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# Fraction

## 30 posts in this topic

So would this have more then one answer? or is it only one unique answer?

well no, there are at least two answers

5823/17469

and

5832/17496

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hey guys this is my first post.

You know you've made the problem harder than it really is

Try this solution4It's basic but logical

((5-4)(2-1)(7-6)(9-8))/3

=(1x1x1x1)/3

=1/3

Simple

but effective

and answers the question

comment if u wish

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Fraction - Back to the Number Puzzles

Can you use all 9 numerals (Edit: each numeral just once) - 1, 2, 3, 4, 5, 6, 7, 8 a 9 - above and below a fraction symbol, to create a fraction equalling 1/3 (one third)?

does it have to be only numerals? can you use parentheses and and functions to, like adding or subtracting? If so, what about this

(9-8) + (7-6)/5-4(1+2+3) = (1) + (1) / 1(6) = 2/6 = 1/3

Fraction - solution

5832/17496 = 1/3

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5823 / 17469 = 1/3

5832 / 17496 = 1/3

Dont ask me how i got. jus wrote a program and program came out with this output

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If one tries to solve this problem without electronic assistance, one can reduce their trial and error attempts with the following information.

As the ratio of the numerator to the denominator is 1/3, our denominator needs to have the same number or one more digit than the denominator, and because there are nine digits this means the numerator will have four digits and denominator will have five. The max carry for 3n, where n is a digit 1 to 9, is 2, therefore the denominator must begin with a 1 or 2. And, by the same token, the smallest number the numerator can begin with is 4. (It can not begin with 3 as 3×3 equals 9, the largest decimal digit, and adding only 1 or 2 will bring the sum to only 10 or 11. There can neither be a 0 (zero) or two 1's in a zeroless pandigital common fraction of 9 digits, therefore the numerator must begin with a 4 or greater.)

For the ratio of 1/3, the denominator also needs to be a multiple of 3, therefore its digital root must be either 3, 6 or 9, and the sum of the digits are modulo 0.

Though this puzzle has already been solved, I shall still post the solution I discovered:

5823/17469 and 5832/17496

Edited by Dej Mar

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