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 .

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Rewrite $\frac{a}{x-Sy}$ to $\frac{K}{S}$? It's possible?

I have the following challenge: Rewrite this fraction: $$ \frac{a}{x-Sy} $$ where $a$, $x$ and $y$ are constants and $S$ is a variable. To this fraction: $$\frac{K}{S}$$ where $K$ is a constant. If its possible, then what are the steps to rewrite…
Oshio
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Is there a mathematical function that inverts a fraction if its less than 1?

Simple question really: has anyone standardized a function that reverses the operators when the result is less than 1, similar to how the absolute value works for addition? That is: $$f(2)=2 $$ $$f(0.5)=2 $$ $$f(0.2)=5 $$ $$f(1)=1 $$
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Proportionality logic

As I know of proportionality, if two things are proportional in degree one, changing (increasing or decreasing) one of them by a factor of say $z$ changes the other by same factor $z$ but what I don't understand is what if the relation is in degree…
Rew
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Value of -1 13/30

I've been working on this for a while now, I've searched the internet but I didn't get any valid solution. The question What's the value of -1 13/30 (mixed fraction, -1, 13 by 30), is it -43/30 or -17/30. I'm really confused, so any help with…
anon
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Comparing Equivalent Fractions

could I compare two fractions with proportional or not proportional sizes two fractions that are to be compared aren't equivalent to each other it's a pre-algebra question any answer you will give will help me reach the right answer
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How to write $a/(c+1)$ as $(a/c) + \cdots$?

I am looking for a way to rewrite $$ \frac{a}{c+1} $$ as $$ \frac{a}{c} + \cdots $$ in other words, move the $+ 1$ part outside of the denominator. (a and c are real numbers) Is this possible? If so, how?
Qqwy
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Fractions exam question

A factory buys 25 tonnes of flour. $17\frac{1}{2}$ tonnes of the flour is used to make scones. $\frac{1}{5}$ of the scones are cheese scones. a) What fraction of the total amount of flour is used to make cheese scones? $17\frac{1}{2}$ *…
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Simplify the algebraic fractions

How could I simplify $\dfrac 8{x+5} - \dfrac 3{5-x}$? I know we should find the LCM for the denominators and then simplify, but this question is little confusing.
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The quotient value of the reciprocal of a fraction from the fraction quotient value

Say $$c = \frac{a}{b}$$ and $$f = \frac{b}{a}$$ where $a, b , c, d, e, f \in \mathbb{R}$ $c = $ quotient $f = $ quotient of the reciprocal of a fraction Is there any relationship between $c$ and $f$? Is it possible to find the quotient of the…
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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. 20% of 200 =1/5*200=40. But, when I convert mixed fraction (16 2/3%) into improper fraction…
Rishabh
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How to simplify $\frac{e^x}{1+e^{x}}$ to $\frac{1}{1+e^{-x}}$?

The two are equivalent, as a check with wolfram alpha shows. I can also solve $\frac{e^x}{1+e^{x}} = A+ \frac{1}{1+e^{-x}}$? and I get that $A=0$. But is there a way that I can directly simplify $\frac{e^x}{1+e^{x}$}$ to get $\frac{1}{1+e^{-x}}$? I…
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How do I get 1/15 of something, only by divide with 2 or 3 and add the result back together?

I'm currently playing the game Satisfactory, where I need to balance the conveyor belts to ensure a 100% efficient factory. To help me in this job I have Merger and Splitter. The Splitter can split belts into 2 or 3 conveyor belts and the Merger can…
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Is there any way to simplify the following fractions? Thank you!

Is there any way to simplify the following fractions? $[n^{3}-1]/[n^{4}-1]$ $n!/n^{n}$
Jenny
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reducing fractions with combinations and powers of large integers

For example, I'm trying to reduce $\frac{49 \choose6}{49^6}$. Is there anyway to reduce this fraction further? Thanks
Tim Weah
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Compare fractions a/b and b/a

I'm trying to implement a mathematical method for calculation of injustice. The formula depends on two variables $a>=1$ and $b>=1$ and returns a fraction $a/b$. $a/b=1$ indicates justice. If $a/b<1$ the injustice is to your advantage. If $a/b>1$ the…
Dough
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