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Math Help - "The arithmetic rule for the sum of two quotients" Please help!

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    "The arithmetic rule for the sum of two quotients" Please help!

    Hi everyone, first post (woohoo)!

    Anyways, on to the math.

    I am reading a book on propositional logic and proof building to help me in my writing of proofs.

    I ran into this problem and the author uses what he calls "the arithmetic rule for the sum of two quotients" and he is using it to rearrange a problem. I googled it, but I could not find anything!

    Here is the problem:

    .1n+.1=a/b+.1 and using this rule, he rearranged it to: a/b+1/10=(10a+b)/10b

    Please explain how he got this, I would be most grateful!

    PS: There is one more problem somewhere in the book that he used it..if this above is not substantial please tell me!
    Last edited by Principia11; December 22nd 2011 at 05:14 PM.
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    Re: "The arithmetic rule for the sum of two quotients" Please help!

    Quote Originally Posted by Principia11 View Post
    Here is the problem:
    .1n+.1=a/b+.1 and using this rule, he rearranged it to: a/b+1/10=(10a+b)/10b
    This one of the strangest post I have seen.
    Surely anyone who would ask this question knows that 0.1=\frac{1}{10}~?
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    Re: "The arithmetic rule for the sum of two quotients" Please help!

    Quote Originally Posted by Plato View Post
    This one of the strangest post I have seen.
    Surely anyone who would ask this question knows that 0.1=\frac{1}{10}~?
    I am asking how the person rearranged it. That first equation is not the entire problem, but is the first equation that the author goes on to rearrange. I want to know how he rearranged it the way he did.

    I am confused about where the n went and how he arranged the a/b's.
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    Re: "The arithmetic rule for the sum of two quotients" Please help!

    Here is more info:

    "Use mathematical induction to show that all natural-number multiples of .1 are rational numbers"

    The first element of this set, 0, is rational, because it can be expressed in the form a/b where "a" is an integer and "b" is a nonzero natural number. Simply let a = 0 and b = 1.

    ... *skipping ahead a little*

    We know that there exists some integer "a" and some nonzero natural number "b" such that .1n = a/b

    Therefore we can rewrite the above expression as .1n + .1 = a/b +.1

    and then the author says: "Using the arithmetic rule for the sum of two quotients we can rearange the above as follows:

    a/b +1/10 = (10a+b)/10b
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    Re: "The arithmetic rule for the sum of two quotients" Please help!

    \displaystyle \frac{a}{b}+\frac{c}{d}= \frac{ad+cb}{bd}
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    Re: "The arithmetic rule for the sum of two quotients" Please help!

    Quote Originally Posted by pickslides View Post
    \displaystyle \frac{a}{b}+\frac{c}{d}= \frac{ad+cb}{bd}
    YES!!! Thank you so much! It all makes sense now ^.^
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