why does this definition not work here ?

[glacial grotto]

seems like the definition of a "whole" does not work when thinking of division as "amount of stuff in a group"

[past igloo]

in a fraction $\frac{a}{b}$

[marble compass]

iaminfinityiq

[past igloo]

$a$ is called the numerator

[marble compass]

iaminfinityiq

[past igloo]

while $b$ is called the denominator

[marble compass]

iaminfinityiq

[past igloo]

and if according to the ones that the user explained, the result is counted as the second one below

[glacial grotto]

yeah but thats not what im asking

[past igloo]

then what do you mean?

[glacial grotto]

look at the picture I posted, the definition is not correct if you think of division like this

whole does not have equal parts in it

[past igloo]

well then the correct definition here is the second line

that one is a whole

[past igloo]

this one means that the result is 2 remainder 1

[glacial grotto]

that souldnt be possible since both are division
first one is thinking of division as "amount of groups" and the second one is "amount of stuff in a group" the definition should work for both

[past igloo]

did you learn multiplication?

the first one says that

how many groups of 2 can fit in 5

[glacial grotto]

yes thats what im saying

[glacial grotto]

you can also think of it as reverse of subtraction

[glacial grotto]

so im 90% sure that the definition is not correct

[glacial grotto]

do you understand what im trying to say here ?

[past igloo]

wdym the definition is not correct

did you learn multiplication

answer me and let me explain

and also decimal numbers

[glacial grotto]

your not listening to what Im saying, first example does not have equal amount of stuff in it, and you said that is true, so Idk how the definition is not correct if it is no true for both ways of thinking of division

[past igloo]

just answer my question

[glacial grotto]

yes ?

[past igloo]

okay

so im going to tell you

[past igloo]

what's the difference between the 2 examples that you drafted

the first one, you got 5 wholes

and divided into groups of 2

you get 2 groups and a remainder of 1 whole

or if a = q * b + r

q as the quotient and r as the remainder

then

$\frac{a}{b} = q$ with a remainder of $r$

[marble compass]

iaminfinityiq

[past igloo]

but in the second example

if a = q * b

(q can be a decimal number)

then $\frac{a}{b}$ actually equals to $q$

[marble compass]

iaminfinityiq

[past igloo]

in your second example:

then the definition means that how much that a group have for 5 to divide into 2 equal groups

or in that case: 5 / 2 = 2.5

[glacial grotto]

that remainder has to be stored somewhere, so its its eather going into first 2 groups (cant since they are full) or he is stored into the 3th group as 0.5 so the 3th group is 0.5
so that would mean
g1 = 1
g2 = 1
g3 = 0.5
so the definition, "tells us how many equal parts are in a whole" is no true, since

1. in the "amount of groups" division we count amount of groups, and not how much stuff is in them
   2.even if the definition would change to "amount of equal groups or amount of equal stuff in groups" that would still not be true since g3 is not equal to g2

but that definition would work for proper fractions

actually the answer "there are 8 parts per whole" also assumes that we are using the "amount of stuff per group"

since in the second example we have 0.875 stuff per group

so that is not true as well

hmm

[past igloo]

stop overthinking

that remainder is not stored anywhere in the first example

like

5 / 2 = 2 R1

that's the first example

and for the second example

if you say that remainder must be stored somewhere

then it divides itself into 2 parts

and spread equally into each group

[glacial grotto]

it is not "stored" bc we are counting how much groups of 2 we have
and we have 2.5 of them

[past igloo]

no no

that's what not i mean

let's give a clear definition

a / b means that

each group should be equal to something

[glacial grotto]

does not have to be that

[past igloo]

in b groups such that all a wholes will be divided equally into b groups

okay?

[glacial grotto]

it should be "amount of stuff PER group" or "amount of stuff IN a group"

[past igloo]

it has to be

[past igloo]

yes

like that

but equally

okay?

[past igloo]

so

5 / 2

means that you try to divide 5 into 2 equal groups

one case is that the remainder is NOT stored anywhere

because you got no way to divide it in terms of whole numbers

the other case

is that you brute force divide those 5 into 2 groups

so each group has 2 wholes but left 1 whole remaining

that 1 whole is split into 2 equal parts and spread equally into 2 groups

first case: 5 / 2 = 2 R1

second case: 5 / 2 = 2.5 (the remainder is split into 2 equal parts and spread equally)

another example is 7 / 4

for the first case

7 / 4 = 1 R3

for the second case

7 / 4 = 1.75 (3 wholes are divided equally into 4 parts, then those parts are spread equally into 4 groups)

[glacial grotto]

what are "parts" here

[past igloo]

okay

that's 5 / 2

7 / 4

the remainder 3 is divided into 4 parts

each part is 0.75

or $\frac{3}{4}$ of a whole

[marble compass]

iaminfinityiq

[glacial grotto]

that is effectively cutting it into 4 equal groups, the "remainder" does not really exist here, that is just there to make it easier for you to cut stuff
in the end you are still cutting the number into 4 equal groups,
so here what is a "whole" im assuming its the number? and amount of groups is "parts" right ?

[past igloo]

i define whole as 1

and the parts i mean by the remainder cut into 4s

[glacial grotto]

here the 7/8
/8 means 8 parts per whole
so 7 is "whole"