Rounding whole numbers: missing digit

WEBVTT
Kind: captions
Language: en

00:00:01.291 --> 00:00:03.666
- What digits could replace
the question mark in the

00:00:03.666 --> 00:00:06.645
hundreds place to make
this statement true?

00:00:06.645 --> 00:00:10.777
Four thousand question
mark hundreds 29 rounds

00:00:10.777 --> 00:00:14.444
to 5000 if we round to
the nearest thousand.

00:00:15.816 --> 00:00:19.649
So we want a number whose
nearest thousand is 5000.

00:00:19.649 --> 00:00:23.700
It's closer to 5000
than any other thousand.

00:00:23.700 --> 00:00:26.603
And what we know about our
number so far is it starts

00:00:26.603 --> 00:00:30.770
with 4000 then we'll fill in
the digit for the hundreds

00:00:31.855 --> 00:00:34.962
and ends with 29.

00:00:34.962 --> 00:00:38.186
So, we want to know what
digits from zero to nine

00:00:38.186 --> 00:00:43.008
can we fill in here so that
this number is closer to 5000

00:00:43.008 --> 00:00:45.008
than any other thousand.

00:00:45.942 --> 00:00:47.949
Well the only other
thousand this could be close

00:00:47.949 --> 00:00:51.242
to is 4000 because we're
starting with a four here,

00:00:51.242 --> 00:00:55.193
all of our numbers will
be between 4000 and 5000,

00:00:55.193 --> 00:00:58.607
so let's draw that, let's
show that on a number line.

00:00:58.607 --> 00:01:02.607
Here's a number line that
goes from 4000 to 5000

00:01:03.579 --> 00:01:05.920
and then the hundreds here
are marked so this would

00:01:05.920 --> 00:01:10.016
be 4100, 4200, 4300,

00:01:10.016 --> 00:01:14.501
4400, so on all the way to 4900

00:01:14.501 --> 00:01:16.418
and then finally, 5000.

00:01:18.488 --> 00:01:21.628
So if we want to fill in
digits here, then we can

00:01:21.628 --> 00:01:25.183
graph them on our number
line and see what are they

00:01:25.183 --> 00:01:26.433
nearest to.

00:01:26.433 --> 00:01:30.600
Are they nearest to 5000 or
are they nearest to 4000?

00:01:31.661 --> 00:01:36.350
Just, for example, if we
plot a number right here,

00:01:36.350 --> 00:01:39.429
whatever number this point
represents, what is its

00:01:39.429 --> 00:01:41.389
nearest thousand?

00:01:41.389 --> 00:01:45.498
Well, it is literally nearest
to 5000, so it would round

00:01:45.498 --> 00:01:49.165
to 5000, that would be
its nearest thousand.

00:01:51.279 --> 00:01:55.659
But, if for example we had
a point that was somewhere

00:01:55.659 --> 00:01:59.970
like this, this points nearest
thousand would be 4000.

00:01:59.970 --> 00:02:03.021
This point would round
down to 4000 because we can

00:02:03.021 --> 00:02:07.699
look and see, it is closer
to 4000 than it is to 5000.

00:02:07.699 --> 00:02:08.782
It is nearer.

00:02:10.796 --> 00:02:12.965
So, let's look back now
at our number and try to

00:02:12.965 --> 00:02:15.627
fill in some digits and
see where they land on this

00:02:15.627 --> 00:02:16.627
number line.

00:02:18.352 --> 00:02:20.388
Let's draw in the first
possible digit we could fill

00:02:20.388 --> 00:02:21.971
in here, is a zero.

00:02:23.413 --> 00:02:27.850
So this would be 4000 zero
hundreds 29, well that

00:02:27.850 --> 00:02:31.794
would be between 4000 and
4100, it's greater than

00:02:31.794 --> 00:02:36.257
4000 but not quite all the
way to 4100, so we could

00:02:36.257 --> 00:02:39.818
put that probably somewhere,
estimating a little bit,

00:02:39.818 --> 00:02:44.317
about right here, a little
closer to 4000 than 4100.

00:02:44.317 --> 00:02:48.433
And now looking at this
number, we can see it is much

00:02:48.433 --> 00:02:52.879
closer to 4000, its nearest
thousand is definitely 4000.

00:02:52.879 --> 00:02:56.945
It takes us far longer to get to 5000,

00:02:56.945 --> 00:03:00.944
so zero will not work.

00:03:00.944 --> 00:03:04.389
So, we can take away, it's
not going to be a zero.

00:03:04.389 --> 00:03:06.343
And I don't know that we
need to try all 10 numbers,

00:03:06.343 --> 00:03:08.736
what we can do is look down
here, let's look at this

00:03:08.736 --> 00:03:12.454
graph and see which section
of it, which section

00:03:12.454 --> 00:03:16.198
of this number line is closer to 5000.

00:03:16.198 --> 00:03:18.807
And the answer will be if
we find right in the middle,

00:03:18.807 --> 00:03:22.974
here, 4500, anything greater than this

00:03:24.097 --> 00:03:26.198
will round up to 5000.

00:03:26.198 --> 00:03:30.577
From the halfway point
up will round up to 5000.

00:03:30.577 --> 00:03:33.349
So, what points knowing that this

00:03:33.349 --> 00:03:37.722
right here is 4500,

00:03:37.722 --> 00:03:41.825
what numbers or what
digits can we fill in here

00:03:41.825 --> 00:03:46.033
to get a number that's greater than 4500?

00:03:46.033 --> 00:03:48.246
Because anything less than
that's going to round down,

00:03:48.246 --> 00:03:49.746
be closer to 4000.

00:03:51.665 --> 00:03:55.582
And so, we could try,
let's just put a five in.

00:03:56.846 --> 00:04:01.013
4529 would be right after 4500,

00:04:02.309 --> 00:04:05.971
somewhere about like this, that is closer,

00:04:05.971 --> 00:04:10.210
just barely but it's closer
to 5000, so five works.

00:04:10.210 --> 00:04:13.043
Five is a digit that we could use.

00:04:14.378 --> 00:04:18.646
What about four, if we fill
in a four here, we have

00:04:18.646 --> 00:04:22.827
4400, well that's going
to be just to the left

00:04:22.827 --> 00:04:25.077
of 4500, this line is 4400,

00:04:28.143 --> 00:04:31.236
here's 4500, so that
point will come somewhere

00:04:31.236 --> 00:04:34.144
around here, which just barely

00:04:34.144 --> 00:04:37.187
rounds down to 4000, it's
close to the middle but

00:04:37.187 --> 00:04:41.319
a little bit closer, a
little bit nearer to 4000,

00:04:41.319 --> 00:04:44.159
its nearest thousand is 4000.

00:04:44.159 --> 00:04:48.578
So, four will not work,
five does work and from here

00:04:48.578 --> 00:04:50.926
I think we can figure out
our solution almost without

00:04:50.926 --> 00:04:52.960
using the number line.

00:04:52.960 --> 00:04:56.816
If 4400 was too small, well then

00:04:56.816 --> 00:05:00.651
4300 is definitely too
small and 200 and 100

00:05:00.651 --> 00:05:03.612
and we already saw zero
hundreds was way here,

00:05:03.612 --> 00:05:05.713
way down here which is way too

00:05:05.713 --> 00:05:08.546
small, and now we know 4529 works,

00:05:10.864 --> 00:05:13.773
that's big enough, so
anything bigger will only

00:05:13.773 --> 00:05:15.605
get closer to 5000.

00:05:15.605 --> 00:05:18.452
Anything bigger than 5
int he hundreds place will

00:05:18.452 --> 00:05:22.341
only move us closer,
farther to the right, so any

00:05:22.341 --> 00:05:25.693
digit five or greater
would work here, would

00:05:25.693 --> 00:05:27.110
round up to 5000.

00:05:28.078 --> 00:05:31.395
So the digits that are
five or greater are five,

00:05:31.395 --> 00:05:36.211
and then six, seven, eight and nine.

00:05:36.211 --> 00:05:40.325
Those are the possible digits
that we could fill into

00:05:40.325 --> 00:05:44.905
our hundreds place so that
our number rounds to 5000

00:05:44.905 --> 00:05:46.901
as its nearest thousand.

00:05:46.901 --> 00:05:51.068
The solutions are five,
six, seven, eight and nine.


Adding whole numbers by their place values

WEBVTT
Kind: captions
Language: en

00:00:01.167 --> 00:00:04.637
- [Voiceover] What is 19
thousands plus seven tens?

00:00:04.637 --> 00:00:07.370
First let's think about
what are 19 thousands,

00:00:07.370 --> 00:00:09.056
and what are seven tens,

00:00:09.056 --> 00:00:11.269
and then from there we can add them.

00:00:11.269 --> 00:00:15.417
So, 19 thousands, would
quite literally be,

00:00:15.417 --> 00:00:18.000
if we had a thousand, 19 times.

00:00:19.434 --> 00:00:22.333
So there's a thousand one time.

00:00:22.333 --> 00:00:26.754
If we had a thousand two
times, we would have 2000.

00:00:26.754 --> 00:00:29.496
If we had a thousand three times,

00:00:29.496 --> 00:00:32.079
we would have 1000, 2000, 3000.

00:00:33.350 --> 00:00:35.656
And the pattern here
should be pretty clear.

00:00:35.656 --> 00:00:39.181
If we have 19 thousands,
or a thousand 19 times,

00:00:39.181 --> 00:00:40.931
we would have 19,000.

00:00:43.285 --> 00:00:46.868
So, 19 thousands is
literally 19 thousands.

00:00:49.133 --> 00:00:51.550
And then seven tens, same thing,

00:00:51.550 --> 00:00:52.896
we could have seven tens.

00:00:52.896 --> 00:00:54.428
We could have 10 seven times.

00:00:54.428 --> 00:00:57.815
So, 10 plus another 10, plus another 10,

00:00:57.815 --> 00:01:00.270
and this one's a little
simpler to do than the 19,

00:01:00.270 --> 00:01:02.848
we only have to list seven tens this time.

00:01:02.848 --> 00:01:05.817
That's six tens, and there's seven tens.

00:01:05.817 --> 00:01:10.344
So, seven tens would be
literally seven tens.

00:01:10.344 --> 00:01:11.594
Or, 10, 20, 30,

00:01:12.543 --> 00:01:13.793
40, 50, 60, 70.

00:01:15.863 --> 00:01:17.613
So, seven tens is 70.

00:01:20.249 --> 00:01:22.132
And then if we want to combine these,

00:01:22.132 --> 00:01:25.549
or add these, we would have 19 thousands,

00:01:28.067 --> 00:01:29.234
zero hundreds,

00:01:31.382 --> 00:01:33.882
the seven tens, and zero ones.

00:01:35.481 --> 00:01:36.314
Or 19,070.

