a few times, and he is able to identify top heavy fractions, if we are mid-discussion on it. He seems to trip up most when we are dealing with another topic and have to deal with a fraction or division out of the blue.


    He is very confident with the traditional (bus shelter) method, as this was his chosen way of solving 4/5 last night. I was trying to get him to see he could find the equivalent 8/10 and convert to 0.8 in his head (once we had 8/10 he was able to identify it was 0.8)


    Initially I thought it may just be a one off, as he is quite a daydreamer, but now I'm wondering if there's an underlying problem with division and the fact it is non-commutative, rather than his fraction skills.
    I might give him a short division and fraction quiz at our next session and see how he goes.
     
  6. if non-commutative may be a problem, how is he at subtraction of larger numbers from smaller - as one-off sums or within a larger column subtraction sum?
     
  7. He understands subtracting a larger number from a smaller number will result in a negative, though thinking back, he has on occasion expressed a subtraction as b-a instead of a-b when pulling information out of a typical wordy SATS question.
     
  8. afterdark

    afterdark Lead commenter

    It may be that does not understand that the commutative rule does not always apply.
    You should try getting him to write calculations for worded questions starting with subtractions.
    Expressing b - a instead of a - b suggests that he relies on symmetry to some extent.
    He needs to understand the asymmetry of subtraction due to it being a 'reverse' operation.
    I would go back to a number line.
     
  9. Yes, we've certainly discussed commutative vs non-commutative calculations before, but I'll definitely be re-visiting it again with him to be certain.


    Thanks for all your help everyone, working as self-employed makes it harder to bounce ideas of other people :)
     

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