#division

45 messages · Page 1 of 1 (latest)

dreamy crow
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here "how many times the denominator goes into the numerator" definition "failed"

its hard to visualize the solution with it
this problem shows up when trying to do stuff like

200000s / 86400s

since here the definition "x amount of the numerator per 1 amount of denominator " fails
and this is the biggest problem when trying to make formulas for more complicated stuff later

so again:

so the questions is how many yo-yos are in a single pack, right ?
so is we think of division as how many times denominator goes into the numerator (and we are ONLY allowed to think of division in this way for now )

14 yo-yos / 7packs = 7 packs go 2 times into 14 yo-yos

how does this information help us answer
how many yo-yos are in a single pack

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dreamy crow
quaint granite
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You can think of a/b as the unique number that, when multiplied by b, gives a

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For example, 14/7 × 7 = 14

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(But also 2 × 7 = 14, so 14/7 = 2)

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Or 200000/86400 = 125/54

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Since 125/54 × 54 = 125, 125/54 × 54 × 1600 = 125 × 1600

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Then 125/54 × 86400 = 200000

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But also 200000/86400 × 86400 = 200000, so 200000/86400 = 125/54

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This is also why you can't divide by zero

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Anything multiplied by 0 is 0, so whatever we say 2/0 is, it must be 0 when we multiply it by 0, and not 2

dreamy crow
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okay this looks dense so I will take some time reading it, but I just remembered a way to visualize both definitions working in this case

you can look at it this way
one sec

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this way both give the same answer
so here think of it as repeated subtraction still works, I think

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so it still gives you indirectly a result "something per 1 unit of something"
really interesting

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this shows you how many "yo yos" each square "ate"

quaint granite
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Yeah, that makes sense

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If you were to try to divide, say, 20 by 7, this would fail, which is what I think you're interested in

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You would get 1 box with 2 and 6 boxes with 3 yo-yos

dreamy crow
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its still confusing if each orange square is a pack a yoyo sadly

quaint granite
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(and actually 20/7 = 2 + 6/7)!

quaint granite
dreamy crow
# dreamy crow

well, when using "x amount of the numerator per 1 amount of denominator "
this will simply tell us
14 yoyo-s / 7 packs = 2 yoyo-s per pack

like in this picture

so yoyo-s are in the numerator and packs are in the denominator

quaint granite
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Yeah

dreamy crow
# dreamy crow

but here its a little bit different
"how many times the denominator goes into the numerator"
14 yoyos / 7 yoyos = 2 yoyos per 1 yoyo

quaint granite
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Oh

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Ah, but in this case, 7 isn't the number of yoyos

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It's the number of yoyos per pack

quaint granite
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You can think about it as a question of how many packs you can make with 14 yoyos, if there's 7 in a pack

dreamy crow
dreamy crow
# dreamy crow

we should be able to solve this using only repeated subtraction

and I cant fully understand how this tells us the number of yoyos per pack

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its close tho, but it still looks like its telling me that there's 2 yo-yo's per 1 yo-yo

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im going to eat something and come back to try to figure this out

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oh nvm

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im stupid

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2 yo-yos per pack

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@quaint granite do you think that this is a nice visual way to prove that both methods can work in this problem/anywhere ?

quaint granite
quaint granite
dreamy crow
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but saying that 7 packages go into 14 yoyos 2 times is a bit weird (bottom picture )