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PostPosted: Thu Jun 23, 2011 10:22 am 
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Please could someone show how to choose between the final two possible answers:

Question is : 1/4 3/8 2/5 2/7 7/32 - which has lowest value?

We crossed off the first three quite quickly-
3/8 bigger than 1/4
2/5 (0.4) bigger than 1/4
1/4 is bigger than 7/32 when converted to 8ths

so that leaves 2/7 and 7/32. What is the easiest way for a 10 yr old to compare these two?

thanks


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PostPosted: Thu Jun 23, 2011 10:35 am 
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I am not a mathematician and this is distinctly NOT a good way of doing it, :roll: but I'd bring the fractions closer together in size to get a better feel for them. So I'd halve the 32s so that makes 3.5/16 and double the 7s so that makes 4/14. As 14 parts of a whole are each larger than 16, then 4/14 must be larger than 3.5/16 but I'm aware that mixing decimals on top of fractions probably makes mathematicians shudder.
At school I'm sure we were made to find a common fraction but it would take me too long to find one if this were an exam question, so if you don't get marks for showing your workings, just for a right answer, this is a quick estimate method.

I hope you get a better reply than this soon!


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PostPosted: Thu Jun 23, 2011 10:45 am 
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You will have to find the LCD (lowest common denominator) and then compare the fractions.
LCD of 4, 8,5,7,32 = 1120

So,
1/4=280/1120
3/8=420/1120
2/5=448/1120
2/7=320/1120
7/32=175/1120

You can see from the above that 7/32 is the lowest in value.

Other, quicketst option I can think of is:
between 2/7 & 7/32 : you can make base common (7x32), so for the first fraction it will be 64 (2x 32) and second will be 49(7x7). So, 7/32 is the smallest.

I hope this helps.

wizard wrote:
Please could someone show how to choose between the final two possible answers:

Question is : 1/4 3/8 2/5 2/7 7/32 - which has lowest value?

We crossed off the first three quite quickly-
3/8 bigger than 1/4
2/5 (0.4) bigger than 1/4
1/4 is bigger than 7/32 when converted to 8ths

so that leaves 2/7 and 7/32. What is the easiest way for a 10 yr old to compare these two?

thanks


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PostPosted: Thu Jun 23, 2011 1:44 pm 
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Joined: Thu Oct 21, 2010 4:38 pm
Posts: 109
wizard wrote:
so that leaves 2/7 and 7/32. What is the easiest way for a 10 yr old to compare these two?

thanks


2/7 is more than a quarter (2/7 > 2/8, because a/b > a/(b+n) for a positive n).

7/32 is less than a quarter (7/32 < 8/32, obviously).


Quote:
You will have to find the LCD (lowest common denominator)


I'd be surprised if that's the intended route to it. 5.7.32 is hardly a five second job to work out by hand, and there's a lot of primes floating around in the question to make it long-winded to do.

I think it's significant that 7/32 is the only one that's less than a quarter. if you just multiply the numerator in each fraction by 4, it's greater than or equal to the denominator in each case (4/4, 12/8, 8/5, 8/7) other than in the last (28/32). So 7/32 is the smallest.


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PostPosted: Thu Jun 23, 2011 3:35 pm 
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Yes I think I would naturally go for the less than a quarter, bigger than a quarter method - but quite how you would "teach" a 10 year old to naturally adopt that method too I don't know ........ I'm thinking.


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PostPosted: Fri Jun 24, 2011 9:47 am 
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Location: Watford, Herts
Although the common denominator method works, it's best to use it pairwise so you don't have to multiply large numbers. It's probably best to have a range of methods available, as in tokyonambu's approach, e.g. you can also use common numerators, reasoning that 2/5 is bigger than 2/7 because 7 is bigger than 5. In this case 2/7 = 14/49 > 14/64 = 7/32.

But here they had 1/4 in the list as a clue, and eliminating it made the problem harder. You started by reasoning

7/32 < 1/4 < 3/8
1/4 < 2/5

Now if you ask where 2/7 fits here, you are led directly to

1/4 < 2/7 < 2/5


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PostPosted: Wed Jun 29, 2011 12:10 pm 
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Joined: Tue Nov 11, 2008 10:06 am
Posts: 54
Thanks for all the replies - useful to have some different methods to look at. I will see which works for my son.


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