Moltiplicazione tra frazioni

Salve,volevo chiedere,qual'è la definizione di moltiplicazione tra frazioni?
Inoltre,perchè per ottenere il risultato di tale operazione,si moltiplicano i numeratori e i denominatori delle due frazioni tra di loro? Cosa giustifica questo modo di procedere?

Moltiplicare un numero per $a/b$ è come moltiplicare per $a$ e poi dividere per $b$. Quindi se facciamo $n/m\cdota/b$ otteniamo $((n\cdota)/m)/b$

Notiamo che dividere prima per $m$ e poi per $b$ è come dividere per $m\cdotb$ quindi scriviamo direttamente $(n\cdota)/(m\cdotb)$

Non so bene se ho risposto ai tuoi dubbi

In order to answer to your question, it is necessary to introduce some crucial and important algebraic structures and some tools, which are dealt in a course of Commutativa Algebra, in particolar the fractions' field of the domain $\mathbb{Z}$ (which is $\mathbb{Q}$).
Intuitively, we have to know that the moltiplication of two fractions is a function which attaches to these two fractions a third fractions, which is defined as you know.

Hi pandistelle007 and welcome to this room, which is dedicated to students from grade 6 to grade 8.
It means that the students will be from 11 to 14 years old.
Maybe your explanations are too much for them...



By the way, where are you from?

Yes, sorry guys. I wanted to do just the idea that it is necessary to have some notions and knowledge of Commutative Algebra (we talk about university level) in order to giustify in a a sense the operations which we do every days.

P.S. I'm a PhD student in Maths in Italy

Ultima modifica di pandistelle007 il 23/09/2021, 21:06, modificato 1 volta in totale.

@pandistelle

Testo nascosto, perché contrassegnato dall'autore come fuori tema. Fai click in quest'area per vederlo.

I mean are you Italian, American, Irish, Iranian ...?

@gio73
Yeah, I'm Italian for a certain percent

Notiamo che dividere prima per $m$ e poi per $b$ è come dividere per $m\cdotb$

In base a cosa possiamo dirlo?

In order to answer to your question, it is necessary to introduce some crucial and important algebraic structures and some tools, which are dealt in a course of Commutativa Algebra.

Do you mean to answer more clearly or to answer in general?

In order to answer to your question, it is necessary to introduce some crucial and important algebraic structures and some tools, which are dealt in a course of Commutativa Algebra.

Do you mean to answer more clearly or to answer in general?

Both of them. It is possible to generalize what happens in $mathbb{Q}$ and at the same time understand better everything