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 Post subject: comparing fractions
PostPosted: Tue Oct 20, 2009 2:21 pm 
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In NFER 11c q14 you are asked to find the largest out of 7/8 3/4 6/9 10/12 3/5. I can not see a common denominatorfor for all these numbers, and converting all of them to decimal could be time consuming in an exam. Has anyone has a really quick way to compare these fractions?


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 Post subject: Re: comparing fractions
PostPosted: Tue Oct 20, 2009 3:20 pm 
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ggd wrote:
In NFER 11c q14 you are asked to find the largest out of 7/8 3/4 6/9 10/12 3/5. I can not see a common denominatorfor for all these numbers, and converting all of them to decimal could be time consuming in an exam. Has anyone has a really quick way to compare these fractions?


System I used with DD. Will vary slightly depending on numbers and whether you are, for example, after biggest or smallest.

For the numbers you give.

Eliminate the smallest numbers.

Do this by looking for those numbers bigger than, say 1/2 or 3/4. 3/4 would seem to be the better choice. 7/8 and 10/12 are obviously bigger than 3/4. Straightaway down to two numbers.

After the biggest of the remaining two numbers.

Both numbers are smaller than 1, so compare and determine how close.

7/8 is 1/8 away, and 10/12 is 2/12 or 1/6 away. 1/8 is the smallest number, so 7/8 is closest to 1 and therefore biggest number.


The method looks a bit long-winded, but in practice, providing child has a reasonable grasp of equivalent fractions, only takes a few seconds, and does not involve any writing down.


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PostPosted: Tue Oct 20, 2009 3:27 pm 
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PS Similar methodology can also be used if decimal fractions and percentages are also added into the mix, although some conversions to, for example, 1/10's or 1/5's may be required.


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 Post subject: Re: comparing fractions
PostPosted: Tue Oct 20, 2009 3:52 pm 
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ggd wrote:
In NFER 11c q14 you are asked to find the largest out of 7/8 3/4 6/9 10/12 3/5. I can not see a common denominatorfor for all these numbers, and converting all of them to decimal could be time consuming in an exam. Has anyone has a really quick way to compare these fractions?


Hi
The common denominator is 360

Therefore
7/8 = 315/360
3/4 = 270/360
6/9 = 240/360
10/12 = 300/360
3/5 = 216/360

Hence the largest is 315/360 i.e 7/8

Hope this helps


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 Post subject:
PostPosted: Tue Oct 20, 2009 3:57 pm 
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yes, I was thinking some elimination would help matters with the cross-comparing. No point even including ones you know aren't in the mix, and then, finding a common denominator which is small enough to be of practical use is far more likely.

EDIT - actually posted before Essexmum's but the machine is hanging here and took a long time to bother sending it - wasn't meaning a dig at 360 being a "useful" common denominator!


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 Post subject:
PostPosted: Tue Oct 20, 2009 5:18 pm 
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Thanks for the suggestions. I think eliminating the obvious seems the way to go and then finding a common denominator.


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 Post subject:
PostPosted: Tue Oct 20, 2009 7:35 pm 
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Location: East Kent
do the elimination then 24 is a CD


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 Post subject:
PostPosted: Wed Oct 21, 2009 12:58 pm 
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Location: Chelmsford and pleased
I would teach this through elimination looking at what is left over. 1/8 of a cake is much smaller than 1/6. A visual aid, such as a pizza or chocolate cake usually helps.


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 Post subject:
PostPosted: Wed Oct 21, 2009 7:06 pm 
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moving wrote:
I would teach this through elimination looking at what is left over. 1/8 of a cake is much smaller than 1/6. A visual aid, such as a pizza or chocolate cake usually helps.


I was normally 7/8 down a bottle of red wine by this stage. Helped both of us.


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 Post subject:
PostPosted: Wed Oct 21, 2009 10:38 pm 
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dadofkent wrote:
[I was normally 7/8 down a bottle of red wine by this stage. Helped both of us.

that's my boy.


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