# Tagged Questions

Questions on fractions, which are expressions (not values) of the form $\frac pq$.

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### Find five positive integers whose reciprocals sum to $1$

Find a positive integer solution $(x,y,z,a,b)$ for which $$\frac{1}{x}+ \frac{1}{y} + \frac{1}{z} + \frac{1}{a} + \frac{1}{b} = 1\;.$$ Is your answer the only solution? If so, show why. I was ...
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### Can you be 1/12th Cherokee?

I was watching an old Daily Show clip and someone self-identified as "one twelfth Cherokee". It sounded peculiar, as people usually state they're "1/16th", or generally $1/2^n, n \in \mathbb{N}$. ...
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### Why rationalize the denominator?

In grade school we learn to rationalize denominators of fractions when possible. We are taught that $\frac{\sqrt{2}}{2}$ is simpler than $\frac{1}{\sqrt{2}}$. An answer on this site says that "there ...
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### Express 99 2/3% as a fraction? No calculator

My 9-year-old daughter is stuck on this question and normally I can help her, but I am also stuck on this! I have looked everywhere to find out how to do this but to no avail so any help/guidance is ...
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### Can you prove why consecutive diagonal intersection points show decreasing fractions inside a rectangle?

When I was in third grade, I was playing with rectangles and diagonal lines, and discovered something very interesting with fractions. I've shown several math teachers and professors over the years, ...
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### Primary/Elementary Pedagogy: What is the rationale for the absent '+' in mixed fractions?

Why are elementary students taught to represent one and a half as 1 1/2 rather than 1 + 1/2? This mode of expression seems standard throughout at least North America. I think it is bad pedagogy for a ...
### Find all natural numbers such that $\sum_{k=1}^{n} \frac{n^k}{k!}$ is an integer
Find all natural numbers such that $\sum_{k=1}^{n} \frac{n^k}{k!}$ is an integer. I've tried to bring all fractions under commmon denominator and it didn't helped me much. With guessing I find out ...
### Numbers whose reciprocals sum to $1$
What are all the numbers that can be written as $a_1+a_2+\dots+a_n$, where $a_1,\dots,a_n$ are positive integers such that $\frac{1}{a_1}+\dots+\frac{1}{a_n}=1$? For instance, such numbers include \$4=...