00:01:40.022 --> 00:01:41.618
We could've also thought
about that question

00:01:41.618 --> 00:01:42.845
in terms of place value

00:01:42.845 --> 00:01:44.860
instead of listing out all the thousands,

00:01:44.860 --> 00:01:46.586
and listing out all the tens,

00:01:46.586 --> 00:01:48.806
we could have thought of the place values.

00:01:48.806 --> 00:01:52.616
We had 19 thousands, which
means we want our last digit,

00:01:52.616 --> 00:01:56.366
the nine, to be in the
thousands place value.

00:01:57.678 --> 00:01:59.416
And then the other digit, we had one,

00:01:59.416 --> 00:02:00.892
would go in front of it.

00:02:00.892 --> 00:02:03.392
So, this is read 19 thousands,

00:02:05.152 --> 00:02:07.483
and by writing that thousands there,

00:02:07.483 --> 00:02:10.769
we covered all these empty place values.

00:02:10.769 --> 00:02:14.019
Or, the three zeros we ended up adding.

00:02:15.595 --> 00:02:18.143
The thousands can be represented by

00:02:18.143 --> 00:02:20.560
these three zeros at the end.

00:02:21.536 --> 00:02:25.914
Whereas, seven tens, we put
a seven in the tens place,

00:02:25.914 --> 00:02:28.094
and again, we have an empty
place value behind it.

00:02:28.094 --> 00:02:30.185
We had no ones with it.

00:02:30.185 --> 00:02:34.352
The tens, by saying tens, we
implied this zero after it.

00:02:35.403 --> 00:02:39.472
So, the thousands added
these three zeros to the end,

00:02:39.472 --> 00:02:42.889
and seven tens added one zero to the end.

00:02:43.853 --> 00:02:45.968
And again, if we combined them,

00:02:45.968 --> 00:02:47.575
like we saw in the previous one,

00:02:47.575 --> 00:02:51.742
we'd have 19 thousands, zero
hundreds, and seven tens.

00:02:55.186 --> 00:02:57.808
So, either way, whether we list out

00:02:57.808 --> 00:03:01.925
what 19 thousands is
literally with 19 thousands,

00:03:01.925 --> 00:03:04.870
or seven tens, literally 10 seven times,

00:03:04.870 --> 00:03:06.844
or we look at it in terms of place value,

00:03:06.844 --> 00:03:08.652
and add the zeros on the end.

00:03:08.652 --> 00:03:11.985
Either way, our solution will be 19,070.

00:03:15.862 --> 00:03:17.095
Here's one more.

00:03:17.095 --> 00:03:21.322
We have five ten-thousands
plus 22 thousands.

00:03:21.322 --> 00:03:25.006
So, two ways again we
could try to solve this.

00:03:25.006 --> 00:03:29.684
One, we could think about
what are five ten-thousands?

00:03:29.684 --> 00:03:32.017
If we had 10,000 five times,

00:03:34.764 --> 00:03:37.915
another 10,000, another, that's three.

00:03:37.915 --> 00:03:41.498
Four ten-thousands,
and five ten-thousands,

00:03:42.349 --> 00:03:45.016
that would be a total of 50,000.

00:03:47.258 --> 00:03:50.008
10,000, 20, 30, 40, 50 thousands.

00:03:51.640 --> 00:03:54.390
So, five ten-thousands is 50,000.

00:03:55.985 --> 00:03:58.735
Let's write that up here, 50,000.

00:04:00.401 --> 00:04:01.984
Plus, 22 thousands.

00:04:04.003 --> 00:04:07.760
22 thousands, remember when
we did the 19 thousands,

00:04:07.760 --> 00:04:12.024
if we wrote one 1000
it would be a thousand.

00:04:12.024 --> 00:04:14.682
If we wrote a thousand two
times, it would be two thousands.

00:04:14.682 --> 00:04:18.849
If we wrote it 22 times, then
it would be 22 thousands.

00:04:20.695 --> 00:04:22.695
There'd be 22 thousands.

00:04:23.763 --> 00:04:26.501
And we could combine these numbers,

00:04:26.501 --> 00:04:30.334
50,000 plus 22,000, will
be a total of 72,000.

00:04:36.780 --> 00:04:39.324
So, one way there, that
first way we talked about,

00:04:39.324 --> 00:04:43.167
is to think about what does
five ten-thousands look like,

00:04:43.167 --> 00:04:45.758
and what do 22 thousands look like,

00:04:45.758 --> 00:04:48.841
to get our numbers and then add them.

00:04:50.028 --> 00:04:51.219
Or, the other way that we could solve this

00:04:51.219 --> 00:04:52.655
is with a place value chart.

00:04:52.655 --> 00:04:54.908
Is, thinking about place value.

00:04:54.908 --> 00:04:57.735
So, let's put a place value chart in here,

00:04:57.735 --> 00:05:01.256
and then put our first number,
which was five ten-thousands.

00:05:01.256 --> 00:05:05.673
So, we have five in the
ten-thousands place,

00:05:05.673 --> 00:05:07.762
five ten-thousands.

00:05:07.762 --> 00:05:09.695
And we can fill in the zeros behind it

00:05:09.695 --> 00:05:11.172
in these empty place values.

00:05:11.172 --> 00:05:14.567
There were no thousands,
hundreds, tens, or ones.

00:05:14.567 --> 00:05:18.951
So, for ten-thousands, we
added four zeros behind it.

00:05:18.951 --> 00:05:22.201
And the other number was 22,000, so 22.

00:05:24.240 --> 00:05:28.538
We read this as 22,000,
always saying the place value

00:05:28.538 --> 00:05:32.147
of the last non-zero digit we see.

00:05:32.147 --> 00:05:34.230
So, 22 and then thousand.

00:05:35.254 --> 00:05:37.016
And then, with thousands like before,

00:05:37.016 --> 00:05:39.766
we'll add three zeros to the end.

00:05:40.821 --> 00:05:42.990
And finally, when we
combine these numbers,

00:05:42.990 --> 00:05:44.353
when we look at the place values,

00:05:44.353 --> 00:05:47.691
we now have seven ten-thousands.

00:05:47.691 --> 00:05:49.217
We have two thousands.

00:05:49.217 --> 00:05:52.550
Still no hundreds, no tens, and no ones.

00:05:53.620 --> 00:05:54.801
So, our solution for

00:05:54.801 --> 00:05:58.718
five ten-thousands plus
22 thousands is 72,000.


Regrouping whole number place values

WEBVTT
Kind: captions
Language: en

00:00:00.453 --> 00:00:04.309
- [Voiceover] Five thousands
equals how many hundreds?

00:00:04.309 --> 00:00:06.147
There's probably a few
ways we could take this on,

00:00:06.147 --> 00:00:07.129
but maybe let's start

00:00:07.129 --> 00:00:10.269
by thinking about these five thousands.

00:00:10.269 --> 00:00:13.269
Five thousands is 1,000, five times.

00:00:16.436 --> 00:00:18.751
So let's think about
each of those thousands,

00:00:18.751 --> 00:00:21.103
each of those five thousands.

00:00:21.103 --> 00:00:24.520
In 1,000, how many hundreds are in 1,000?

00:00:26.358 --> 00:00:28.941
1,000 equals how many hundreds?

00:00:30.630 --> 00:00:32.226
Well let's see, let's count by hundreds

00:00:32.226 --> 00:00:33.966
until we get to 1,000,

00:00:33.966 --> 00:00:35.346
and I'll keep a little tally mark

00:00:35.346 --> 00:00:37.542
so we can keep count of how
many hundreds it takes us

00:00:37.542 --> 00:00:38.875
to get to 1,000.

00:00:40.158 --> 00:00:42.158
100, 200, 300, 400, 500,

00:00:44.346 --> 00:00:46.513
600, 700, 800, 900, 1,000.

00:00:49.134 --> 00:00:53.262
So it took 10 hundreds, to get to 1,000.

00:00:53.262 --> 00:00:55.262
So 1,000 is 10 hundreds.

00:00:57.008 --> 00:00:58.925
So what would 5,000 be?

00:01:01.473 --> 00:01:04.640
5,000 is five times as many thousands.

00:01:06.834 --> 00:01:11.001
So we're also gonna have
five times as many hundreds.

00:01:11.842 --> 00:01:13.259
So five thousands

00:01:15.131 --> 00:01:17.964
will equal five times 10 hundreds,

00:01:21.035 --> 00:01:23.282
because we have 5,000 this time,

00:01:23.282 --> 00:01:26.115
so we have five times 10 hundreds,

00:01:29.596 --> 00:01:31.138
or five times 10.

00:01:31.138 --> 00:01:32.805
Five times 10 is 50.

00:01:34.749 --> 00:01:37.082
So 5,000 equals 50 hundreds.

00:01:41.698 --> 00:01:44.157
Another way we could think
about this is place value,

00:01:44.157 --> 00:01:45.310
so let's do that.

00:01:45.310 --> 00:01:48.143
Let's look at a place value chart.

00:01:49.150 --> 00:01:50.422
Here we have a place value chart

00:01:50.422 --> 00:01:53.589
and if we fill in five under thousands

00:01:55.509 --> 00:01:59.158
we can see that we have
three empty spaces.

00:01:59.158 --> 00:02:02.157
We have no hundreds, no tens and no ones,

00:02:02.157 --> 00:02:05.407
So we need to fill those in with zeros,

00:02:06.947 --> 00:02:07.780
or 5,000.

00:02:09.083 --> 00:02:11.029
Again, it's 5,000.

00:02:11.029 --> 00:02:15.456
Writing the word thousands
essentially replaced

00:02:15.456 --> 00:02:16.501
those three zeros.

00:02:16.501 --> 00:02:19.500
Five thousands is the same as five

00:02:19.500 --> 00:02:21.871
with three zeros behind it,

00:02:21.871 --> 00:02:24.691
and now we want to change
these five thousands

00:02:24.691 --> 00:02:25.941
to be hundreds.

00:02:27.019 --> 00:02:28.724
Well when we read this place value chart,

00:02:28.724 --> 00:02:31.087
when we read five, when we stopped here,

00:02:31.087 --> 00:02:33.366
five is the last number we read

00:02:33.366 --> 00:02:37.052
and then we read the place
value above it, thousands.

00:02:37.052 --> 00:02:38.875
So for hundreds we'll do the same thing

00:02:38.875 --> 00:02:40.317
up until the hundreds.

00:02:40.317 --> 00:02:41.587
We'll read the place value chart

00:02:41.587 --> 00:02:44.203
until the place value we want

00:02:44.203 --> 00:02:46.161
and then the place value.

00:02:46.161 --> 00:02:49.911
So five thousands is
the same as 50 hundreds.

00:02:52.316 --> 00:02:55.566
Five thousands is equal to 50 hundreds,

00:02:58.858 --> 00:03:02.398
and we don't have to include
these last zeros on the end

00:03:02.398 --> 00:03:06.729
because just like thousands
implied three zeros,

00:03:06.729 --> 00:03:08.932
hundreds, by saying hundreds

00:03:08.932 --> 00:03:13.156
we've essentially implied
that these zeros are there.

