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!
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