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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Is this fraction non-terminating?

I recently stumbled upon an observation: the fraction $\frac{x}{y}$ terminates if and only if $y$ only has prime factors $2$ and $5$. For example: $$\frac{1}{20} = \frac{1}{2\cdot2\cdot5} = 0.05$$ $$\frac{1}{6} = \frac{1}{2\cdot3} = 0.1\bar6$$ I…
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Triple fractions (and more complex fractions)

Usually $$\frac{a}{\frac{b}{c}} = \frac{ac}{b}$$ i.e. $b/c$ is seen as the denominator, and $a$ is the numerator. If you have $a/b/c/d$, what do you choose to take as the denominator? $$\frac{b}{\frac{c}{d}} , \frac{c}{d},\text{ or } d\text{?}$$…
Idios
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How to divide the fraction $1/1+1$?

This has to do with re-calculating the sigmoid function in ai. It isn't really important, but the simplest way to put it is I need a math guru to help my monkey brain do this: $$\frac{1}{1+e}$$ to like $$\frac{1}{something} + \frac{1}{e}$$ Please…
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Finding the number of chairs

In a school hall, $7/31$ of chairs is arranged in rows of 5, $11/31$ of chairs is arranged in rows of 13. The rest of chairs are not used. The total number of chairs does not exceed 4000. Find the number of chairsAttempts: $x= 31k$ since 31 is the…
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Cancellation fractions; why this is not equal to this?

I'm very bad with math, i will go right to the question: Why i can't make this cancellation? (or why this is False, I tested this in symbolab and gave false)... $$\frac{3^{-m}\cdot 3^{-2m+3}+27^{-m+2}}{81\cdot…
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How does this numerators and denominators relate with the fraction?

Suppose if we have two fractions $\frac{a}{b}$ and $\frac{c}{d}$ then how are their values related with the fraction $\frac{a+c}{b+d}$ ? I have observed this inequality: $\frac{a}{b}\le\frac{a+c}{b+d}\le\frac{c}{d}$. Does this hold true $\forall…
ashwani
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Can someone explain to me how this simplification of a fraction works?

Can someone explain to me why is the answer $30b^{3}/4(a+b)$ considering that on the previous line we multiply $[5b][a+b]/{[4][6b^2]}$. It's as if we multiply the numerator of the first term with the denominator of the second term. Is there a…
Onyx
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Simple fraction calculation

I'm trying to write this expression as one fraction: \begin{align} \frac{5}{y+1}\cdot\frac{1}{5}+\frac{y}{\frac{y+1}{3}} &= \frac{5y}{5y+5}+\frac{3y}{y+1} \\ &= \frac{5y^2+5+15y^2+15y}{5y^2+10y+5} \\ &= \frac{20y^2+15y+5}{5y^2+10y+5} \\ &=…
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Convert mibibyte-days to gibibyte-months.

I have a web host that charges $1 for every Gibibyte (1024 MiB) that I use per month. Currently I am using about 7.6 MiB (Mibibytes) per day. I tried to do this myself and ended up with hopelessly large numbers that I didn't know the meaning of. Can…
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How to cancel out a negative in a denominator?

The question was to make $y$ the subject in $x=5-3y$ (i.e. solve for $y$). My working was this: $$\begin{align*} x&=5-3y \\ -3y&=x-5 \\ y&=(x-5)/(-3) \end{align*}$$ But this was apparently wrong and the correct answer was $(5-x)/3$. Does anyone know…
emma
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fraction multiplication - having trouble with picture

I have this problem where 3/4 x 2/3 and answer is 1/2 however, I am having hard time finding the correspondent picture from the attach file. Is the answer H or O? if yes why? I am helping my son and it's been a long while I done this.
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fraction simplication, resolution with one variable

I'm having some problems to understand a simplification and I know the correct answer but I'd like to understand why my method is wrong or what rule I'm breaking. I have an equation like the following: $$Fr \cdot \left( \frac1{Sr} + \frac1{Sp}…
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Simplify complex fraction

This is a really low level question. I'm trying to simplify $$f(x) = \frac{36x^{-2} -3x^{-1} -18}{12x^{-2} -25x^{-1} +12}$$ After factoring, removing negative exponents, and flipping the second fraction I get $$f(x) = \frac{1}{3(3x+2)(4x-3)} …
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Simplify the fraction

I want to simplify this fraction $ \frac {1+a+a^2+...+a^n}{1+a^{-1}+a^{-2}+...+a^{-n}} $ where, $ a \in {\mathbb R^*} $ and $ n \in {\mathbb N^*} $ I think is some kind of formula here
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SAT question... confused

At a certain university, 1/4 of the applicants failed to meet the minimum standards and were rejected immediately. Of those who met the standards, 2/5 were accepted. If 1200 applicants were accepted, how many applied ? please help me in this…
naru
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