00:03:13.156 --> 00:03:16.656
So five thousands is equal to 50 hundreds.

00:03:17.828 --> 00:03:19.121
We weren't asked about tens

00:03:19.121 --> 00:03:22.192
but we could look here
and figure it out, I bet.

00:03:22.192 --> 00:03:24.609
Tens I would say, is 500 10s.

00:03:25.769 --> 00:03:28.976
We'd read up through the
tens and then the tens place

00:03:28.976 --> 00:03:31.893
because 10s have one zero after them.

00:03:31.893 --> 00:03:35.108
That zero is implied when you say 10,

00:03:35.108 --> 00:03:38.072
and then finally, if we
went all the way to the end,

00:03:38.072 --> 00:03:42.239
we could also say that this
number is equal to 5,000 ones.

00:03:45.032 --> 00:03:47.944
So any of those, five thousands,

00:03:47.944 --> 00:03:52.635
50 hundreds, 500 tens or
5,000 ones, are equivalent.

00:03:52.635 --> 00:03:55.048
They're all equal to each other,

00:03:55.048 --> 00:03:57.484
but the one we were
asked about was hundreds.

00:03:57.484 --> 00:04:00.484
So five thousands equal 50 hundreds.

00:04:03.207 --> 00:04:04.252
Here's another one.

00:04:04.252 --> 00:04:07.346
30 tens equals how many hundreds?

00:04:07.346 --> 00:04:11.564
So this time we're looking
at tens and hundreds.

00:04:11.564 --> 00:04:15.124
So let's think about how
tens and hundreds relate.

00:04:15.124 --> 00:04:16.207
How many tens

00:04:18.892 --> 00:04:20.523
are in 100?

00:04:20.523 --> 00:04:24.298
How many tens are in 100 and
we could write one hundred,

00:04:24.298 --> 00:04:26.798
the word or the number in 100.

00:04:29.338 --> 00:04:31.534
Well to figure that out
if we don't know already,

00:04:31.534 --> 00:04:32.589
we can count tens.

00:04:32.589 --> 00:04:35.243
We can count by 10s and see
how many 10s it takes us

00:04:35.243 --> 00:04:37.330
to get to a hundred.

00:04:37.330 --> 00:04:39.747
One ten is 10, 20, 30, 40, 50

00:04:42.411 --> 00:04:44.078
60, 70, 80, 90, 100.

00:04:46.310 --> 00:04:50.066
So we got to a hundred
and it took us 10 tens.

00:04:50.066 --> 00:04:52.149
There are 10 tens in 100.

00:04:53.788 --> 00:04:56.121
So if there's 10 tens in 100

00:04:57.338 --> 00:05:00.088
how many hundreds are in 30 tens?

00:05:01.155 --> 00:05:04.430
Well to get from 10 tens to 30 tens,

00:05:04.430 --> 00:05:07.358
that's three times as many tens,

00:05:07.358 --> 00:05:11.846
so we'll also have three
times as many hundreds,

00:05:11.846 --> 00:05:13.346
or three hundreds.

00:05:15.026 --> 00:05:17.776
30 tens is three sets of 10 tens.

00:05:20.198 --> 00:05:22.130
10 tens are a hundred.

00:05:22.130 --> 00:05:24.806
So another way to think of that is 30 tens

00:05:24.806 --> 00:05:28.556
is three sets of hundreds,
or three hundreds.

00:05:29.537 --> 00:05:32.984
We could also think about
this in terms of place value.

00:05:32.984 --> 00:05:35.303
Here we have this tens

00:05:35.303 --> 00:05:39.033
and we know that tens can
be represented by a zero.

00:05:39.033 --> 00:05:43.645
So instead of 30 10s, we
could simply write a 30

00:05:43.645 --> 00:05:47.963
with a zero on the end,
that zero for tens,

00:05:47.963 --> 00:05:52.440
and then over here, equal
to, we have hundreds

00:05:52.440 --> 00:05:56.268
and hundreds can be
represented by two zeros.

00:05:56.268 --> 00:05:58.248
So to make these equivalent,

00:05:58.248 --> 00:06:00.851
what number will need
to fill in this spot?

00:06:00.851 --> 00:06:05.018
And the answer again, is a three
like we already saw up top.

00:06:06.191 --> 00:06:09.274
So 30 10s is equal to three hundreds.


Canceling zeros when dividing

WEBVTT
Kind: captions
Language: en

00:00:01.001 --> 00:00:04.668
- [Voiceover] Let's
solve 350 divided by 50.

00:00:05.812 --> 00:00:08.775
So, one way to think about
this is if we had 350

00:00:08.775 --> 00:00:12.306
of something, let's say,
something delicious like brownies.

00:00:12.306 --> 00:00:16.546
If we had 350 brownies
and we were dividing them

00:00:16.546 --> 00:00:21.026
into groups of 50, how many
groups of 50 could we get?

00:00:21.026 --> 00:00:25.702
Well, one idea is to count
by 50's until we get to 350

00:00:25.702 --> 00:00:28.006
and see how many groups there are.

00:00:28.006 --> 00:00:30.392
One group of 50 would be 50,

00:00:30.392 --> 00:00:33.765
plus another group of 50 would be 100,

00:00:33.765 --> 00:00:36.432
plus another group of 50 is 150,

00:00:37.989 --> 00:00:40.744
another one will be 200,

00:00:40.744 --> 00:00:42.327
200 plus 50 is 250,

00:00:44.124 --> 00:00:46.041
plus another 50 is 300,

00:00:47.078 --> 00:00:49.825
and plus one more 50 is 350.

00:00:49.825 --> 00:00:53.996
So, when we added all these
50's, these groups of 50,

00:00:53.996 --> 00:00:56.746
50, 100, 150, 200, 250, 300, 350,

00:00:59.756 --> 00:01:01.542
we ended up with 350.

00:01:01.542 --> 00:01:05.468
So, 350 can be divided into
this many groups of 50,

00:01:05.468 --> 00:01:07.173
and how many groups is this?

00:01:07.173 --> 00:01:10.506
One, two, three, four, five, six, seven.

00:01:12.641 --> 00:01:16.224
So, 350 divided into
groups of 50 is seven.

00:01:17.815 --> 00:01:19.130
Now, let's look at that quotient,

00:01:19.130 --> 00:01:22.804
that solution of seven
and let's say something.

00:01:22.804 --> 00:01:25.804
If we had simply divided 35 by five,

00:01:27.084 --> 00:01:28.976
we would have also gotten seven.

00:01:28.976 --> 00:01:33.143
35 divided into groups of
five is also equal to seven.

00:01:36.156 --> 00:01:39.290
So, in a way, these zeroes didn't matter,

00:01:39.290 --> 00:01:41.773
they didn't affect our answer.

00:01:41.773 --> 00:01:43.982
We were able to cancel them out.

00:01:43.982 --> 00:01:47.348
Having the zero in the first
number is cancelled out

00:01:47.348 --> 00:01:50.375
by having that zero in the second number.

00:01:50.375 --> 00:01:52.421
And, let's look at why that is.

00:01:52.421 --> 00:01:54.902
Let's think about why that is.

00:01:54.902 --> 00:01:58.626
Division is really the same as a fraction.

00:01:58.626 --> 00:02:01.243
So, if we wrote this as a fraction,

00:02:01.243 --> 00:02:03.076
let's say 350 over 50,

00:02:07.047 --> 00:02:10.343
well this fraction bar
right here is the same

00:02:10.343 --> 00:02:12.578
as the division sign up here.

00:02:12.578 --> 00:02:16.328
350 divided by 50 is
the same as 350 over 50.

00:02:19.483 --> 00:02:22.633
And, when we have a fraction
like this fraction down here,

00:02:22.633 --> 00:02:24.852
we can simplify it.

00:02:24.852 --> 00:02:27.981
In this case, because
there's zeroes on the end,

00:02:27.981 --> 00:02:30.360
we know they're both multiples of 10,

00:02:30.360 --> 00:02:33.110
so we can divide them both by 10.

00:02:34.991 --> 00:02:39.955
We can divide our numerator
and our denominator by 10.

00:02:39.955 --> 00:02:42.970
And, when we divide whole numbers by 10,

00:02:42.970 --> 00:02:46.567
we have a trick we can
use, a pattern, really,

00:02:46.567 --> 00:02:50.594
which is that the whole
number, in this case 350,

00:02:50.594 --> 00:02:54.822
when it's divided by 10 we
drop a zero from the end.

00:02:54.822 --> 00:02:57.155
So, 350 divided by 10 is 35.

00:03:00.604 --> 00:03:04.000
350 could be divided into 10 groups of 35.

00:03:04.000 --> 00:03:08.128
And, then 50 divided by
10 will be the same thing.

00:03:08.128 --> 00:03:12.237
When we divided 50 by 10, we
drop that zero off the end,

00:03:12.237 --> 00:03:14.043
or another way to think about it is

00:03:14.043 --> 00:03:18.599
50 divided into groups of
10 would make five groups.

00:03:18.599 --> 00:03:20.836
And, then we end up with
our simplified fraction

00:03:20.836 --> 00:03:23.753
of 35 fifths or 35 divided by five,

00:03:25.781 --> 00:03:27.512
which is the same thing here.

00:03:27.512 --> 00:03:30.393
So, in both of these cases, we can see

00:03:30.393 --> 00:03:34.560
that 350 divided by 50 is
the same as 35 divided by 5.

00:03:36.947 --> 00:03:39.283
So, when both whole numbers,

00:03:39.283 --> 00:03:41.159
when we're dividing whole numbers

00:03:41.159 --> 00:03:45.326
and they both end in zeroes,
we can cancel those zeroes.

00:03:46.318 --> 00:03:48.549
Basically, we're factoring out a 10.

00:03:48.549 --> 00:03:51.714
We're taking the 10, the divided
by 10 out of both of them,

00:03:51.714 --> 00:03:53.170
out of both numbers.

00:03:53.170 --> 00:03:55.833
So, we can cancel those zeroes

00:03:55.833 --> 00:03:57.682
which leaves us with smaller numbers

00:03:57.682 --> 00:04:00.753
and at least for me, I
find division a lot simpler

00:04:00.753 --> 00:04:04.578
when I'm working with smaller numbers.

00:04:04.578 --> 00:04:06.282
Let's try a few more.

00:04:06.282 --> 00:04:09.365
Let's try one like 420 divided by 70.

00:04:15.017 --> 00:04:17.699
So, we can see we have two whole numbers,

00:04:17.699 --> 00:04:19.116
both end in zero.

00:04:20.273 --> 00:04:22.516
So, we're gonna cancel those zeroes,

00:04:22.516 --> 00:04:25.754
basically we're dividing
a ten out of both numbers

00:04:25.754 --> 00:04:28.549
and end up with a simpler division problem

00:04:28.549 --> 00:04:30.466
of 42 divided by seven.

