>Multiplication is repeated addition >2*5 is the same as

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>>8919378
>multiplication is repeated adding
>2.3692 groups of 2.59285

>>8919488
That makes perfect sense.

You can have 2 groups of a number then take a fraction of the number n, thus have 2.n groups of a number

2.5 * 10 = 10 +10 + 5

>>8919378
I think what you are really asking is "why when you multiply two negative numbers together do you get a positive number?".

It's a natural result of the abstract algebra structure known as a "field" that follows from its axioms.
https://en.wikipedia.org/wiki/Field_(mathematics)

I don't feel like writing up the LaTeX, but this guy walks you through the proof.
http://www.school-for-champions.com/algebra/product_of_two_negative_numbers.htm

>>8919510
What if both numbers are rational

It doesn't mean anything to have a negative group of something. In general we define the multiplication of integers as:
If [math]a,b\in\mathbb{N}[/math],
then [math]a\cdot b=\underbrace{b+b+\cdots+b}_{a~\text{times}}[/math].
If [math]a\in\mathbb{Z}\setminus\mathbb{N},b\in\mathbb{N}[/math], then [math]a\cdot b=-(\underbrace{b+b+\cdots+b}_{-a~\text{times}})\,.[/math]
so in your case with -5*-2 we have
and -5* - 2=- (-2+-2+-2+-2+-2)=--(2+2+2+2+2)=10

>>8919586
i probably meant that b is in the set of integers

>>8919378
Maybe think in terms of money. Say you pay 10k in taxes per year, so that over 5 years you pay 50k, so you have a net gain of -50k. This is 5*(-10k)=-50k. Now for (-5)*(-10k) is if instead of paying 10k per year for 5 years, you instead receive 10k per year for 5 years, which is a net gain of 50k.

>>8919378
suppose -2*-2 = -4.
then since -2*2 = -4, it follows that 2 = -2, a contradiction
therefore -2*-2=4.

>>8919510
That's 3 groups, not 2.5 groups, you just changed the value in the third group to try to fix your definition which doesn't make sense.

>>8919378
Multiplication isn't actually repeated addition, that's a simplification for ease of understanding for children.

That said, the examples you give are trivially describable as repeated addition

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>>8919378

>Can anyone explain to me what it means to have negative groups of something?

Don't look at it that way. The idea is: with positive integers, multiplication is defined (or let's take it as a definition, it doesn't change the argument) as adding groups of the same size. I think it comes from examples like this

S S S S S
S S S S S

You have two ways to count that: you either add 5 times the number 2 (count columns) or add 2 times the number 5 (count rows). As you're counting the same thing, both procedures should give the same result: 5×2=2×5=10.

When extending this idea to integers in general, you may lose the intuition you had in the positive integers. Why it works? That's another story.

Moral of the story: when you win some, you lose some as well.

>>8919378
Here anon, it explains it perfectly:

https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-mult-divide-negatives/v/why-a-negative-times-a-negative-is-a-positive

>>8919531
a = p/q
b = m/n
ab = pm/qn
p,q,m,n € Z (so the repeated addition shit makes sense, just take the ratio afterwards)

>>8919784
>multiplication isn't actually repeated addition
most examples people try to use to "prove" this are brainlet-tier misunderstandings

so show off your stuff

Sometimes analogies don't work well. We use them to build intuition, understanding that in less than perfect situations they may not literally apply.