Tagged Questions
6
votes
5answers
201 views
An interesting problem with fractions
These are a few examples of how "forbidden" procedures can lead us to the correct answer:
$$\displaystyle\frac{1\not4^1}{2\not8_2} = \frac{11}{22}=\frac{1}{2}$$
...
1
vote
1answer
63 views
How to chose a rational with a non-repeating fractional part in an arbitrary base?
How can I choose an $x\in[a,b)\subseteq[0,1)$, where $a,b\in\mathbb{Q}$, such that $x$ has a non-repeating fractional part in some chosen base?
For example, say I'm looking at ...
1
vote
2answers
148 views
Function with a Modular Inverse
For a combinatorics problem I have a function, $h(x)$ that is always divisible by five, but it is calculated in pieces, e.g. $h(1) = 43 + 7$.
The final function that I need is $f(x) = (h(x) / 5) ...
7
votes
2answers
221 views
Writing $1$ in form of $\frac{1}{t_1}+\cdots+\frac{1}{t_n}$ [duplicate]
Possible Duplicate:
Prove that any rational can be expressed in the form $\sum\limits_{k=1}^n{\frac{1}{a_k}}$, $a_k\in\mathbb N^*$
Can anyone help me with this problem? It's a little ...
3
votes
1answer
135 views
Counting fractions with $n$ digits in the numerator and denominator
Playing around with fractions, I eventually had to consider the following question:
Is there a formula for counting how many proper fractions in lowest terms with
$n$ base-$b$ digits in both the ...
4
votes
3answers
407 views
Computing a rational number between two others, minimizing numerator and denominator
Given two positive rational number $\frac{a_1}{b_1}$ and $\frac{a_3}{b_3}$ (written in lowest terms) such that $$\frac{a_1}{b_1} < \frac{a_3}{b_3},$$
I want to find a rational number
...
13
votes
2answers
823 views
Why is the decimal representation of 1/7 “cyclical”?
1/7 = 0.(142857)...
with the digits in the parentheses repeating.
I understand that the reason it's a repeating fraction is because 7 and 10 are coprime. But this...cyclical nature is something ...