00:04:34.973 --> 00:04:37.556
42 divided by seven equals six,

00:04:38.605 --> 00:04:42.272
therefore 420 divided
by 70 also equals six.

00:04:46.714 --> 00:04:48.642
And, here's one last one.

00:04:48.642 --> 00:04:51.475
What is we had 5600 divided by 80?

00:04:58.254 --> 00:05:01.509
So, the first thing I notice
is I have zeroes at the end

00:05:01.509 --> 00:05:03.842
of both of my whole numbers.

00:05:04.784 --> 00:05:08.300
If I cancel out this
one, I can cancel out one

00:05:08.300 --> 00:05:09.550
on the other side.

00:05:09.550 --> 00:05:13.284
I can't cancel both of 'em
over here, there were two,

00:05:13.284 --> 00:05:15.181
with cancelling we have
to cancel the same amount

00:05:15.181 --> 00:05:17.181
of zeroes on both sides,

00:05:18.071 --> 00:05:21.738
and now we end up with
560 divided by eight.

00:05:25.508 --> 00:05:27.478
This leaves us with a new division problem

00:05:27.478 --> 00:05:29.170
that's still a little bit tricky,

00:05:29.170 --> 00:05:32.034
but easier than dividing by 80.

00:05:32.034 --> 00:05:35.284
So, here we can think of 560 as 56 10's

00:05:36.792 --> 00:05:39.340
because of the zero on the end,

00:05:39.340 --> 00:05:43.507
and 56 10's or 560 could be
rewritten as 10 times 56.

00:05:48.014 --> 00:05:49.192
Theses are equivalent.

00:05:49.192 --> 00:05:50.859
560 and 10 times 56,

00:05:52.468 --> 00:05:56.635
because 10 times 56 is a
56 with a zero on the end.

00:05:57.730 --> 00:06:01.551
And, rewriting it this way makes it so now

00:06:01.551 --> 00:06:03.489
I have a division problem right here,

00:06:03.489 --> 00:06:06.322
56 divided by 8 that we can solve,

00:06:07.289 --> 00:06:10.523
56 divided by eight is seven,

00:06:10.523 --> 00:06:13.965
and then we still have
this 10 and the times sign

00:06:13.965 --> 00:06:16.382
and 10 times seven equals 70.

00:06:19.231 --> 00:06:23.398
So, our solution here, when we
divided 560 by eight was 70,

00:06:25.059 --> 00:06:29.226
so that means our solution up
here for 5600 divided by 80

00:06:30.071 --> 00:06:30.988
is also 70.

00:06:32.819 --> 00:06:35.822
Because, when we cancel zeroes and divide,

00:06:35.822 --> 00:06:38.372
we still get the same solution.

00:06:38.372 --> 00:06:42.158
But, remember, we have to
cancel the same amount of zeroes

00:06:42.158 --> 00:06:45.119
in each number, here we
couldn't cancel both zeroes.

00:06:45.119 --> 00:06:48.185
If we cancel one zero in the dividend,

00:06:48.185 --> 00:06:51.269
we can cancel one zero in the divisor.

00:06:51.269 --> 00:06:53.829
And, another thing to
remember about this trick,

00:06:53.829 --> 00:06:55.690
first thing to remember
is we need to cancel

00:06:55.690 --> 00:06:57.647
the same amount of zeroes,

00:06:57.647 --> 00:07:00.172
and the second, the zeroes
have to be at the end

00:07:00.172 --> 00:07:01.644
of the problem.

00:07:01.644 --> 00:07:03.898
So, if we had a division problem,

00:07:03.898 --> 00:07:07.648
something for example
like 506 divided by 20,

00:07:10.563 --> 00:07:12.813
here we cannot cancel the zeroes,

00:07:12.813 --> 00:07:15.064
we cannot cancel the
zeroes because this zero

00:07:15.064 --> 00:07:16.935
is not on the end.

00:07:16.935 --> 00:07:20.848
So, the new problem this would
give us, 56 divided by two,

00:07:20.848 --> 00:07:25.633
is not equivalent, does not
equal the top division problem.

00:07:25.633 --> 00:07:28.713
So, we can't cancel
zeroes, that does not work.

00:07:28.713 --> 00:07:31.054
We cannot cancel zeroes
unless they are at the end

00:07:31.054 --> 00:07:33.128
of the problem,

00:07:33.128 --> 00:07:36.387
and we cancel the same
amount in both the dividend

00:07:36.387 --> 00:07:37.720
and the divisor.


Quotients that are multiples of 10

WEBVTT
Kind: captions
Language: en

00:00:00.715 --> 00:00:04.632
- [Voiceover] Let's solve
240 divided by three.

00:00:05.782 --> 00:00:10.012
To solve this, we could take
this large three-digit number

00:00:10.012 --> 00:00:12.605
and divide it by a one-digit number,

00:00:12.605 --> 00:00:15.678
or we could take what we know about 10s,

00:00:15.678 --> 00:00:19.590
about zeroes and 10s, and try
to break this up into numbers

00:00:19.590 --> 00:00:22.926
that might be easier for us to work with.

00:00:22.926 --> 00:00:26.176
So 240, because of the zero on the end,

00:00:27.633 --> 00:00:30.459
I know is the same as 24 10s,

00:00:30.459 --> 00:00:31.292
or 24

00:00:33.156 --> 00:00:33.989
times 10.

00:00:35.587 --> 00:00:39.669
24 times 10, any time we multiply by 10,

00:00:39.669 --> 00:00:43.243
will have the original
number, 24 in this case,

00:00:43.243 --> 00:00:45.576
with a zero on the end, 240.

00:00:47.195 --> 00:00:49.612
So 240 is the same as 24 10s,

00:00:51.374 --> 00:00:52.624
or 10 times 24.

00:00:54.296 --> 00:00:57.729
So we can come back over here
and write this number 240

00:00:57.729 --> 00:00:58.979
as 24 times 10,

00:01:01.989 --> 00:01:06.156
and then still have the
divided by three at the end.

00:01:07.463 --> 00:01:11.546
So what we changed was we
changed 240, or 24 10s,

00:01:12.389 --> 00:01:13.889
to be 24 times 10.

00:01:15.459 --> 00:01:19.113
What we did not change is the solution.

00:01:19.113 --> 00:01:21.340
These expressions are still equal,

00:01:21.340 --> 00:01:23.384
they equal the same number,

00:01:23.384 --> 00:01:28.190
so we can solve either one
to get the same solution.

00:01:28.190 --> 00:01:30.595
And down here, we have a
little bit simpler of numbers

00:01:30.595 --> 00:01:34.641
to work with, so I'll work
with this one down here.

00:01:34.641 --> 00:01:36.309
The next thing I'm
gonna do is look at this

00:01:36.309 --> 00:01:39.744
multiplication problem, 24 times 10,

00:01:39.744 --> 00:01:42.066
and I know that in
multiplication, I can multiply

00:01:42.066 --> 00:01:43.149
in any order.

00:01:44.125 --> 00:01:47.463
For example, if I have something like

00:01:47.463 --> 00:01:50.175
two times three, which is six,

00:01:50.175 --> 00:01:54.336
that's the same as three
times two, which is also six.

00:01:54.336 --> 00:01:56.624
Two threes or three twos is six,

00:01:56.624 --> 00:02:00.345
we can change the order
without changing the answer.

00:02:00.345 --> 00:02:03.330
So over here, let's do that.

00:02:03.330 --> 00:02:04.247
10 times 24

00:02:07.350 --> 00:02:08.767
divided by three.

00:02:10.226 --> 00:02:12.132
So we've changed the expression,

00:02:12.132 --> 00:02:14.504
we've changed what's written
here, but we have not changed

00:02:14.504 --> 00:02:18.011
what it equals, we have
not changed the solution.

00:02:18.011 --> 00:02:20.585
And now I can see a division
problem that, for me,

00:02:20.585 --> 00:02:23.829
is far simpler than this big
three-digit division problem

00:02:23.829 --> 00:02:25.340
up here.

00:02:25.340 --> 00:02:28.757
24 divided into groups of three is eight,

00:02:30.956 --> 00:02:34.253
that's eight, and then we'll
bring down our times 10,

00:02:34.253 --> 00:02:38.176
bringing down this 10 and the times sign,

00:02:38.176 --> 00:02:40.144
and then we can use the
pattern we already know

00:02:40.144 --> 00:02:42.438
that we talked about up here.

00:02:42.438 --> 00:02:45.112
When we multiply by 10,
we take our whole number,

00:02:45.112 --> 00:02:46.949
in this case eight,

00:02:46.949 --> 00:02:49.949
and we add a zero to the end, or 80.

00:02:52.309 --> 00:02:56.103
So our solution, we came up with 80,

00:02:56.103 --> 00:02:58.594
which means our solution
to the original expression

00:02:58.594 --> 00:02:59.511
is also 80.

00:03:01.727 --> 00:03:03.394
240 divided by three

00:03:05.683 --> 00:03:07.350
is eight 10s, or 80.

00:03:09.900 --> 00:03:11.861
One other way we could've
thought about this

00:03:11.861 --> 00:03:14.993
is 240, as we've already said,

00:03:14.993 --> 00:03:15.826
is 24 10s.

00:03:19.187 --> 00:03:21.604
If we divide 24 10s by three,

00:03:22.884 --> 00:03:24.967
we end up with eight 10s,

00:03:27.114 --> 00:03:29.531
and eight 10s is equal to 80.

00:03:31.316 --> 00:03:34.613
If we have eight 10s, that equals 80.

00:03:34.613 --> 00:03:37.468
So this is one other way that
we could've thought about it,

00:03:37.468 --> 00:03:41.650
both ways using the zero
or our knowledge of 10s

00:03:41.650 --> 00:03:43.877
to break this division problem down

00:03:43.877 --> 00:03:47.138
so we didn't have to deal with
a large three-digit number

00:03:47.138 --> 00:03:50.888
but could deal with
simpler, smaller numbers.

00:03:52.178 --> 00:03:54.451
Let's try another one, this
time let's do thousands,

00:03:54.451 --> 00:03:55.607
let's make this one trickier.

00:03:55.607 --> 00:03:58.364
What about something like

00:03:58.364 --> 00:04:00.114
42 hundred, or 4,200,

00:04:04.285 --> 00:04:07.868
divided by, and let's
see, how about seven,

00:04:09.021 --> 00:04:10.438
divided by seven.

00:04:12.260 --> 00:04:15.610
So here, again we can
break this number down.

00:04:15.610 --> 00:04:18.527
42 hundred, this number 42 hundred,

00:04:19.676 --> 00:04:20.509
or 4,200,

00:04:21.775 --> 00:04:23.442
can be written as 42

00:04:25.696 --> 00:04:28.946
times 100, because our pattern tells us

00:04:30.516 --> 00:04:34.111
when we have a number, like
a whole number like 42,

00:04:34.111 --> 00:04:38.938
and we multiply by 100, we
keep our whole number of 42

00:04:38.938 --> 00:04:41.105
and we add two zeroes now.

