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# Intro to remainders

Sal shows how a remainder is what's left over in a division problem. Created by Sal Khan.

Video transcript

Let's take the number
7 and divide it by 3. And I'm going to
conceptualize dividing by 3 as let me see how many groups
of 3 I can make out of the 7. So let me draw 7 things--
1, 2, 3, 4, 5, 6, 7. So let me try to
create groups of 3. So I can definitely create one
group of 3 right over here. I can definitely create
another group of 3. So I'm able to create
two groups of 3. And then I can't create
any more full groups of 3. I have essentially this thing
right over here left over. So this right over here, I
have this thing remaining. This right over
here is my remainder after creating as many
groups of 3 as I can. And so when you see
something like this, people will often
say 7 divided by 3. Well, I can create
two groups of 3. But it doesn't divide evenly, or
3 doesn't divide evenly into 7. I end up with
something left over. I have a leftover. I have a remainder of 1. So this is literally saying 7
divided by 3 is 2 remainder 1. And that makes sense. 2 times 3 is 6. So it doesn't get
you all the way to 7. But then if you have
your extra remainder, 6 plus that 1 remainder
gets you all the way to 7. Let's do another one. Let's imagine 15 divided by 4. Let me draw 15 objects-- 1, 2,
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Now, let me try to divide
it into groups of 4. So let's see, that's
one group of 4. That's another group of 4. And then that's
another group of 4. So I'm able to create
three groups of 4. But then I can't create
a fourth full group of 4. I am then left with this
remainder right over here. I have a remainder
right over here of 3. I have 3 left over. So we could say that 15
divided by 4 is 3 remainder 3. 4 goes into 15 three times. But that only gets us to 12. 4 times 3 is 12. To get all the way to 15, we
need to use our remainder. We have to get 3 more. So 15 divided by 4,
I have 3 left over. Now, let's try to
think about this doing a little bit of our
long division techniques. So let's say that I have 4. Let's say I want
to divide 75 by 4. Well, traditional long
division techniques. 4 goes into 7 one time. And If you're looking
at place value, we're really saying the 4
is going into 70 ten times, because we're putting
this in the tens place. And then we say, 1 times 4 is 4. But really, once again,
since it's in the tens place, this is really
representing a 40. But either way, we
subtract 4 from the 7. We get a 3. And then we bring down this 5. And we say 4 goes into 35. Well, let's see. 4 times 8 is 32. 4 times 9 is 36. That's too big. So it goes 8 times. 8 times 4 is 32. You subtract 35 minus 32 is 3. And 4 doesn't go into 3 anymore. So here I have this 3 left over. I have a remainder of 3. So you could say that 75 divided
by 4 is equal to 18 remainder 3.