Questions tagged [fractions]

Questions on fractions, i.e. expressions (not values) of the form $\frac ab$, including arithmetic with fractions. Not to be confused with the tag (rational-numbers): fractions denote rational numbers, but the same rational number may be written in different ways as a fraction.

2,249 questions
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The prime $p$ divides the numerator of $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{p-1}$ [duplicate]

Let $p \ge5$ be a prime number, and let $a$ and $b$ be natural numbers. If $\sum_{k=1}^{p-1}\frac{1}{k}=\frac{a}{b}$, prove that $p|a$.
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Find the solutions of second derivative [on hold]

If $$f(x)=\frac {2x}{x^{2}-3x+2}$$ find the solutions of $$f''(x)=0$$ This problem is from a test. Is it possible to solve this without a calculator and without hard work? Maybe this fraction can be ...
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How to rewrite the following equation as x in terms of y?

How to convert the following function y of x $y=f(x)=\frac{x}{x+a}+\frac{x}{x+b}$ into a function x of y $x=g(y)=?$ in its simplest form. This is part of an integration problem so having no ...
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How to transform a continued fraction so that all denominators are positive?

I came across this quote: "Every continued fractions $a_1, a_2, ..., a_n$ can be transformed to a unique canonical form $\beta_1, \beta_2, ...., \beta_m$, where all $\beta$ 's are positive or all ...
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Doubt in Fraction and percentage

There's a question in a book, 16 2/3% of 600 gm - 33 1/3% of 180 gm I was solving it like regular method which i use to find x% of a number, for eg. ...
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Why is the reciprocal used in fraction division?

I don't know if this is a basic question or whatever, but I can't seem to find an answer. As far as I understand the reciprocal of a number the inverse of that number, that still doesn't clarify why ...
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How do I convert fraction percentage into mixed fraction?

I know how to convert a fraction into decimal but I want to make my calculation faster so I want to learn how to convert between fractions and percentage. I found this on a book: ...
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moving fraction into denominator

Hello Mathematics Stackexchange I had a quick question. I do sincerely apologize if this type of question was asked before. Im having trouble simplifying this fraction specifically I am not sure how ...