00:04:42.932 --> 00:04:45.972
So 42 times 100, and then
we still need to have

00:04:45.972 --> 00:04:49.292
our divided by seven at the end.

00:04:49.292 --> 00:04:52.510
Reverse these numbers so
that 42 and seven can be next

00:04:52.510 --> 00:04:53.677
to each other,

00:04:54.778 --> 00:04:58.316
42 divided by seven, because
that's a division problem,

00:04:58.316 --> 00:05:00.926
a division factor we might already know.

00:05:00.926 --> 00:05:04.176
42 divided into groups of seven is six,

00:05:05.603 --> 00:05:08.021
and bring down the 100 and the times sign,

00:05:08.021 --> 00:05:09.104
100 times six

00:05:10.058 --> 00:05:10.891
is 600.

00:05:13.906 --> 00:05:16.063
So our solution, going back up here

00:05:16.063 --> 00:05:18.230
to 4,200 divided by seven,

00:05:19.149 --> 00:05:19.982
is 600.

00:05:22.050 --> 00:05:23.826
Or we could've thought about it again,

00:05:23.826 --> 00:05:26.359
still thinking about place
value but using words here

00:05:26.359 --> 00:05:29.692
instead of digits, 4,200 is 42 hundreds,

00:05:32.382 --> 00:05:35.549
42, I can write that out, 42 hundreds,

00:05:38.207 --> 00:05:41.887
and if you divide 42
hundreds into groups of seven

00:05:41.887 --> 00:05:46.587
or into seven groups, each
group will have six hundreds,

00:05:46.587 --> 00:05:47.670
or 600 in it.

00:05:50.536 --> 00:05:54.619
So either way, 42 hundred,
4,200 divided by seven

00:05:56.153 --> 00:05:56.986
is 600.

00:05:58.639 --> 00:06:01.754
So here again, we were able
to solve a tricky problem,

00:06:01.754 --> 00:06:04.039
one that had a four-digit number,

00:06:04.039 --> 00:06:06.248
without using any long division,

00:06:06.248 --> 00:06:08.982
but instead using what
we know about place value

00:06:08.982 --> 00:06:10.899
or hundreds and zeroes.


Comparing multi-digit numbers

WEBVTT
Kind: captions
Language: en

00:00:00.922 --> 00:00:01.990
- [Voiceover] Compare

00:00:01.990 --> 00:00:02.823
98,989

00:00:04.713 --> 00:00:05.630
and 98,899.

00:00:08.176 --> 00:00:09.886
So we want to compare these two numbers

00:00:09.886 --> 00:00:12.015
and to do that, let's first
think about what these

00:00:12.015 --> 00:00:12.957
digits mean.

00:00:12.957 --> 00:00:16.291
What do these numbers actually mean?

00:00:16.291 --> 00:00:18.112
Looking first at our number on the left,

00:00:18.112 --> 00:00:20.406
we have a 9 all the way to the right,

00:00:20.406 --> 00:00:22.304
or in the ones place value,

00:00:22.304 --> 00:00:23.650
which means just that.

00:00:23.650 --> 00:00:25.233
It means nine ones.

00:00:27.251 --> 00:00:30.989
Beside that, we have an
8 in the 10s place value,

00:00:30.989 --> 00:00:33.156
so that's eight 10s or 80.

00:00:36.281 --> 00:00:39.481
This number, these two right here, 89

00:00:39.481 --> 00:00:41.981
is the same as an 80 plus a 9.

00:00:43.558 --> 00:00:47.529
Beside the 8, we have a 9
in the 100s place value,

00:00:47.529 --> 00:00:50.362
so again, we can look at that, 989

00:00:51.496 --> 00:00:54.829
is the same as a 900 plus an 80 plus a 9

00:00:56.076 --> 00:00:58.143
and let's keep going and
fill in these last two.

00:00:58.143 --> 00:01:00.893
We have an 8 in the 1,000s place,

00:01:02.456 --> 00:01:05.429
and finally, a 9 in the 10,000s place,

00:01:05.429 --> 00:01:08.346
which means nine 10,000s or 90,000,

00:01:10.421 --> 00:01:12.421
so 98,989 is the same as

00:01:14.167 --> 00:01:17.667
90,000 plus 8,000 plus 900 plus 80 plus 9.

00:01:19.928 --> 00:01:22.745
Which of these place values
now seems like the most

00:01:22.745 --> 00:01:27.132
important one if we're
deciding how big a number is?

00:01:27.132 --> 00:01:29.856
Which one of these has the
biggest impact on the size

00:01:29.856 --> 00:01:31.023
of our number?

00:01:32.277 --> 00:01:34.928
And the answer is the one
all the way to the left,

00:01:34.928 --> 00:01:37.927
whatever place value
is farthest to the left

00:01:37.927 --> 00:01:39.846
is the greatest place value,

00:01:39.846 --> 00:01:43.646
so it is the most important
in deciding how big

00:01:43.646 --> 00:01:45.757
or how small a number is.

00:01:45.757 --> 00:01:48.719
So when we compare these
numbers, we're going to start

00:01:48.719 --> 00:01:51.263
by comparing the largest place value that

00:01:51.263 --> 00:01:53.281
either of them has.

00:01:53.281 --> 00:01:57.352
In this case, 10,000s is
the largest place value

00:01:57.352 --> 00:01:59.574
both of them has,

00:01:59.574 --> 00:02:01.549
and in both cases, it's a 9,

00:02:01.549 --> 00:02:03.549
so both of these numbers

00:02:04.767 --> 00:02:06.184
start with 90,000

00:02:07.026 --> 00:02:08.154
which is equal,

00:02:08.154 --> 00:02:10.084
we can't tell yet which one is greater,

00:02:10.084 --> 00:02:13.106
so we're going to move to
the next biggest place value.

00:02:13.106 --> 00:02:16.753
The next largest place value is the 1,000s

00:02:16.753 --> 00:02:19.575
and again, we can see in both cases,

00:02:19.575 --> 00:02:21.408
we have an 8 or 8,000,

00:02:22.821 --> 00:02:25.198
so looking at what we've
compared so far, these numbers

00:02:25.198 --> 00:02:26.376
are identical,

00:02:26.376 --> 00:02:28.987
neither is larger than the other,

00:02:28.987 --> 00:02:31.130
so we're going to keep going
and again, we're going to pick

00:02:31.130 --> 00:02:33.547
the next largest place value,

00:02:34.495 --> 00:02:35.912
which is the 100s

00:02:37.207 --> 00:02:40.238
and our first number on the
left, we have nine 100s,

00:02:40.238 --> 00:02:41.372
nine 100s,

00:02:41.372 --> 00:02:44.123
but on the right, we have

00:02:44.123 --> 00:02:45.040
eight 100s,

00:02:46.647 --> 00:02:49.730
so eight 100s is less than nine 100s,

00:02:50.772 --> 00:02:53.689
so this number on the right is less

00:02:54.597 --> 00:02:55.577
than our first number,

00:02:55.577 --> 00:02:57.495
the number on the left,

00:02:57.495 --> 00:03:01.680
or we could say, the
900 is greater than 800

00:03:01.680 --> 00:03:04.680
so the number on the left is greater

00:03:06.257 --> 00:03:08.543
and this is our greater
than symbol because we want

00:03:08.543 --> 00:03:12.802
the open side to be
facing the larger number.

00:03:12.802 --> 00:03:17.243
We want the open side
facing the larger number.

00:03:17.243 --> 00:03:18.590
So we'd read this as

00:03:18.590 --> 00:03:20.007
98,989 is greater

00:03:23.041 --> 00:03:24.041
than 98,899.

00:03:27.308 --> 00:03:28.902
And you might be thinking,
but wait, we didn't look

00:03:28.902 --> 00:03:31.134
at the 10s and look at the 10s.

00:03:31.134 --> 00:03:32.876
Here, we have eight 10s,

00:03:32.876 --> 00:03:35.246
but on the right we have nine 10s.

00:03:35.246 --> 00:03:38.830
Well, nine 10s is definitely
greater than eight 10s

00:03:38.830 --> 00:03:42.497
but it doesn't make up
for having less 100s.

00:03:43.382 --> 00:03:45.938
100s are far bigger, 10 times bigger,

00:03:45.938 --> 00:03:48.850
than 10s, so they matter more,

00:03:48.850 --> 00:03:51.401
they had a bigger impact
on which of these numbers

00:03:51.401 --> 00:03:52.963
was larger.

00:03:52.963 --> 00:03:57.216
So, we compare until we find
the greatest place value

00:03:57.216 --> 00:03:59.199
that's different

00:03:59.199 --> 00:04:01.902
and then whichever of those
has the greater number

00:04:01.902 --> 00:04:05.294
in that place value is the greater number.

00:04:05.294 --> 00:04:06.877
Let's try one more.

00:04:08.485 --> 00:04:11.621
So here we're comparing 53,000

00:04:11.621 --> 00:04:12.621
and 350,000.

00:04:14.412 --> 00:04:16.073
At a quick glance, you might be thinking,

00:04:16.073 --> 00:04:19.593
okay, first number 5, first number 3.

00:04:19.593 --> 00:04:21.568
The highest place value is bigger here,

00:04:21.568 --> 00:04:22.994
it's a 5.

00:04:22.994 --> 00:04:24.272
But that's not quite enough.

00:04:24.272 --> 00:04:26.095
We still have to be
sure we're comparing the

00:04:26.095 --> 00:04:27.595
same place values.

00:04:28.712 --> 00:04:31.268
This largest place value here,

00:04:31.268 --> 00:04:32.611
this 5,

00:04:32.611 --> 00:04:34.611
is in the 10,000s place.

00:04:35.674 --> 00:04:38.252
But the largest place
value over here, the 3,

00:04:38.252 --> 00:04:41.096
is in the 100,000s place.

00:04:41.096 --> 00:04:44.096
So we are actually comparing 300,000

00:04:46.049 --> 00:04:46.882
to 50,000.

00:04:48.425 --> 00:04:50.956
Those are two different place values.

00:04:50.956 --> 00:04:54.614
We want to compare 100,000s to 100,000s,

00:04:54.614 --> 00:04:55.974
so looking over here,

00:04:55.974 --> 00:04:59.525
how many 100,000s did this number have?

00:04:59.525 --> 00:05:02.177
And the answer is a great, big zero.

00:05:02.177 --> 00:05:04.679
It has zero 100,000s,

00:05:04.679 --> 00:05:06.929
so we can say zero 100,000s

00:05:08.139 --> 00:05:11.549
and when we compare that to 300,000,

00:05:11.549 --> 00:05:12.869
that's far less.

00:05:12.869 --> 00:05:16.628
No 100,000s is much less
than three 100,000s,

00:05:16.628 --> 00:05:20.128
so actually, this second number is larger,

00:05:21.330 --> 00:05:24.741
so be careful not just to
compare the first number

00:05:24.741 --> 00:05:27.074
but the largest place value,

00:05:28.064 --> 00:05:30.489
and if there's no digit
in that place value,

00:05:30.489 --> 00:05:34.495
we can fill in a zero and then compare.

