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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 3

Lesson 14: Remainders- Intro to remainders
- Understanding remainders
- Divide with remainders (2-digit by 1-digit)
- Interpreting remainders
- Long division with remainders: 3771÷8
- Long division with remainders: 2292÷4
- Divide multi-digit numbers by 6, 7, 8, and 9 (remainders)
- Multi-digit division

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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.

## Want to join the conversation?

- Isn't there a way to make the remainder a fraction?(156 votes)
- Yes, the numerator will be the remainder, and the denominator will be the divisor.

Example:

13/4 = 3 with a remainder of 1, so the answer will be 3 1/4(139 votes)

- When do we use remainders in real life?(42 votes)
- I use it when dividing packages of candy canes and chocolates into goody bags for my piano students. I don't want anyone to get less than another. My husband eats the remainders. :)(92 votes)

- do you like leftovers those leftovers are remainders(9 votes)
- Is long division the easiest way to finding remainders. Or is there another way?(5 votes)
- It's the easiest with large numbers, for smaller ones, say 10 divided by 3, that's pretty easy to do counting out or however you'd wanna do it.(5 votes)

- how are u like givng it the regrouping part(3 votes)
- By "regrouping part" do you mean the remainders? Or do you mean regrouping in the subtraction part?

For the remainders, whatever is left after the subtracting is the remainder.

For regrouping in the subtraction part, you just need to be very careful with how you write it. Make the 1 that you small and try to put it below the first subtraction line to keep things tidy.(4 votes)

- at first the dot rectangle thing looks like flute or a recorder right?(3 votes)
- how to divide double digit and double digit and get a remainder.(3 votes)
- would a decimal be a remainder?(3 votes)
- When you do division, your remainder is basically where you get the decimal from, yes. When you do division, you end up with either a remainder, or you end up with the final result being a decimal. Ultimately, the decimal is the remainder divided by the divisor. So 7 / 2 is 3 with a remainder of 1, and you can divide 1 by 2 to get one half or 0.5, which you then add to the original 3. So 7 / 2 = 6/2 + 1/2, which is 3 + 0.5, or 3.5(0 votes)

- R is a left over

👾👽💩😶🌫️😶🌫️🤯🐰🍁🐱🐨🐯🐻❄️🦠🦠🐻🐻🦁🍂🌾🐱🐵🐹🐻❄️🌺👽😶🌫️🐹🐵🐨🌼🙊💩🍀👾💩🤯🐰😶🌫️👽👾💩😶🌫️🤯😶🌫️👽😶🌫️🤯👽👾💩🤯😶🌫️💩👾💩😶🌫️🤯😶🌫️👽👾👽😶🌫️😶🌫️🤯👽👽👽😶🌫️😶🌫️👾👾💩🤯😶🌫️🤯🤯(2 votes) - I dont understand these videos but other wise im good🌶️🍌🌷😁(2 votes)

## 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.