# Thread: How to Calculate This?

1. 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.

2.

3. 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.

4. 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?

5. 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

6. Originally Posted by IAlexN
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!

7. 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.

8. Originally Posted by IAlexN
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)

9. Originally Posted by DrRocket
20!/32! = 1/(32*31*30*...*21)
Thank you.

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