00:05:34.495 --> 00:05:37.357
So to read this, we'll say 53,000

00:05:37.357 --> 00:05:38.190
is less,

00:05:39.528 --> 00:05:40.361
less,

00:05:41.584 --> 00:05:42.667
than 350,000,

00:05:44.315 --> 00:05:47.985
and this symbol is less
than because the larger side

00:05:47.985 --> 00:05:50.069
is open to the bigger number

00:05:50.069 --> 00:05:52.840
and the bigger number
is the second number,

00:05:52.840 --> 00:05:55.423
so 53,000 is less than 350,000.


Multiplying 10s

WEBVTT
Kind: captions
Language: en

00:00:01.198 --> 00:00:04.323
- [Voiceover] Let's multiply 40 times 70.

00:00:04.323 --> 00:00:07.240
So 40 times, we have the number 70.

00:00:08.321 --> 00:00:10.465
So we could actually list that out,

00:00:10.465 --> 00:00:13.876
the number 70, 40 different
times and add it up.

00:00:13.876 --> 00:00:16.843
But that's clearly a lot
of computations to do.

00:00:16.843 --> 00:00:18.992
And there's gotta be a faster way.

00:00:18.992 --> 00:00:22.343
So another way is to
stick with multiplication,

00:00:22.343 --> 00:00:24.661
but see if we can break these numbers up,

00:00:24.661 --> 00:00:27.800
this 40 and this 70, decompose them,

00:00:27.800 --> 00:00:30.149
break them up in some way to get numbers

00:00:30.149 --> 00:00:33.324
that might be a little
easier to multiply with.

00:00:33.324 --> 00:00:35.974
For me, multiplying by
10 is the easiest number,

00:00:35.974 --> 00:00:38.374
because I know the pattern to add a zero.

00:00:38.374 --> 00:00:42.457
So, I'm gonna break up 40
and say, instead of 40,

00:00:43.658 --> 00:00:44.825
four times 10.

00:00:46.423 --> 00:00:49.464
Four times 10 and 40 are equivalent.

00:00:49.464 --> 00:00:52.194
They're the same thing,
so I can replace the 40

00:00:52.194 --> 00:00:53.944
with a four times 10.

00:00:55.156 --> 00:00:57.614
And then for my 70, same thing.

00:00:57.614 --> 00:01:02.095
I can break this up and
write seven times 10.

00:01:02.095 --> 00:01:03.771
Seven times 10.

00:01:03.771 --> 00:01:07.304
So these two expressions, 40 times 70

00:01:07.304 --> 00:01:10.661
and four times 10 times seven times 10,

00:01:10.661 --> 00:01:12.150
are equal; they're equivalent.

00:01:12.150 --> 00:01:14.836
So they'll have the same solution.

00:01:14.836 --> 00:01:17.023
But for me, this one down here is simpler

00:01:17.023 --> 00:01:19.539
to work out because of these times 10s.

00:01:19.539 --> 00:01:21.385
So I'll solve this one, knowing

00:01:21.385 --> 00:01:23.900
that I'll get the same
solution as I would have

00:01:23.900 --> 00:01:26.345
for this top expression.

00:01:26.345 --> 00:01:30.213
So what we can do is we
can re-order these numbers

00:01:30.213 --> 00:01:32.641
in a different order to, again, continue

00:01:32.641 --> 00:01:35.590
making this question
easier for us to solve.

00:01:35.590 --> 00:01:38.393
Because in multiplication,
the order doesn't matter.

00:01:38.393 --> 00:01:41.481
If we have five times two, for example,

00:01:41.481 --> 00:01:44.124
that would be the same as two times five.

00:01:44.124 --> 00:01:45.420
They're both 10.

00:01:45.420 --> 00:01:48.490
Five twos or two fives,
either way, it's 10.

00:01:48.490 --> 00:01:51.350
So we can change the order of the numbers

00:01:51.350 --> 00:01:53.104
without changing the answer.

00:01:53.104 --> 00:01:55.657
So again, we're going to change
our expression a little bit,

00:01:55.657 --> 00:01:59.132
but what we're not going
to change is the solution.

00:01:59.132 --> 00:02:01.954
So I'm gonna put my
one-digit numbers first.

00:02:01.954 --> 00:02:03.371
Four times seven.

00:02:06.632 --> 00:02:09.839
And then, I'll put the
two-digit numbers, the 10s,

00:02:09.839 --> 00:02:12.506
times 10 and the other times 10.

00:02:15.442 --> 00:02:17.424
So we have all the same factors,

00:02:17.424 --> 00:02:20.108
all the same numbers, in
both of these expressions.

00:02:20.108 --> 00:02:23.124
They've just been re-ordered.

00:02:23.124 --> 00:02:25.363
And now, I'll solve going across.

00:02:25.363 --> 00:02:27.280
Four times seven is 28.

00:02:29.682 --> 00:02:32.123
And now we have 28 times 10,

00:02:32.123 --> 00:02:33.873
and times another 10.

00:02:34.924 --> 00:02:37.644
Well, the pattern for
times 10 that we know

00:02:37.644 --> 00:02:42.201
is when we multiply a whole
number like 28 times 10,

00:02:42.201 --> 00:02:44.113
we will add a zero to the end.

00:02:44.113 --> 00:02:46.475
One zero for that zero in 10,

00:02:46.475 --> 00:02:48.975
because 28 times 10 is 28 10s,

00:02:50.263 --> 00:02:51.096
28 10s,

00:02:53.024 --> 00:02:53.857
or 280.

00:02:55.546 --> 00:02:57.319
And that multiplied 28 times 10,

00:02:57.319 --> 00:02:59.086
and then if we multiply by this other 10,

00:02:59.086 --> 00:03:01.662
well we have to add another zero.

00:03:01.662 --> 00:03:04.490
Multiplying by 10 adds a zero,

00:03:04.490 --> 00:03:08.534
so if we multiply by two
10s, we add two zeros.

00:03:08.534 --> 00:03:11.451
So, 28 times 10 times 10, is 2,800.

00:03:13.718 --> 00:03:17.508
Which means that this
original expression we had,

00:03:17.508 --> 00:03:21.008
40 times 70, also has a solution of 2,800,

00:03:22.705 --> 00:03:25.288
or two thousand, eight hundred.

00:03:27.253 --> 00:03:28.447
Let's try another example

00:03:28.447 --> 00:03:30.684
where we're multiplying 10s like this.

00:03:30.684 --> 00:03:32.667
Let's try, let's do
something like, let's say,

00:03:32.667 --> 00:03:34.834
maybe 90 times, how about,

00:03:37.076 --> 00:03:38.689
30.

00:03:38.689 --> 00:03:39.689
90 times 30.

00:03:40.638 --> 00:03:44.046
So the first thing I'm gonna
do is break up these numbers

00:03:44.046 --> 00:03:46.703
so that I have 10s, because again, for me

00:03:46.703 --> 00:03:50.976
10s are easier to multiply
than numbers like 90 and 30.

00:03:50.976 --> 00:03:54.488
So for 90, I'll write nine times 10,

00:03:54.488 --> 00:03:57.571
and for 30 I'll write three times 10.

00:03:58.940 --> 00:04:01.089
The expressions are equivalent.

00:04:01.089 --> 00:04:03.655
We've just written it in another way.

00:04:03.655 --> 00:04:07.030
And now, I'll re-order these numbers

00:04:07.030 --> 00:04:09.150
to put the one-digit numbers first.

00:04:09.150 --> 00:04:10.900
So, nine times three,

00:04:14.484 --> 00:04:18.860
and then I'll put the
10s: times 10, times 10.

00:04:18.860 --> 00:04:20.660
Because we need to have
all the same numbers,

00:04:20.660 --> 00:04:22.583
even if we change the order.

00:04:22.583 --> 00:04:24.833
So we have the nine, three,

00:04:26.782 --> 00:04:29.365
the first 10 and the second 10.

00:04:31.738 --> 00:04:34.237
And now, finally, we multiply.

00:04:34.237 --> 00:04:36.154
Nine times three is 27.

00:04:38.013 --> 00:04:40.263
27 times 10 will be 27 10s,

00:04:43.067 --> 00:04:45.842
or 27 with a zero on the end.

00:04:45.842 --> 00:04:48.592
And 270 times 10 will be 270 10s,

00:04:50.140 --> 00:04:52.640
or 270 with a zero on the end.

00:04:54.379 --> 00:04:56.982
So going back to the original question,

00:04:56.982 --> 00:04:59.482
90 times 30 is equal to 2,700.

00:05:03.933 --> 00:05:06.516
Or two thousand, seven hundred.


Multiplying 1-digit numbers by multiples of 10, 100, and 1000

WEBVTT
Kind: captions
Language: en

00:00:01.298 --> 00:00:04.723
- [Voiceover] Let's
multiply four times 80.

00:00:04.723 --> 00:00:06.278
So we can look at this a few ways.

00:00:06.278 --> 00:00:11.062
One way is to say four
times, we have the number 80.

00:00:11.062 --> 00:00:14.301
So we have the number 80 one time,

00:00:14.301 --> 00:00:15.134
two times,

00:00:16.112 --> 00:00:17.112
three times,

00:00:18.004 --> 00:00:19.328
four times.

00:00:19.328 --> 00:00:22.660
Four times we have the number 80.

00:00:22.660 --> 00:00:25.446
And we could do this
computation, add all of these,

00:00:25.446 --> 00:00:27.780
and get our solution.

00:00:27.780 --> 00:00:29.011
But let's look at it another way.

00:00:29.011 --> 00:00:32.053
Let's try to stick with multiplication.

00:00:32.053 --> 00:00:36.337
And one way we can do that
is to break up this 80.

00:00:36.337 --> 00:00:38.960
We know a pattern for multiplying by 10,

00:00:38.960 --> 00:00:42.745
so let's try to break
up this 80 to get a 10.

00:00:42.745 --> 00:00:46.412
So if we have four
times, and instead of 80,

00:00:48.202 --> 00:00:50.285
let's say eight times 10.

00:00:52.440 --> 00:00:55.928
Because 80 and eight times 10 are equal;

00:00:55.928 --> 00:00:57.043
those are equivalent;

00:00:57.043 --> 00:01:00.793
so we can replace our
80 with eight times 10.

00:01:01.768 --> 00:01:03.614
And then we have this times 10 back here

00:01:03.614 --> 00:01:06.319
which is super helpful 'cause
there's a nice neat pattern

00:01:06.319 --> 00:01:10.475
in math that we can use to
help us with the times 10 part.

00:01:10.475 --> 00:01:11.752
So let's start to solve this.

00:01:11.752 --> 00:01:13.669
Four times eight is 32.

00:01:16.350 --> 00:01:19.267
And then we still have 32 times 10.

