Introduction to regrouping (borrowing)

<div style="color: #000000; font-family: Arial, Helvetica, sans-serif; font-size: 12px; font-size: 12px; width: 555px;">
<table border="0" cellpadding="0" cellspacing="0"><tbody><tr><td rowspan="2" valign="top" width="140"><div style="border: 1px solid #999999; margin: 0px 10px 5px 0px;"><a href="http://www.youtube.com/watch?v=egjDLFX9VHg&amp;feature=youtube_gdata"><img alt="" src="http://i.ytimg.com/vi/egjDLFX9VHg/default.jpg" /></a></div></td>
<td valign="top" width="256"><div style="font-size: 12px; font-weight: bold;"><a href="http://www.youtube.com/watch?v=egjDLFX9VHg&amp;feature=youtube_gdata" style="font-size: 15px; font-weight: bold;">Introduction to regrouping (borrowing)</a>
<br /></div>
<div style="font-size: 12px; margin: 3px 0px;"><span>Introduction to regrouping (borrowing)</span></div></td>
<td style="font-size: 11px; line-height: 1.4em; padding-left: 20px; padding-top: 1px;" valign="top" width="146"><div><span style="color: #666666; font-size: 11px;">From:</span>
<a href="http://www.youtube.com/channel/UC4a-Gbdw7vOaccHmFo40b9g">Khan Academy</a></div>
<div><span style="color: #666666; font-size: 11px;">Views:</span>
0</div>
<div style="white-space: nowrap; text-align: left;"><img align="top" alt="" src="http://gdata.youtube.com/static/images/icn_star_empty_11x11.gif" style="border: 0px none; margin: 0px; padding: 0px; vertical-align: middle; font-size: 11px;" /> <img align="top" alt="" src="http://gdata.youtube.com/static/images/icn_star_empty_11x11.gif" style="border: 0px none; margin: 0px; padding: 0px; vertical-align: middle; font-size: 11px;" /> <img align="top" alt="" src="http://gdata.youtube.com/static/images/icn_star_empty_11x11.gif" style="border: 0px none; margin: 0px; padding: 0px; vertical-align: middle; font-size: 11px;" /> <img align="top" alt="" src="http://gdata.youtube.com/static/images/icn_star_empty_11x11.gif" style="border: 0px none; margin: 0px; padding: 0px; vertical-align: middle; font-size: 11px;" /> <img align="top" alt="" src="http://gdata.youtube.com/static/images/icn_star_empty_11x11.gif" style="border: 0px none; margin: 0px; padding: 0px; vertical-align: middle; font-size: 11px;" /></div>
<div style="font-size: 11px;">0
<span style="color: #666666; font-size: 11px;">ratings</span></div></td></tr>
<tr><td><span style="color: #666666; font-size: 11px;">Time:</span>
<span style="color: #000000; font-size: 11px; font-weight: bold;">05:27</span></td>
<td style="font-size: 11px; padding-left: 20px;"><span style="color: #666666; font-size: 11px;">More in</span>
<a href="http://www.youtube.com/videos?c=24">Entertainment</a></td></tr></tbody></table></div>

- [Voiceover] So let's see
if we can subtract 25 from 83

or if we can figure out
what 83 minus 25 is.

I encourage you to pause the video

and see if you can work through it.

So I'm assuming you've had a try.

And when you try to work through it,

you probably first went to the
ones place right over here.

And you probably said, "Hey,
I have three ones on top

"and from that I want
to subtract five ones."

But you said, "Wait, I can't subtract

"five ones from three ones.

"Five is more than three.

"What do I do?"

And what you do is what
I'm about to show you.

You do something called regrouping.

You take some of the value
that's in the tens place

and put it into the ones place.

What am I talking about?

I'm gonna do it three different ways.

So you really hopefully
understand what's going on.

Well, you want this three to be more ones.

You want it to be at least
as large as five or larger.

So how do you do that?

Well you could take a
10 from the tens place.

So instead of having eight tens here,

you could take one of them away

and then you're going
to have seven tens here.

And then if you take a 10,

you could just put 10 away from here.

You put in the ones place,
that's going to be 10.

So 10 plus three is 13.

10 plus three is 13.

So what did I do again?

83 is eight tens and three ones.

You could also think of it
as seven tens and 13 ones.

And I'm going to do it again in a couple

of different ways to make that clear.

But let's just work through this now

because now you have
13 ones minus five ones

which is going to be eight ones.

And then you go to the
tens place and you say,

"Seven tens minus two tens,

"well that's going to be five tens."

So your answer is going to be

five tens and eight ones or 58.

Now I said I would do this several ways

so that it makes a little bit
more sense so let's do that.

So another way that you could write

83 is you could write this,

this is the same thing as

80 plus three.

80 plus three.

That's the same thing as 83.

Eights tens, three ones,
eight tens, three ones.

And 25 is the same thing

as 20 plus five.

20 plus five.

Now we're going to subtract 20 plus five.

So let's write this instead as...

We're going to subtract 20.

We're going to subtract two tens

and we're going to subtract five ones.

So subtracting 25 is the same thing

as subtracting 20 and
then subtracting five.

So now let's try to work
through it just like we did.

Well we go to the ones place again.

Ones again was a five.

If I want to take five away from three,

that's hard, I don't know
how to do that just yet.

But what if I take ten from here?

So if I take a 10, if
I take 10 from there,

that's going to be 70.

And if I put that 10 in the ones place,

well 10 plus three is going to be 13.

Notice, I haven't changed
the value of the numbers.

70 plus 13 is the exact same thing

as 80 plus three which is 83.

But what's useful about this is now,

in the ones place, I can
subtract five from 13.

If I subtract five from
13, I'm gonna get an eight.

And then if I subtract
two tens from seven tens

or 20 from 70, I'm going to get 50.

I'm going to get 50.

So this is going to end
up being 50 plus eight

which is the exact same thing as 58.

Five tens and eight ones.

Now I said I would do the third way.

And these are all the same way.

I'm just writing it
down in different ways.

So I could also write 83.

I could write this down as eight tens

plus three ones.

All right, this is the tens place.

This is the ones place.

Eight tens, three ones.

I'm gonna subtract two tens and five ones.

So I could write...

So this is going to be minus

two tens

and minus three ones.

I'm sorry, and minus five ones.

Minus five ones.

25 is the same thing as 20 and five.

If I'm subtracting 25,
that's the same thing

as subtracting 20 and
then subtracting five.

And that's the same thing as subtracting

two tens and then subtracting five ones.

Two tens and five ones.

So let's then work this out.

So this is going to be...

Well, as soon as we try
to subtract five ones

from three ones, we say,
"It doesn't make any sense."

Let me make the value here larger.

And I'm gonna do that by
regrouping from the tens place.

Instead of writing this as eight tens,

I'm gonna take one of those tens away.

I'm gonna write it as seven tens.

And then put that 10 in the ones place.

Well one 10 is equal to 10 ones.

So if I added it to the three,
this is going to be 13 ones.

And now I can subtract.

13 ones minus five ones is eight ones.

And seven tens minus
two tens is five tens.

Five tens.

We are done.

These are all different ways of doing

the exact same problem with regrouping.