How do I divide? I've watched so many 3rd grader lesson videos on youtube and read basic division books but it never clicks in. I just can't work out where you imagine the numbers from
Are remainders real?
This is something a 6 year old should know why can't I figure it out?
9 / 4 is 2.25 but all the youtube videos tell me it's 2 with remainder 1 and I can't even figure out where the 2 came from
Is there some mental division method I'm missing?
Multiplication...but backwards.
Just think about how many times one number can go into another
The way I think of multiplication is like if 3 x 2 is 6 that's 2 lots of 3
But to do the same with multiplication would be to take 6 and cut it into 2. I can imagine that like cutting something in half, it'd be 3 but then to I can't wrap my head around how to image what the number would be to cut it into 3s or 7s or 9s
If I was having trouble multiplying something by 7 or 9 I could just take the number and add it 7 or 9 times but you can't go that slowly with division, you have to figure it out all in one
You have a dozen eggs, and want to give them equally to five people. Try it. You can give them each 2 eggs, but then you will have two left over that you can't give equally to all five people. The two left over are called the remainder, because they remain undivided, because you can't split the eggs into peices.
Now imagine instead of eggs they were all donuts. Then you could give everyone their two donuts, and then cut up the remaining two so that they can be split evenly. Then everyone receieves 2 donuts and 2/5 of a donut which equals 2.4 donuts.
This shows two ways of dividing. You can't split the eggs, so you are left with a remainder at the end, but with the donuts, you can divide the remainder to give everyone a fraction of a donut. Both ways can be right, depending on if you are dividing something which can be split fractionally or not.
Wait so if I had 9 / 4
I put 4 into 9, I can still fit another 4 in and then I have 1 left over. I can work through that bit by bit but I don't know what to do with that 1 to turn the answer of 2 into 2.25
If I had 23 / 7 I can put 7 into 23 three times with 3 left over but I don't understand how to turn 3 with 3 left over into 3.2
I actually think your post has helped me, that method does feel like multiplication backwards
You can divide the remainders? but only some remainders? Also I haven't understood your example but I think it's just that I'm a bit tired. Is there a name for dividing the remainders? Something that I can look up to continue studying? All the content I've been able to find on division has been for 6 year olds and it seems to stop there.
I appreciate all the help you've given me, I feel one step closer to understanding division
It's 2 and 1/4
Is that by taking the remainder 1 and diving it by the 4 to get 0.25 and then adding it onto the answer? But what if it was a situation where the remainder division led to another remainder? do I divide it again and so on?
I would stick with dividing all remainders, there's very little use to remainders until you start dividing algebraic expressions
You don't divide the remainders in algebra? So remainders are real? er I don't want to derail with a discussion of it to much, I feel pretty far away before in other fundamentals before I'm ready to begin with algebra if that's okay with you
>You can divide the remainders?
No, its only called a remainder if you can't divide them.
1. Start division
2. Divide all the whole pieces
3. Is there any left over? No=done / Yes=step#4
4. Can you divide the leftovers? (This depends on the situation, or in class a teacher should specify whether she wants you to leave remainders) If not, then the leftover is the remainder. If yes, then use fractions.
if that were to happen, yes, you would just repeat the process and add.
This sound very gay.
What would be a situation that the remainders couldn't be divided? Now knowing that you can continue to divide the remainders indefinitely of course assuming the work you're doing isn't asking from remainders
Ah bugger I've gotta go I should have made this thread when I had more free time
Thank you all for your help, I've learnt something today about division and I'm sure I'll reach the end of the tunnel soon
>What would be a situation that the remainders couldn't be divided?
If you and your husband are divorcing and want to split your 3 kids between the two of you, then you have 1 remainder kid, because you can't split her.
Usually, however, you can keep dividing, so practice it with the fractions, because thats more useful.
You don't need decimals, if you have completely divided, as in the remainder is less than the number being divided by, you can just put the remainder over that number.
9/4 = 8/4 + 1/4 = 2 + 1/4 = 2.25
What's the intuition behind dividing fractions with fractions? I get dividing a fraction by a whole number, you're just dividing a piece into a smaller piece, but the former just doesn't make sense
Just move the decimals then divide.
30.251/4.8 = 30251/4800
1.Fraction * 2.Fraction flipped upside down. That's math for six graders.
Using this user's example, you can also imagine having a big tank of 30.251 liters of water and having to pour them in smaller buckets to carry them around.
