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.

A fraction is simply an expression $\frac{a}{b}$, where $a$ and $b$ are typically integers (where $b\neq 0$). This tag may be used, when $a$ and $b$ are more general expressions or algebraic objects; however, consider adding a more specific tag also:

Fractions are distinct from rational numbers because they are a representation: $\frac 34$ and $\frac{30}{40}$ are different fractions that happen to represent the same rational number.

For arithmetic with fractions, this tag is appropriate along with .

2981 questions
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Algorithm for converting fraction into (recurring) decimal

I need to determine whether fraction is recurring decimal or not (what are conditions for it?), find period and output it as $\frac{1}{3}=0.\bar{3}$. If it is not recurring, then I already have algorithm.
eMathHelp
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Find the value of $\frac{ x_1^2}{1-x_1}+\frac{x_2^2}{1-x_2}+...+\frac{x_n^2}{1-x_n}.$

Suppose, $x_1+x_2+...+x_n=1\space (x_i\in \mathbb{R}, x_i ≠1)$ and $\frac{ x_1}{1-x_1}+\frac{x_2}{1-x_2}+...+\frac{x_n}{1-x_n}=1.$$\\$ Find the value of $\frac{ x_1^2}{1-x_1}+\frac{x_2^2}{1-x_2}+...+\frac{x_n^2}{1-x_n}.$
Soham
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Fractions of an amount

I need help with the following problem: Catalin works in an office. One week he divides his time between these tasks: $\frac{1}{4}$ of his time in meetings $\frac{5}{8}$ of his time writing reports the rest of his time doing the accounts He…
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Why does this hold?

$$\frac{(n+1)(n+1)}{(n+1)(n+2)}=1-\frac{1}{n+2}$$ I have tried WolframAlpha but I don't get any step by step solutions.
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Does there lie a logic/reason behind precedence rule of mathematical operators?

To add two fractions (let's say, 4/7 and 2/3), instead of using LCM, why I can't simply add numerators first (4+2), and divide it by sum of denominators (7+3) ? Well, I know the division has more precedence than addition, so we can't perform 4+2…
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Stuck on some fraction

In the following manipulation $$\frac{-(M-\frac{1}{2}\Omega)+\sqrt{(M-\frac{1}{2}\Omega)^2+2\lambda\Omega}}{\Omega} =…
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Is a decimal number, such as 0.345 a fraction?

Just by semantics alone, would you consider it a fraction when it is not written in a 'fractional' format?
lawonga
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Formal definition of fraction

What is the formal definition of fraction? Everyone says something different. Thank you for your answers.
rain
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Simplify $\ \frac{(0.81)^2 × (0.6×0.21)^2}{35^5 × 0.252} $ into $2^n × 3^m×5^p×7^k$

$\ \frac{(0.81)^2 × (0.6×0.21)^2}{35^5 × 0.252} $ Simplify the following equation into this form : $2^n × 3^m×5^p×7^k$ where $n, m, p, k$ are integers.
rgbxx
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Fraction walk through

$$0.824 = \frac{n/20\cdot 1}{n/20\cdot 1+(1-n/20)\cdot 0.5}$$ Source. Please answer this question with step by step. Thank you so much
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How did they get 2n + 10 here?

Daniel can encode a paper in $5$ hours and together he and Dennis can encode it in $2$ hours, how long would it take Dennis to encode the same paper alone? If Daniel can encode a paper in $5$ hours, then he encodes $\frac15$th paper per hour. Let…
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