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Thread: How to Calculate This?

  1. #1 How to Calculate This? 
    Forum Freshman IAlexN's Avatar
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    This is not homework; I'm just curious. And would like to know if there is another way to calculate this:

    (12/32)*(11/31)*(10/30)...*(2/20)*(1/19)

    Without having to enter all of the fractions in a calculator?

    Thank you.


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  3. #2  
    Forum Ph.D. Leszek Luchowski's Avatar
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    Find common factors in nominators and denominators and reduce.

    The first thing that meets the eye is 12/32 = (3*4)/(8*4) = 3/8.

    But you can reduce between the individual fractions, as they are all being multiplied by each other - so the 11 in the second fraction can be reduced with the 22 in the last fraction but three.

    Of course this will be more work than typing everything into a calculator, but it may be worth it, for example if you want to avoid the digital errors of floating-point numbers and get a proper fraction as a result.

    Good luck, and keep us posted - L.


    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
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  4. #3  
    Forum Ph.D. Leszek Luchowski's Avatar
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    Hey, there is something wrong! Exactly how many fractions do you have in your expression?

    From 12 to 1 inclusive, with a step of 1, you have 12 numerators.

    But from 32 to 19 inclusive, with a step of -1, you have 14 denominators.

    Am I missing something?
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
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  5. #4  
    Forum Freshman IAlexN's Avatar
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    Quote Originally Posted by Leszek Luchowski
    Hey, there is something wrong! Exactly how many fractions do you have in your expression?

    From 12 to 1 inclusive, with a step of 1, you have 12 numerators.

    But from 32 to 19 inclusive, with a step of -1, you have 14 denominators.

    Am I missing something?
    Oh.. Yeah, I think it's supposed to be: (12/32)*(11/31)*(10/30)...*(2/22)*(1/11)

    Sorry
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  6. #5  
    . DrRocket's Avatar
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    Quote Originally Posted by IAlexN
    Quote Originally Posted by Leszek Luchowski
    Hey, there is something wrong! Exactly how many fractions do you have in your expression?

    From 12 to 1 inclusive, with a step of 1, you have 12 numerators.

    But from 32 to 19 inclusive, with a step of -1, you have 14 denominators.

    Am I missing something?
    Oh.. Yeah, I think it's supposed to be: (12/32)*(11/31)*(10/30)...*(2/22)*(1/11)

    Sorry
    That is worse. Now you have 12 terms based on the numerators and 23 terms based on the denominators.

    Do you really mean (12/32)*(11/31)*(10/30)...*(2/22)*(1/21) ?

    In which case the product is 12!*20!/32!
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  7. #6  
    Forum Freshman IAlexN's Avatar
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    Quote Originally Posted by DrRocket
    That is worse. Now you have 12 terms based on the numerators and 23 terms based on the denominators.

    Do you really mean (12/32)*(11/31)*(10/30)...*(2/22)*(1/21) ?

    In which case the product is 12!*20!/32!
    Yes, that is correct, I meant 1/21. I once again apologize; I was in a hurry and never noticed my mistake, thank you for acknowledging that.

    Might someone elaborate as to how you reached 12!*20!/32!, as I'm not entirely sure how you reached the 20! in your answer.
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  8. #7  
    . DrRocket's Avatar
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    Quote Originally Posted by IAlexN
    Quote Originally Posted by DrRocket
    That is worse. Now you have 12 terms based on the numerators and 23 terms based on the denominators.

    Do you really mean (12/32)*(11/31)*(10/30)...*(2/22)*(1/21) ?

    In which case the product is 12!*20!/32!
    Yes, that is correct, I meant 1/21. I once again apologize; I was in a hurry and never noticed my mistake, thank you for acknowledging that.

    Might someone elaborate as to how you reached 12!*20!/32!, as I'm not entirely sure how you reached the 20! in your answer.
    20!/32! = 1/(32*31*30*...*21)
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  9. #8  
    Forum Freshman IAlexN's Avatar
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    Quote Originally Posted by DrRocket
    20!/32! = 1/(32*31*30*...*21)
    Thank you.
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