# Thread: Arrange the numbers 1 to 9 in a fraction which is equal to 1/3...

1. ## Arrange the numbers 1 to 9 in a fraction which is equal to 1/3...

Arrange the numerals 1, 2, 3, 4, 5, 6, 7, 8 and 9, in a single fraction that equals exactly 1/3. For example (which don't work), 1234/56789 = 0.0217.

2. Hey,

5832/17496 = 1/3.

3. Is there any formula or method to work this out?

4. Probably not, just guess-and-check. (Or, use Google search. )

This reminds me of a problem that was given to our math class in 4th grade. Find a 3-digit number n such that n, 2n and 3n use the digits 1 to 9 exactly once. I was the first to get an answer, which was 327, 654, and 981. I recently found out that this was not the only answer, however. There are three other possible values for n. Can you find them (without using Google )?

01

5. ## another

5823 / 17469 = 1/3

Examples of others:
1/2: 6729 / 13458
1/4: 3942 / 15768
1/5: 2697 / 13485
1/6: 2943 / 17658
1/7: 2394 / 16758
1/8: 3187 / 25496
1/9: 6381 / 57429

No formula.
Shortcuts:
1: find 5digit number = 3 times 4digit number (easier than dividing)
2: both numbers must be either odd or even

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# 3 equivalent fractions using all the digit from 1to9 each exactly once

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