# 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.

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### Given a fraction a, what's the terminology for a fraction b, which when added to a equals 1?

As the title says... Given a fraction x, what's the terminology for a fraction y, which when added to x equals 1? I'm assuming there must be a name for this. Something similar 'reciprocal' in ...
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### Is this fraction a natural number only in case ${n_1}^2+{n_2}^2+{n_3}^2={m_1}^2+{m_2}^2+{m_3}^2$?

Suppose that $m_1,m_2,m_3,n_1,n_2,n_3 \in \mathbb N$ and $m_1<m_2<m_3$ and $n_1<n_2<n_3$. If $\dfrac {{n_1}^2+{n_2}^2+{n_3}^2-3}{{m_1}^2+{m_2}^2+{m_3}^2-3}$ is a natural number, ...
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### Simplify simple fractions after Hospital's rule

I'm having trouble simplifying the result of complicated limits which contain mutliple fractions. I understand this is basic math level, but i find it difficult to find exercices to practice that ...
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### Simplify the following expression

$$\left(\frac{4}{27}\right)^{3/2}$$ I am trying to figure out how to solve this problem and my teacher was not explaining it well enough for me to grasp it. Can anybody maybe help me with step-by-...
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### unique ringhomomorphism from the Field of fractions to another field

$R$ is a ring, $L$ a field and $K$ the fraction field constructed from $R$. For any injective ring homomorphism $f=R \rightarrow L$, there is a unique ring homomorphism $\tilde{f}:K \rightarrow L$ ...
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### Equation to find when two cycles of different periods synchronize naturally

I am trying to find an equation that will predict exactly when two cycles of different periods will re-synchronize naturally. Here is a pic of some cycles with different periods: https://i.stack....
What is the best way to solve this integral? \int_{0}^{\pi/2}\bigg(\frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{1}}e^{m\frac{\sin^{2}\left(x\right)}{\sin^{2}\left(x\right)+c_{1}}} + \...
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 ...