Main content

## 5th grade

### Course: 5th grade > Unit 5

Lesson 4: Multi-digit division- Long division with remainders: 2292÷4
- Long division with remainders: 3771÷8
- Introduction to dividing by 2-digits
- Basic multi-digit division
- Dividing by 2-digits: 9815÷65
- Dividing by 2-digits: 7182÷42
- Dividing by a 2-digits: 4781÷32
- Division by 2-digits
- Multi-digit multiplication and division: FAQ

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Introduction to dividing by 2-digits

Learn the art of dividing by two-digit numbers. Watch how to approximate numbers for easier division and practice this skill with examples. The video emphasizes the importance of trial and error in learning multi-digit division.

## Want to join the conversation?

- Why is so hard but easy at the same time?(25 votes)
- No clue at all.(2 votes)

- defanition of MATH,

Mental

Abuse

To

Humans.

-PS Sorry,

MATH lovers(20 votes) - For me, it's kinda hard to divide multi-digit numbers. Anyone else?😟(16 votes)
- I commented on this two years ago and I said that this was hard. Well, now I can do this really easily! This just shows with pratice, things become easier!(6 votes)

- 1:26did he round that right?(8 votes)
- Yep, 186 is closer to 30*6 than any other multiple of 30. Next closest would be 30 * 7, which is 24 away instead of 6 away.(9 votes)

- Flag all the “doges”. Please don’t think about posting it either.(12 votes)
- is anyone still on here(5 votes)
- I dont understand remainders(1 vote)
- When you divide something, sometimes a number doesn’t come in the divisor’s time tables. You would write the closest number but smaller than the dividend and then subtract the number from the dividend. That’s what a remainder is.(9 votes)

- 1:02i don't understand(2 votes)
- Hello!

At1:02Sal says 31 is close to 30 and 30 is equal to 3*10. So if you know your multiplication table of 3, you just need to multiply your result by 10. For example:

30*9= 10*3*9 (remember, 30= 10*3)

10*3*9= 10*27 (because 3*9=27)

10*27=270. So 30*9=270.

In the problem posed in the video, we are trying to divide 186 by 31. So let's find a multiple of 30 which is close to 186. (Why 30? because 30 is close to 31, and it is easier to calculate with 30 than 'with 31)

30*2= 10*3*2= 10*6=60

30*3= 10*3*3 = 10*9= 90

30*4= 10*3*4= 10*12= 120

30*5= 10*3*5= 10*15= 150

30*6= 10*3*6= 10*18=180. 180 is close to 186 so maybe 6 (because 30*6 is 180) is the result of 186 divided by 31. Sal verifies it in the video at01:55. (He multiplies 6 by 31 and he gets 186)

I hope I helped you!(7 votes)

- Why must we find numbers that are close to but not exact? I'm sure it's just my ignorance, but I think this is an error in human knowledge that we have accepted as an axiom because it works. The "if it fits it ships" model.(6 votes)
- If we weren't to round to the nearest number it would take more steps and would make it harder, but usually if it's school work and it tells you to round then you should do it.(0 votes)

- Why does it say "At4:40Sal says plus three but meant to say plus five."(4 votes)

## Video transcript

- [Instructor] What we're
going to do in this video is start trying to divide
by two-digit numbers. And as we'll see, this is
a super important skill that a lot of the rest of
mathematics will build off of, but it's also interesting
'cause it's a bit of an art. So let's just start by trying to compute what
186 divided by 31 is. And of course, we could
also write this as 186 divided by 31. Pause the video, and see
if you can figure it out. All right, now let's work
through this together. I assumed you've given it a go at it. So I don't have my 31
times tables memorized, so I can't just immediately
tell you the answer. But my brain tries to
approximate these numbers so that my times tables
knowledge does come in handy. For example, 31 is close to 30. And this is why I'm saying
it's a bit of an art, but I'm saying, hey, look,
this is pretty close to 30. And if I think about multiples of 30, well, those are just
the multiples of three with an extra zero or the
multiples of three times 10. So the multiples of 30 are 30, 60, 90. Instead of three times four is 12, 30 times four is 120, 150 instead of 15, 180 instead of 18 for 30 times six, and gee, this looks pretty close to 180. So this looks close to 30 times six. And if this is close to 30, well, maybe, maybe this is, maybe this is going to
be six right over here. And I'm gonna put a question mark because then the natural
thing to do is to actually try it out. Figure out what is six times 31? I'll put the question mark here again. Is this equal to six? Well, the art part is you've made a good, or we've made a good guess here. Now let's try to verify that maybe it is six, maybe it isn't. So let's multiply six, or let's multiple 31 times six. 31 times six, one times six is six, and then three times six,
which is really 30 times six, is gonna be 180 right over here. So this is 186. So it all works out. 186 divided by 31 is indeed six. We can get rid of this question mark here. Let's do another example. So let me delete. Let me delete that as well. Let's say we want to figure out what 336 divided by 48 is equal to. So pause this video, and see
if you can figure it out. So the way I would think about it, this thing right over here is close to 50, close to 50. And this thing, well, if you think about the multiples of 50, you have things like 300,
which would be 50 times six. And then you have 350, which
would be 50 times seven, because five times seven is 35. And so let's think about this, and actually let me
write these things down. If I were to say 50 times six, that's the same thing as, well, that's gonna be five times
six times 10, which is 300. If I say 50 times seven, that's going to be 350. Five times seven is 35, and then you're multiplying that by 10. But this number is someplace
in between 300 and 350. So my candidates for
what this is going to be, well, I'm saying, hey, maybe this is six, maybe this is seven. And what I would do is I
would try out each of them. So let's try out 48 times six. So let's try that, this first candidate out. 48 times six, so eight times six is going to be 48. Four times six is 24, plus four is 288. So that actually seems a
good bit lower than this. It actually seems almost exactly 48 lower. So I could probably, I'm
feeling pretty confident that I can squeeze another 48 into this. So instead of squeezing, instead of being able to
divide 6/48 into this, I'm feeling pretty good that
maybe seven is the answer, but let me try it out. So this, so six is not going to be my answer, I tried it out. Let me try 48 times seven. 48 times seven, eight times seven is 56, four times seven is 28, plus three, 336. That's exactly right. So there you have it, with a
little bit of trial and error, but it was an informed trial and error, we got 336 divided by 48 is equal to seven. This is what I meant,
that it's a bit of an art.