00:01:20.263 --> 00:01:24.001
And then we can use our
pattern for multiplying by 10,

00:01:24.001 --> 00:01:27.948
which is that anytime we
multiply a whole number times 10

00:01:27.948 --> 00:01:31.524
we take that whole
number, in this case 32,

00:01:31.524 --> 00:01:34.113
and we add a zero to the end.

00:01:34.113 --> 00:01:35.946
So 32 times 10 is 320.

00:01:39.175 --> 00:01:41.033
And there's a reason that pattern works;

00:01:41.033 --> 00:01:42.554
we went into it in another video,

00:01:42.554 --> 00:01:44.365
but here just real quickly,

00:01:44.365 --> 00:01:46.282
32 times 10 is 32 tens.

00:01:48.974 --> 00:01:50.588
And we can do a few examples.

00:01:50.588 --> 00:01:53.171
If we had, say, three times 10,

00:01:55.220 --> 00:01:58.308
that would be three tens,
or a 10 plus another 10

00:01:58.308 --> 00:02:01.058
plus another 10, which equals 30:

00:02:02.372 --> 00:02:06.354
our whole number with a zero on the end.

00:02:06.354 --> 00:02:09.199
If we had something like 12 times 10,

00:02:09.199 --> 00:02:11.463
well, that would be 12 tens.

00:02:11.463 --> 00:02:15.004
And if we listed out 10 12
times and counted 'em up,

00:02:15.004 --> 00:02:19.323
there would be 120, it
would add up to 120,

00:02:19.323 --> 00:02:22.539
which again is our whole
number with a zero on the end,

00:02:22.539 --> 00:02:24.956
or 12 with a zero on the end.

00:02:25.836 --> 00:02:29.737
So we can use that pattern
here to see that 32 times 10

00:02:29.737 --> 00:02:32.154
is 32 with a zero on the end.

00:02:34.764 --> 00:02:35.820
Let's try another one.

00:02:35.820 --> 00:02:39.408
Let's do something like,
let's say 300 this time,

00:02:39.408 --> 00:02:43.158
we'll do hundreds instead
of tens, times six.

00:02:44.586 --> 00:02:49.288
300 we can break up, like we
did with 80 in the last one,

00:02:49.288 --> 00:02:52.871
and we can say that
300 is 100 three times,

00:02:54.164 --> 00:02:56.474
or 100 times three.

00:02:56.474 --> 00:03:00.474
And then we still have
our times six after that.

00:03:01.618 --> 00:03:03.871
So these two expressions,

00:03:03.871 --> 00:03:07.985
300 times six and 100
times three times six,

00:03:07.985 --> 00:03:12.235
are equivalent 'cause we
replaced our 300 with a 100.

00:03:12.235 --> 00:03:14.742
And then from here we can multiply.

00:03:14.742 --> 00:03:16.670
And let's start with
our one-digit numbers.

00:03:16.670 --> 00:03:18.527
Let's multiply those first.

00:03:18.527 --> 00:03:20.360
Three times six is 18.

00:03:21.813 --> 00:03:24.813
And then we still have 18 times 100,

00:03:26.181 --> 00:03:27.431
or 18 hundreds,

00:03:28.444 --> 00:03:30.694
so we can write that as 18,

00:03:33.216 --> 00:03:37.383
and then to show hundreds
we'll put two zeros on the end,

00:03:38.556 --> 00:03:39.389
or 1800.

00:03:41.830 --> 00:03:45.497
Just like up here, just
like we saw that 300

00:03:48.494 --> 00:03:50.827
is equal to three times 100,

00:03:51.977 --> 00:03:55.227
or our three with two zeros on the end,

00:03:56.842 --> 00:03:58.072
same thing here.

00:03:58.072 --> 00:04:01.822
18 times 100 is 18 with
two zeros on the end,

00:04:02.670 --> 00:04:03.920
or 18 hundreds.

00:04:05.213 --> 00:04:07.630
So 300 times six equals 1800.

00:04:11.389 --> 00:04:13.398
Let's try another one,
but this time let's go

00:04:13.398 --> 00:04:16.405
even another place
value and try thousands.

00:04:16.405 --> 00:04:19.155
Something like seven times 7,000.

00:04:23.104 --> 00:04:24.624
So like in the previous ones

00:04:24.624 --> 00:04:27.167
we're gonna break up our thousands.

00:04:27.167 --> 00:04:30.417
7,000 is the same as seven times 1,000.

00:04:33.286 --> 00:04:35.503
1,000 seven times.

00:04:35.503 --> 00:04:37.802
And we still have our times seven

00:04:37.802 --> 00:04:40.391
in the front here to bring down.

00:04:40.391 --> 00:04:43.560
And again, we can multiply
our single digits first,

00:04:43.560 --> 00:04:44.663
our one-digit numbers.

00:04:44.663 --> 00:04:46.663
Seven times seven is 49.

00:04:48.622 --> 00:04:52.455
And then 49 times 1,000
is going to be 49,000,

00:04:55.077 --> 00:04:57.632
which we can write as 49,

00:04:57.632 --> 00:05:00.430
and this time, maybe the
pattern's becoming clear,

00:05:00.430 --> 00:05:03.193
we're going to have
three zeros on the end,

00:05:03.193 --> 00:05:06.943
so it'll be a 49 with
three zeros, or 49,000.

00:05:10.101 --> 00:05:13.479
Just like up here, seven times 1,000

00:05:13.479 --> 00:05:16.057
was a seven with three zeros,

00:05:16.057 --> 00:05:20.224
49 times 1,000 is a 49 with
three zeros, or 49,000.

00:05:22.361 --> 00:05:24.479
Let's look at this as a pattern.

00:05:24.479 --> 00:05:25.838
If we show this as a pattern,

00:05:25.838 --> 00:05:29.005
let's do something like nine times 50.

00:05:32.862 --> 00:05:36.862
And then in another one
let's do nine times 500.

00:05:39.363 --> 00:05:43.030
And one last one we can
do nine times 5,000.

00:05:46.291 --> 00:05:48.184
I encourage you to pause here

00:05:48.184 --> 00:05:49.496
and see if you can work these out.

00:05:49.496 --> 00:05:51.377
See if you can come up with solutions

00:05:51.377 --> 00:05:53.710
for these three expressions.

00:05:55.208 --> 00:05:57.507
Now we can work them out together.

00:05:57.507 --> 00:05:58.590
Nine times 50

00:06:00.398 --> 00:06:04.148
will be the same as nine
times five times 10,

00:06:06.969 --> 00:06:10.963
'cause we broke up our
50 into a five times 10.

00:06:10.963 --> 00:06:13.505
And then if we multiply across,

00:06:13.505 --> 00:06:15.338
nine times five is 45,

00:06:17.278 --> 00:06:19.914
and to the end we're
going to add one zero.

00:06:19.914 --> 00:06:23.443
The pattern for times
10 is to add one zero.

00:06:23.443 --> 00:06:25.382
We can keep going here.

00:06:25.382 --> 00:06:29.549
Nine times 500 will be nine,
and then times five times 100.

00:06:32.882 --> 00:06:36.965
500 is five hundreds, just
like 50 was five tens.

00:06:38.827 --> 00:06:42.994
Multiplying across, nine
times five still equals 45,

00:06:43.877 --> 00:06:47.794
but this time we will
add two zeros to the end,

00:06:49.307 --> 00:06:50.140
or 4500.

00:06:52.465 --> 00:06:54.857
And finally, nine times 5,000 will be

00:06:54.857 --> 00:06:57.190
nine times five times 1,000;

00:07:00.615 --> 00:07:03.282
because 5,000 is five thousands,

00:07:04.510 --> 00:07:06.177
or 1,000 five times.

00:07:07.726 --> 00:07:10.726
Working across, nine times five, 45.

00:07:12.324 --> 00:07:15.074
And this time we add three zeros,

00:07:16.558 --> 00:07:17.391
so 45,000.

00:07:20.842 --> 00:07:23.896
So when we multiply each
of these expressions

00:07:23.896 --> 00:07:26.438
we can see the only thing that changed

00:07:26.438 --> 00:07:29.736
was the number of zeros on the end.

00:07:29.736 --> 00:07:33.915
So the pattern: anytime we
multiply a whole number times 10

00:07:33.915 --> 00:07:36.841
we add one zero to the end of our number;

00:07:36.841 --> 00:07:39.302
anytime we multiply a
whole number times 100

00:07:39.302 --> 00:07:41.102
we'll have two zeros;

00:07:41.102 --> 00:07:45.130
and times 1,000 we'll have three zeros.

00:07:45.130 --> 00:07:48.207
And once we know that pattern,
we can use it to help us

00:07:48.207 --> 00:07:51.411
with questions like this
where initially we don't see

00:07:51.411 --> 00:07:55.278
a 10; a 100; or a 1,000;
but we can get one;

00:07:55.278 --> 00:07:58.157
we can break up or decompose these numbers

00:07:58.157 --> 00:08:02.324
to get a 10 or 100 or 1,000
to help us solve the problem.


Multiplying 1-digit numbers by 10, 100, and 1000

WEBVTT
Kind: captions
Language: en

00:00:00.773 --> 00:00:02.186
- [Voiceover] Let's talk about multiplying

00:00:02.186 --> 00:00:03.936
by 10, 100, and 1000.

00:00:05.620 --> 00:00:06.940
There's some cool number patterns

00:00:06.940 --> 00:00:08.647
that happen with each of these.

00:00:08.647 --> 00:00:11.875
So let's start here with
something like four times 10,

00:00:11.875 --> 00:00:15.036
one that maybe we're comfortable
with or already know.

00:00:15.036 --> 00:00:17.619
Four times 10 would be the same

00:00:18.945 --> 00:00:20.028
as four tens.

00:00:22.625 --> 00:00:23.458
Four tens.

00:00:25.481 --> 00:00:26.648
And four tens,

00:00:27.989 --> 00:00:32.477
one way we could represent
that is a 10 plus a second 10

00:00:32.477 --> 00:00:35.407
plus a third 10 plus a fourth 10.

00:00:35.407 --> 00:00:36.490
Or four tens.

00:00:38.554 --> 00:00:40.252
And now let's count that.

00:00:40.252 --> 00:00:41.651
10 plus 10 is 20,

00:00:41.651 --> 00:00:42.760
plus 10 is 30,

00:00:42.760 --> 00:00:44.253
plus 10 is 40.

00:00:44.253 --> 00:00:45.503
So our solution

00:00:47.444 --> 00:00:49.861
is 40, or a four with a zero.

00:00:53.248 --> 00:00:56.681
And this is the pattern
that we've seen before.

00:00:56.681 --> 00:00:59.371
When we multiply four times 10,

00:00:59.371 --> 00:01:02.238
we keep our whole number of four

00:01:02.238 --> 00:01:06.071
and we add a zero to the
end for the times 10.

00:01:07.228 --> 00:01:09.623
So another example of
that might be something

00:01:09.623 --> 00:01:11.290
like eight times 10.

