## experimentX 3 years ago Can anyone explain this to me? The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s. We shall consider fractions like, 30/50 = 3/5, to be trivial examples. There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator. If the product of these four fractions is given in its lowest common terms, find the value of the denominator.

1. ghazi

49/98 = 4/8 could be a mathematical fallacy

2. ghazi

but i can prove it

3. experimentX

don't post answer ... i just need explanation http://projecteuler.net/problem=33

4. ghazi

|dw:1349020445163:dw| don't get irked please :)

5. experimentX

Woops!!

6. ghazi

lol

7. experimentX

funny!!

8. experimentX

i guess i understand what i means!!

9. ghazi

10. experimentX

this isn't my question if it were mine i would have already solved it.

11. experimentX

i didn't expect the nine would be cancelled to give right answer.

12. ghazi

i know :)

13. ghazi

but in the example 30/50 cancel out zeroes you're gonna get that you're lookin for..sorry, let me try this

14. experimentX

9*9*9 possibilities ... if you get out trivial case ... 9*9*9 - 10 possible cases.

15. ghazi

no, i think there are exactly 4 possibilities and if they are expressed as lowest fraction you'll have denominator of it will be equal to ?? the other example is 16/64

16. experimentX

told ya .. don't post answer. this is supposed to be challenge Q.

17. experimentX

programming challenge ..

18. ghazi

well the answer is equal to = 2*5*4*2 and another example is 40/80

19. ghazi

$\frac{ 30 }{ 50 },\frac{ 48 }{ 98 }, \frac{ 16 }{ 64 }, \frac{ 40 }{ 80 }$

20. experimentX

zeros are trivial cases.

21. ghazi

sorry forgot that

22. experimentX

Yep .. got'em all

23. ghazi

??

24. ghazi

@experimentX what are those? i just got two

25. mukushla

there are 4 equation to solve$\frac{ab}{cb}=\frac{a}{c}$$\frac{ba}{cb}=\frac{a}{c}$$\frac{ba}{bc}=\frac{a}{c}$$\frac{ab}{bc}=\frac{a}{c}$if u wanna do it by hand of course :) these are easy to solve i think

26. experimentX

yep .. thanks for idea. looks like i hit jackpot. well ... the answers are 16 64 19 95 26 65 49 98

27. ghazi

no

28. ghazi

@experimentX 26/65 seems in correct

29. experimentX

they are multiples of 13

30. ghazi

exactly ..i was in haste ...nice you've got the jack pot ..cool