Help for an idiot

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i've never seen that style of notation used, but then again i probably grew up in different parts of the world. anyway, here's the idea, i'm sure you'll be able to adapt it.

let's divide 3584 by 6

you start from the left of the big number.

does 6 fit into 3? nope. add the next number.
does 6 fit into 35? yes. how many times? 5 times.
is there a remainder? 5*6=30 therefore yes, there is a remainder of 5.
that remainder now takes the position of the right-most number we've worked on so far, ie the second from the left (x5).
now we're back to the algorithm.

does 6 fit into 5? it better not be, because we declared 5 a remainder. therefore, add the next number towards the right.
does 6 fit into 58? yes. how many times? 9 times.
is there a remainder? 9*6=54 therefore yes, there is a remainder of 4.
the 4 is now the third position from the left (xx4).
back to the algorithm.

does 6 fit into 4? nope. add the next number.
does 6 fit into 44? yes, 7 times.
remainder is 2.

now the "how many times" numbers give us the result of the divison.
3584 divided by 6 is 597 with a remainder of 2.

picture is how i would write that down in school. mark your starting number (35). write down the "how many times" on the right so it spells the result. write the remainder in the line below, then carry the next number down.

>>54882
Think about it as a step-wise approximation of the quotient (result). You determine in each step a digit, beginning with the highest one.

You write in each step single digits as in your example or in >>54901 but the interpretation is that you compare and subtract "big" numbers.

If you divide 3584 by 6 as in >>54901 :

You first check if the first digit, 3, is divisible by 6 which is not possible. This means that the result is less than 1000:

3584 : 6 < 1000

Next, you take the first two digits, 35, and see that 6 fits 5 times in this result. This means

3584 : 6 = 500 + r where r < 100

That is, the higher-most digit is determined.

If you multiply by 6,
3584 = 6 (500) + 6r = 3000 +6r

Simplify:
3584 - 3000 = 584 = 6r

And therefore
584 : 6 = r

And you can repeat the steps above to determine the next digit (remind that the first result for the quotient is 500 + r where r < 100, that is, it doesn't change the digit 5.