Mathematics Stack Exchange
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Questions tagged [rational-numbers]

Questions about numbers expressible as the quotient of two integers. For questions on determining whether a number is rational, use the (rationality-testing) tag instead.

A rational number is any number that can be expressed as the quotient or fraction $\frac pq$ of two integers, with the denominator $q$ not equal to zero. Since $q$ may be 1, every integer is a rational number. The set of all rational numbers is usually denoted by $\Bbb Q$; it was thus named in 1895 by Peano after quoziente, Italian for "quotient".

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Is every integer a rational number?

Why is this the case? $0$ is an integer and it can't be divided by $0$... It's on my textbook, as it says We conclude that every integer is a rational number, and so the rational numbers form an extension of the integers.
Eric R.
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Why is it not possible to cross out common denominator(?) in a rational expression? (Example)

I tried this(couldn't find latex code to cross over): $$\frac{3}{5}-\frac{4}{5x}+\frac{1}{x}=\frac{3}{5}\cdot5x-\frac{4}{5x}\cdot5x+\frac{1}{x}\cdot5x\neq 3x-4+5$$ Why is this not possible? My spesific problem is that I was under the impression…
Hills
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Why do we switch the denominator and numerator when we divide fractions?

Why do we switch the denominator and numerator when we divide fractions? I've been trying to find out why and I've asked several people and checked many websites but none that give me a good answer. Help?
Anna
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simplify this expression 2-√(2+√3)/√(2+√3)

2-√(2+√3)/√(2+√3) I need to simplify this. Can I multiplay with 2-√3 the numerator and dominator? I need your help.
dona12
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Can the set of positive rational numbers be decomposed into two non-empty, disjoint parts such that closed by the addition for?

I can't get started, and I'm pushing for a deadline. I can't start, Thank you! Can the set of positive rational numbers be decomposed into two non-empty, disjoint parts such that closed by the addition for?
panda
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Problem with rational numbers

Let $x\in\mathbb{R}$. Demonstrate that if the numbers $a = x^3–x$ and $b = x^2 +1$ are rational, then $x$ is rational.
Alexx
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why is -4 a rational number

I need to know why -4 is a rational I am very confused. I am doing my homework and have been stuck on this question the whole time I thought that it would be a intger. edit:thanks for the help
Princess Nik
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The difference between two rational numbers always is a rational number

Claim: The difference between two rational numbers always is a rational number Proof: You have a/b - c/d with a,b,c,d being integers and b,d not equal to 0. Then: a/b - c/d ----> ad/bd - bc/bd -----> (ad - bc)/bd Since ad, bc, and bd are integers…
Tvisha Gopi
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Recurring duodecimals fractions

I get the idea about duodecimals from what I read till I reach the fractions point where: $\frac{1}{8}=0.16$ instead of $0.15$ $\frac{1}{9}=0.14$ instead of $0.13333333$ $\frac{1}{5}=0.249797979797$ instead of $0.24$ Why is that happening I…
user3566929
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Rational Numbers Proof

Apologies for the vagueness before, I'm new here. I hope this clears it up: Show that, for all non zero $b\in \Bbb Z$, $${(0,b)}=((a',b')\in F:a'=0)$$ $$F=((a,b)\in \Bbb Z*\Bbb Z: b\ne 0))$$ where F defines $\Bbb Q$ The problem states that it is a…
Benjamin
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