The bucket can be filled with 4.8 liters.
How many times do you have to refill the bucket if you want to transport the 30.251 liters?
Now if you fill 1 bucket with 4.8 liters of water, there's 30.251-4.8=25.451 liters of water left.
You can keep subtracting until the first number's less than the second, but you can also say "well 4.8 is about 5 liters and 6*5 is 30 so will probably need to fill my bucket at least 6 times"
But! You've got to add the difference of 4.8 and 5 back to the first number like so:
30.251-(5*6) + (0.2*6)=0.251 + (0.2*6)=1.451
We're left with 1.451 liters which can be carried in one bucket.
Now we ask the question "how much of my bucket is filled up if I put 1.451 in it?"
What we do is this:
1.451/4.8 = (1.44 + 0.011)/4.8= (3*0.48 + 0.011)/4.8 => (we're leaving the 0.011 out for now, since that's a really small number) => (3*0.48)/4.8
Now we have 1/10th of 4.8 times 3 (0.48=4.8/10)
which is 3*1/10=3/10
So with the last bucket, 3/10th of the bucket is filled with water.
Stories like these make calculation take a bit longer, but if you practice a lot you'll soon get the hang of it and this'll just flow out of your pen like nothing!
Remainder is a dumb made up concept meant to promote long-division, which most people forget literally after the sixth grade.
Just multiply by the reciprocal.
>1 to turn the answer of 2 into 2.25
after putting 4 into 9 two times, you have 1 remainder - how many times can 1 go into 4? a quarter, or 0.25
16 / 5 = 3.20
so 5 goes into 16 three times, giving us the remainder of 1... how many times does 1 go into 5? 20% or 0.20
>remainder is a dumb made up concept
>what is modulo arithmetic
Please stop posting.
Could you give an example of how modular arithmetic can be useful in CS? My friend knows a really bright PhD mathematician that works as an inventor for some software firm. He said his work was just trivia applications of modular arithmetic; that the engineers and computer programmers just didn't get it. He said its all just remainders of division of integers to them, and that they never learn the power of bidirectional congruence or to learn to think in terms of residue class rings.
I know the algebraic terms from above; we can define an arithmetic on the remainders of division of integers that has the same internal structure as the integers. Perhaps i'm not far enough in both CS or algebra because it isn't obvious to me in what way this stuff can be applied. I've only had CS101
perhaps i shouldn't say it has the same internal structure as the integers; rather, it has a very similar structure
Lets go back to the basics first user. Multiplication is the amount of time you plus a same number, e.g. 2+2+2 = 2*3
Division is finding out how many times you added the same number together: e.g. 6/2 = finding out how many times 2+2 to make 6.
Now remainders: if you have 9 apples, and you gotta give it to 4 kids, how many will each kid get equally? 9/4 = (8+1)/4 = Each kid get 2 and you have one remain, because you can't really give it to any of them. However, the situation changes when you cut the apple into 4, which is 0.25 of an apple or 1/4 of an apple, and give a part to each kid, which makes it that each kid gets 2.25 apples.
Turning the problem into finding out numbers of times: youre finding how much each kid get equally to get 9 apples in total, or #apple + #apple +#apple + #apple = 9 (its 4 #apple because there are four kids)
Just say they're isomorphic, that's what the term you're looking for is.
Modular arithmetic is used a lot in encryption algorithms, look up RSA as an example
Didnt read the thread, sorry senpai but this is how i think of it.
9/4 = 8/4+1/4 = 2+ 0.25 = 2.25
Long division wise it looks like
_
4|9
2 with remainder of 1 which is expressed as 2 + 1/4
genius here, this is how i divide and subtract:
one minus five is one plus negative five:
1-5 = 1 + (-5) = -4
five divided by ten is five times one over ten:
5/10 = 5 * (1/10) = 0.5
I just had a level 6 math exam today, consisting of vector calculus/laplace & fourier transform theory, yet OP got me all fucked up.
I forgot about remainders, when we were 6 and had to divide 12/5 and got 2.4 why did we have to say 2 REMAINDER 2. Why the fuck does "remainders" even exist, I can't think of a mathematical application in which a remainder is relevant, well at least for 8 year olds anyway.
Why aren't we just taught that 12/5 = 2.4 from the start?
wouldn't it be a homomorphism though?
will do, thanks.
see
Yeah, pretty late, so I confused myself here.
Could just go the extra mile and say that the quotient ring of the integers by some ideal is isomorphic to it.