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1/11 > .....> 1/12

 Sep 7, 2015
 #1
avatar+2353 
+5

Hi there,

 

there's lot's of answers to your question, but I think you're just looking for an example of a fraction that is in between these two.

 

Let me give you some help here. Suppose I have 1 pizza and I cut it in 4 equal slices then if I take 1 slice I'll have 1/4 pizza. However if I cut the pizza in 8 slices and take 2 slices I'll still have 1/4 pizza.

 

Now suppose I have 1 pizza and I cut it in 11 equal slices then if I take 1 slice I'll have 1/11 pizza. However if I cut the pizza in 22 slices and take 2 I'll still have 1/11 pizza. Therefore we can say 1/11 = 2/22.

 

With similar reasoning we can also say that 1/12 = 2/24 (try to think of this pizza experiment yourself.)

 

So the question 1/11<...<1/12 is actually the same question as  2/22<...<2/24.

 

Now, I can divide a pizza in 22 slices, I can divide a pizza in 24 slices, but I could also divide it in 23 slices (Don't ask me to actually do it though, it would be very cumbersome).

 

Now if I have 2 slices of the pizza that is cut in 22 pieces those pieces will be bigger than 2 slices of the pizza that is cut in 23 pieces and those will again be bigger than the 2 slices of the pizza that is cut in 24 pieces.

 

Therefore we can state 2/22<2/23<2/24.

 

Now remember that we found that 1/11=2/22 and 1/12=2/24.

 

Hence we can also write 1/11<2/23<1/12.

 

And there you have an answer to your question, note however that it is not the only answer.

 

Suppose I cut the pizza in 44 slices and take 4 for myself I'd also have 1/11th pizza. 

 

Similarly as above we can therefore also reason that 4/44<4/45<4/46<4/47<4/48 and therefore that

 

1/11<4/45<4/46<4/47<1/12 (try to follow the reasoning above and do this for yourself.)

 

 

I hope this helped cool

Reinout

 Sep 7, 2015
 #2
avatar
0

If you wnat to know if 1/11 is greater than 1/12, just subtract them thus:

 

1/11 -1/12=1/132, so 1/11 is greater 1/12 by 1/132, because,

1/132 +1/12=1/11

 Sep 7, 2015

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