# Tagged Questions

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### 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 ...
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### 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 ...
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 ...
### Why is the decimal representation of $\frac17$ “cyclical”?
$\frac17 = 0.(142857)$... 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 ...