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### Course: Numbers & Operations - The Real & Complex Number Systems 176-188 > Unit 1

Lesson 3: Regroup whole numbers# Regrouping whole numbers: 675

Sal regroups 675 into various addition problems. Created by Sal Khan.

## Want to join the conversation?

- I'm not understanding the concept of regrouping whole numbers in this video lecture. Are subtracting from these whole numbers to simplify the equation? I'm lost on this information. Crossing the numbers out and throwing lower numbers don't tell me anything. I throw my hands up in the air.(43 votes)
- So I think where people get confused on this is that they're trying to figure out WHY you would want to do this. Under normal circumstances, you probably wouldn't sit down and actually write all of this out. The idea here is that you can take a number and break it down into many different combinations of parts and still end up with the same total.

200 = 100 + 100

200 = 50 + 50 + 50 + 50

200 = 13 + 37 + 50 + 100

and so on...

You get the idea. It's just a basic concept.(25 votes)

- Great information, but my question would be is why would anyone would actually want to actually regroup whole numbers? or, is this going to be useful later in lessons somewhere?(2 votes)
- Money! If you owe someone $25, do you have to pay them 2 tens and 5 ones? No, You could pay them 5 fives; or 25 ones; or 1 ten and 3 fives; or 1 ten 2 fives and 5 ones; etc.(21 votes)

- Can someone please clarify why I would ever want to regroup whole numbers? I do not think I have ever done so...(0 votes)
- Regrouping is needed in subtraction like 28-9=
*__*both the 8 and 9 is in the ones place but you cant take 9 from 8 so you regroup the 28 so the 2 would change to 1 and 8 into 18 so 18-9=9 and 10-00=10then just add to get the answer of 19(14 votes)

- regrouing is important in math why?(6 votes)
- The concept is used as the basis for other things like borrowing and carrying.(3 votes)

- How to round 234,489.0754 to the nearest thousand?(2 votes)
- Thousand or thousandths? There is a huge difference between the two.

Once you know which place value you want to round to, find that place in your number. Let's say you want to round to the nearest hundredth in your number. That's the second decimal place and it has a 7 in it. Find the number just to the right of that number. In this case, it's a 5 so we will round up. 234,489.0754 rounded to the nearest hundredth is 234,489.08.

Rounding works the same with or without decimals. Look at the number just to the right of the place value you want to round to. That number will tell you if you should round up or round down.(8 votes)

- when its like 86 and they say round to the nearest hundred how do I do that(0 votes)
- Let's say you want to round 123 to the nearest hundred. You look at the number to the right of the one you want to round to.

You want to round to the nearest hundred, so the place just to the right of that is the tens place. If that number is 5 or bigger, you round up. If it's 4 or smaller, you round down.

So with 123, the number in the tens place is a 2. That's 4 or smaller so you round down. 123 becomes 100.

Now let's look at 289 rounded to the nearest hundred. The number in the tens place is an 8. That's 5 or bigger so we round up. 289 becomes 300.

But what happens with numbers like 89?

Same thing. You want to round to the hundreds place so you look at the number in the tens place. What is it? 8. That's 5 or bigger so we round up. That means we have to increase the number that's in the hundreds place by 1. So what number is in the 100's place? 0. What's the next number up? 1. 89, rounded to the nearest hundred, is 100.(9 votes)

- I do not understand the concept(1 vote)
- What if a zero is in the thousands place when you regroup your number?(1 vote)
- It would be 0 thousands. For example 11527 would be 1 ten thousands + 1 thousands + 5 hundreds + 2 tens + 7 ones and could be regrouped to be 1 ten thousands + 0 thousands + 15 hundreds + 2 tens + 7 ones(0 votes)

## Video transcript

Let's think about
different ways that we can represent the number 675. So the most obvious
way is to just look at the different place values. So the 6 is in the
hundreds place. It literally represents 600. So that's 600. I'm going to do that
in the red color-- 600. The 7 is in the tens place. It represents 7 tens, or 70. And then the 5 in
the ones place. It represents 5. So let me copy and paste
this and then think about how we can regroup the
value in the different places to represent this
in different ways. So let me copy and
let me paste it, and maybe I'll do
it three times. So let me do it once, and
let me do it one more time. So one thing that we could do is
we could regroup from one place to the next. So, for example,
we could take if we wanted to-- we could take
1 from the hundreds place. Taking 1 from the hundreds
place will make this a 5. That's essentially
taking 100 away. So this is really
making this a 500. And we could give
that 100 to-- well, we could actually give
it to either place, but let's give it
to the tens place. So we're going to give
100 to the tens place. Now, if you give 100
to the tens place and you already had 70 there,
what's it going to be equal to? Well, it's going
to be equal to 170. Well, how would we
represent that is tens? Well, 170 is 17 tens. So we could just say
that 7 becomes 17. Now, we could keep doing that. We could regroup some of
this value in the tens place to the ones place. So, for example, we could
give 10 from the tens place and give it to the ones place. Let's do that. So let's take 10 away from here. So that becomes 160. This becomes 16. And let's give that
10 to the ones place. Well, what does the
ones place now become? Well, 10 plus 5 is 15. So this 5 is now a 15. Let's do another scenario. Let's do something nutty. Let's take 200 from
the hundreds place. So this is going to now 4, and
this is going to become 400. That's what this
4 now represents. And let's give 100
to the tens place. And let's give another
100 to the ones place. So in other words, I'm
just regrouping that 200. Those 200's, I've taken
from the hundreds place, and I'm going to give it
to these other places. So now the tens place
is going to be 170. We're going to have 170
here, which is 17 tens. So you could say that
the tens place is now 17. And now the ones
place, well, I had 5, and now I'm going
to add 100 to it. So it's going to be 105. And 105 ones is literally 105. And notice, this is 400 plus
17 tens, which is 170 plus 105. You add these together,
you're still going to get 675. Let's do that again. So let's take, I don't know. Let's take all of
the hundreds away. Let's take all of
the hundreds away. So that goes zero. That goes zero. And let's give 400
to the tens place. So let's give 400
to the tens place. Well, that'll make that 470. Let me do that in
that green color. That will make that 470, which
is the same thing as 47 tens. And then I still have 200
to give to the ones place. So let me do that. So I still have 200 to
give to the ones place. And so that's going
to go from 5 to 205. Once again, all
I've done is I've regrouped the value
in the number 675. Any of these still
represent 675. You can add these
numbers on the right. They all add up to 675.