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Viết phân số 25/27;15/16 thành tổng 3 phân số có mẫu số khác nhau và dều có tử số là 1.

Guest Jul 7, 2017
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#1
+91239
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Write 25/27, 15/16 as the sum of three fractions with different denominators, and have a numerator of 1.

But I still do not understand        Why are there 2 fractions ?  Anyone got any thoughts?

Melody  Jul 7, 2017
#4
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Possibly find three fractions with a numerator of one that will add up to 25/27 (problem one) and 15/16 (problem two). I tried 15/16 quickly as it seems this might be a nice challenge unless I'm over thinking it. (1/2)+(1/4)+(1/8)= 14/16 which is off from 15/16

Guest Jul 7, 2017
#2
0

Two fractions, two questions ?

(Can't do either).

BTW, what's the language ?

Guest Jul 7, 2017
#5
+91239
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Yes, Vietnamese :)

Melody  Jul 7, 2017
#3
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VIETNAMESE??

Guest Jul 7, 2017
#6
+79881
+2

We can use the concept of "Egyptian" fractions, here

25/27

Take the ceiling function for the division of 27 by 25  =  2

Write this as the denominator of a fraction with a numerator of 1 =  1/2

Subtract this from 25/27

25/27 - 1/2  = 23/54

Take the ceiling function for the division of 54 by 23  =  3

Write this as the denominator of a fraction with a numerator of 1 =  1/3

Subtract this from 23/54 - 1/3  = 5/54

Take the ceiling function for the division of 54 by 5  =  11

Write this as the denominator of a fraction with a numerator of 1 =  1/11

Subtract this from 5/54

5/54 - 1/11  = 1/594

We can now stop the process since the last subraction results in a unit fraction

So.....25/27  can be represented  as the sum of these unit fractions

1/2  +  1/3 + 1/11 +  1/594

BTW.....this is the shortest length possible...in other words.....this fraction cannot be represented by  the sum of any fewer than 4 unit fractions

15/16

Using a similar process this can be represented as the sum of the following unit fractions :

1/2 + 1/3 + 1/10 + 1/240

Again....this fraction cannot be represented by the sum of any fewer than four  unit fractions

Here is website devoted to Egyptian Fractions....it is rather interesting :

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html

CPhill  Jul 7, 2017
edited by CPhill  Jul 7, 2017
edited by CPhill  Jul 7, 2017
#7
+91239
+1

I am very impressed Chris,   I have never seen anything like that before

Melody  Jul 8, 2017
#8
+79881
+1

Thanks, Melody.....other than exposing the forum members  [ and guests ] to, perhaps, a new concept, I can't really take much credit for the answers. I just ran across that website one day. Before that, I had never heard of this, either !!!!

CPhill  Jul 8, 2017

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