comparing fractions

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ggd
Posts: 26
Joined: Fri Jun 19, 2009 3:17 pm

comparing fractions

Post by ggd »

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?
dadofkent
Posts: 515
Joined: Tue Jan 01, 2008 2:05 pm

Re: comparing fractions

Post by dadofkent »

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.
dadofkent
Posts: 515
Joined: Tue Jan 01, 2008 2:05 pm

Post by dadofkent »

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.
essex-mum18
Posts: 218
Joined: Sun Nov 25, 2007 12:09 am

Re: comparing fractions

Post by essex-mum18 »

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
Milla
Posts: 2556
Joined: Mon Nov 24, 2008 2:25 pm

Post by Milla »

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!
ggd
Posts: 26
Joined: Fri Jun 19, 2009 3:17 pm

Post by ggd »

Thanks for the suggestions. I think eliminating the obvious seems the way to go and then finding a common denominator.
yoyo123
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Joined: Mon Jun 18, 2007 3:32 pm
Location: East Kent

Post by yoyo123 »

do the elimination then 24 is a CD
moved
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Location: Chelmsford and pleased

Post by moved »

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.
dadofkent
Posts: 515
Joined: Tue Jan 01, 2008 2:05 pm

Post by dadofkent »

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.
Milla
Posts: 2556
Joined: Mon Nov 24, 2008 2:25 pm

Post by Milla »

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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