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Math Help - I think I discovered a new math trick(with ratios), correct me if it is not new?

  1. #1
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    I think I discovered a new math trick(with ratios), correct me if it is not new?

    Try these problems on a sheet of paper so you can (VISUALLY) see my new math trick and see how it works.


    Problem 1.

    Lets say you have any given ratio like 3/4, and then you multiply it by a ratio that has the same number in the numerator and the denominator (like 2/2 ) and you will get an answer (which is 3/4 * 2/2 = 6/8) Then you combine the numerators from 3/4 and the answer (6/8) and you will get the number 36. Then you combine the denominators from 3/4 and the answer (6/8) and you will get 48.
    Then the numbers 36 and 48 will make a new ratio(36 will be the numerator and 48 will be the denominator). This new ratio will reduce down back to 3/4, which is the original ratio.

    Problem 2.

    Lets say you have the given ratio 1/4, and then you multiply it by a ratio that has the same number in the numerator and the denominator (like 3/3) and you will get an answer (1/4 * 3/3 = 3/12). Then you combine the numerators from 1/4 and the answer (3/12) and you will get the number 13. Then you combine the denominators from 1/4 and the answer (3/12) and you will get 412. Then the numbers 13 and 412 will make a new ratio(13 will be the numerator and 412 will be the denominator). Now since there is one DIGIT more in the number 412 than in the number 13 (we take the number 412 and count its digits which = 3 digits, then we take the number 13 and count its digits which = 2 digits, then subtract 2 digits FROM 3 digits to get 1 digit), we will have to take the denominator from the original ratio (1/4) and the answer(3/12) , (which both denominators appear in the number 412, which is the denominator of our new ratio). You take the denominator from 3/12 and since 412 is ONE DIGIT larger than 13, the number 1 in the denominator of 3/12 will be taken out (because ONE DIGIT will tell you that you need to take off the number 1 in the number 12 because you ALWAYS take ONE DIGIT off the left digit in the number 12 (which is 1)), and you add the number 1 to the denominator of the original ratio(1/4), which 4 + 1 = 5. So the number 1 in the number 12 is cancelled and you are left with number 2. Then you take 5(which came from the step we did from above) and the 2 and you combine them to make 52. 52 will be the NEW denominator and 13 will be the numerator(remember 13 from a while back from the previous steps) and you make a new ratio off of those. So 13/52 will be the new ratio. Now this ratio will always reduce back down to 1/4(which is the original ratio)




    I know these might be hard to visualize but try this trick with any given ratio and it will work.
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  2. #2
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    Problem 1:

    I would have to disagree with you that all ratios work. Try  \frac{17}{8} \times  \frac{8}{8}

    I will also show why your trick works with smaller ratios with algebra:

     \frac{a}{b} \times \frac{n}{n} = \frac{an}{bn}

    'Combining (as defined by you)' numerators and denominators:
     \frac{10a + an}{10b + bn} = \frac{a (10 + n)}{b(10+n)} = \frac{a}{b}

    It doesn't work for the example I have given because by 'combining' you assume multiplication by 100 for 'a' but only 10 for 'b'

    Problem 2:

    It's slightly incomprehensible to me so I didn't follow it all the way through. But I believe you did introduce a correction factor for the 'combining' discrepencies between the numerator and denominator. Again though, it's just algebraic manipulation. It's similar to saying

     m =  (m + 9m) \times \frac{2m}{5} \times \frac{1}{2m} - m = m
    Last edited by Gusbob; February 17th 2010 at 03:55 PM.
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  3. #3
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    17/8 works fine.

    The number you would get is 17136/864. Then 17136 becomes 17+1 = 18. Then combine it with the 36. So it would be 1836/864, which would reduce down to 17/8.

    Instead of doing the denominator, I did the numerator. I think if there is one digit short in the numerator, than you chage the DENOMINATOR. If it is one digit short in the denominator, than you change the NUMERATOR.
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  4. #4
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    Quote Originally Posted by noskillz View Post

    I know these might be hard to visualize but try this trick with any given ratio and it will work.
    Not hard to visualise at all:

    Start with a/b. Multiply by m/m for the equivalent fraction am/bm.

    Combine [as you say] and form (10a+am)/(10b+bm)

    = [a(10+m)]/[b(10+m)] = a/b with usual restrictions on the denominator.
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  5. #5
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    Thank you for the proof Diagonal.
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