00:01:13.155 --> 00:01:17.072
Well, eight times 10 is
the same as eight tens.

00:01:18.011 --> 00:01:19.701
And this time let's just count them.

00:01:19.701 --> 00:01:20.726
If we count eight tens,

00:01:20.726 --> 00:01:23.059
it'll be 10, 20, 30, 40, 50,

00:01:24.144 --> 00:01:25.061
60, 70, 80.

00:01:26.677 --> 00:01:30.752
So when I counted eight
tens, the solution was 80,

00:01:30.752 --> 00:01:33.669
or an eight with a zero on the end.

00:01:35.678 --> 00:01:40.437
So times 10, when we multiply
a whole number times 10,

00:01:40.437 --> 00:01:44.789
the pattern is that we
end up adding a zero

00:01:44.789 --> 00:01:47.372
to the end of our whole number.

00:01:48.472 --> 00:01:51.300
So let's take now what we
already know about tens

00:01:51.300 --> 00:01:53.241
and let's apply it to hundreds.

00:01:53.241 --> 00:01:55.741
Something like, let's say, two

00:01:57.722 --> 00:01:58.555
times 100.

00:02:00.485 --> 00:02:02.740
There's a couple ways
we can think about this.

00:02:02.740 --> 00:02:06.907
One way is to say that this
is the same as two hundreds.

00:02:09.333 --> 00:02:10.416
Two hundreds,

00:02:11.483 --> 00:02:13.983
which is 100 plus another 100.

00:02:14.909 --> 00:02:17.966
There's quite literally two hundreds,

00:02:17.966 --> 00:02:19.966
which is a total of 200,

00:02:22.672 --> 00:02:25.422
or two with two zeros on the end.

00:02:26.268 --> 00:02:29.702
Now we have two zeros on the end.

00:02:29.702 --> 00:02:32.743
Or another way to think about this is two,

00:02:32.743 --> 00:02:35.676
two times 100, instead
of saying times 100,

00:02:35.676 --> 00:02:38.259
we could say times 10 times 10.

00:02:39.292 --> 00:02:42.542
Because 10 times 10 is the same as 100.

00:02:45.306 --> 00:02:49.473
And two times 10, we know as
a two with a zero on the end,

00:02:51.063 --> 00:02:52.202
which is 20,

00:02:52.202 --> 00:02:54.274
and 20 times 10

00:02:54.274 --> 00:02:57.524
then will be 20 with a zero on the end.

00:02:58.709 --> 00:03:01.081
Because we multiplied by 10 twice,

00:03:01.081 --> 00:03:02.664
we added two zeros.

00:03:04.079 --> 00:03:06.008
And multiplying by 100 is just that.

00:03:06.008 --> 00:03:06.971
It's exactly that.

00:03:06.971 --> 00:03:09.480
It's multiplying by 10 twice.

00:03:09.480 --> 00:03:11.964
So, if times 10 adds one zero,

00:03:11.964 --> 00:03:16.047
then times 100, or times
10 twice, adds two zeros

00:03:17.103 --> 00:03:18.270
to our answer.

00:03:20.737 --> 00:03:23.950
And we can go even further
and think about thousands.

00:03:23.950 --> 00:03:27.367
Let's try something like nine times 1000.

00:03:30.399 --> 00:03:33.621
Well, we could think of
this as nine thousands,

00:03:33.621 --> 00:03:36.505
and if we have nine thousands,

00:03:36.505 --> 00:03:40.005
then we have 1000, 2000, 3000, 4000, 5000,

00:03:41.222 --> 00:03:42.234
that was five,

00:03:42.234 --> 00:03:44.151
6000, 7000, 8000, 9000.

00:03:45.820 --> 00:03:48.804
So when I counted to 1000 nine times,

00:03:48.804 --> 00:03:50.637
our solution was 9000.

00:03:52.251 --> 00:03:53.898
Or looking at the numbers,

00:03:53.898 --> 00:03:56.905
a nine, our original whole number,

00:03:56.905 --> 00:03:59.072
with three zeros after it.

00:04:00.399 --> 00:04:01.899
So nine times 1000

00:04:02.823 --> 00:04:05.656
is 9000, or nine with three zeros.

00:04:06.535 --> 00:04:08.488
And we can go back to what we did before.

00:04:08.488 --> 00:04:10.607
Thinking about this in terms of tens

00:04:10.607 --> 00:04:12.346
we've worked out,

00:04:12.346 --> 00:04:14.723
when multiplying by 10 adds a zero,

00:04:14.723 --> 00:04:18.644
so let's think about
1000 in terms of tens.

00:04:18.644 --> 00:04:19.727
1000 is equal

00:04:21.939 --> 00:04:23.939
to 10 times 10 times 10.

00:04:27.004 --> 00:04:28.587
10 times 10 is 100,

00:04:30.986 --> 00:04:32.736
and 100 tens is 1000.

00:04:35.273 --> 00:04:38.131
So instead of 1000, we can write

00:04:38.131 --> 00:04:40.210
10 times 10 times 10.

00:04:40.210 --> 00:04:41.823
These are equivalent.

00:04:41.823 --> 00:04:44.472
And so, when we multiply
a number times 10,

00:04:44.472 --> 00:04:45.639
we add a zero.

00:04:46.692 --> 00:04:49.209
But here we're multiplying by three tens,

00:04:49.209 --> 00:04:51.042
so we add three zeros.

00:04:54.021 --> 00:04:57.252
So let's look at that all as one pattern.

00:04:57.252 --> 00:05:00.476
Let's take seven, the number seven,

00:05:00.476 --> 00:05:03.510
and let's multiply it by 10,

00:05:03.510 --> 00:05:04.343
by 100,

00:05:05.993 --> 00:05:06.993
and by 1000,

00:05:08.727 --> 00:05:10.477
and see what happens.

00:05:11.499 --> 00:05:15.582
Seven times 10 is going
to be seven with one zero

00:05:16.712 --> 00:05:18.629
'cause we have one ten.

00:05:19.492 --> 00:05:23.142
Seven times 100 will
be seven with two zeros

00:05:23.142 --> 00:05:27.493
because, again, 100 is
the same as 10 times 10.

00:05:27.493 --> 00:05:30.365
So this is seven times 10 twice

00:05:30.365 --> 00:05:32.115
so we have two zeros.

00:05:33.242 --> 00:05:36.383
And seven times 1000 will be 7000,

00:05:36.383 --> 00:05:39.258
or seven with three zeros

00:05:39.258 --> 00:05:43.091
because 1000 is equal
to 10 times 10 times 10,

00:05:46.491 --> 00:05:47.658
or three tens.

00:05:48.499 --> 00:05:51.166
So we had one, two, three zeros.

00:05:52.990 --> 00:05:54.988
And so, we can see the pattern here.

00:05:54.988 --> 00:05:58.879
When we multiply by
10, which has one zero,

00:05:58.879 --> 00:06:01.774
we add one zero to the
end of our whole number.

00:06:01.774 --> 00:06:04.731
When we multiply a whole number times 100,

00:06:04.731 --> 00:06:08.398
which has two zeros, we
add two zeros for hundreds.

00:06:08.398 --> 00:06:11.517
And for thousands, when
we multiply by 1000,

00:06:11.517 --> 00:06:15.684
we'll add three zeros to
the end of a whole number.


Place value when multiplying and dividing by 10

WEBVTT
Kind: captions
Language: en

00:00:01.453 --> 00:00:05.145
- [Voiceover] What is 7 100s times 10?

00:00:05.145 --> 00:00:06.306
Well, let's focus first

00:00:06.306 --> 00:00:10.296
on this times 10 part of our expression.

00:00:10.296 --> 00:00:13.567
Because multiplying by 10
has some patterns in math

00:00:13.567 --> 00:00:16.660
that we can use to help us solve.

00:00:16.660 --> 00:00:19.641
One pattern we can think
of when we multiply by 10

00:00:19.641 --> 00:00:23.423
is if we take a whole number
and multiply it by 10,

00:00:23.423 --> 00:00:25.340
we'll simply add a zero

00:00:27.329 --> 00:00:29.832
to the end of our whole number.

00:00:29.832 --> 00:00:33.350
So, for example, if we have
a whole number like nine,

00:00:33.350 --> 00:00:35.567
and we multiply by 10,

00:00:35.567 --> 00:00:40.470
our solution will be a nine
with one zero at the end.

00:00:40.470 --> 00:00:41.876
Or 90.

00:00:41.876 --> 00:00:45.847
Because nine times 10
is the same as nine 10s,

00:00:45.847 --> 00:00:47.764
and nine 10s is ninety.

00:00:49.657 --> 00:00:53.058
So let's use that pattern
first to try to solve.

00:00:53.058 --> 00:00:54.899
Here we have seven 100s.

00:00:54.899 --> 00:00:57.077
So, seven times we have 100,

00:00:57.077 --> 00:00:57.910
or 700,

00:00:59.926 --> 00:01:03.388
and we're multiplying again times 10.

00:01:03.388 --> 00:01:05.390
Use this pattern over here.

00:01:05.390 --> 00:01:08.687
Our solution will add a zero at the end.

00:01:08.687 --> 00:01:11.437
So if we had 700, 10 times,

00:01:11.437 --> 00:01:14.854
we would have 700 with a zero on the end.

00:01:15.974 --> 00:01:16.807
Or 7,000.

00:01:18.618 --> 00:01:22.201
So seven 100s times
ten, is equal to 7,000.

00:01:25.044 --> 00:01:28.268
But there's another
pattern we could use, here.

00:01:28.268 --> 00:01:32.177
Another pattern to think
about when we multiply by 10.

00:01:32.177 --> 00:01:34.703
And that is that when we multiply by 10,

00:01:34.703 --> 00:01:37.703
we move every digit one place value,

00:01:40.587 --> 00:01:41.920
one place value,

00:01:43.021 --> 00:01:44.167
left.

00:01:44.167 --> 00:01:46.417
Or one place value greater.

00:01:47.300 --> 00:01:51.701
So let's look at that one
on a place value chart.

00:01:51.701 --> 00:01:53.142
Here we have a place value chart.

00:01:53.142 --> 00:01:58.062
To use that earlier example
when we had nine ones,

00:01:58.062 --> 00:02:01.064
and we multiplied it by 10,

00:02:01.064 --> 00:02:03.894
our nine moved one
place value to the left.

00:02:03.894 --> 00:02:05.078
It moved up to the 10s.

00:02:05.078 --> 00:02:07.436
Now, we had nine 10s.

00:02:07.436 --> 00:02:09.060
And we filled in a zero here,

00:02:09.060 --> 00:02:12.328
because there were no ones
left; there were zero ones left.

00:02:12.328 --> 00:02:15.078
And so, we saw that nine times 10

00:02:16.694 --> 00:02:18.027
was equal to 90.

00:02:21.672 --> 00:02:24.141
So again, it's the same as
adding a zero at the end,

00:02:24.141 --> 00:02:25.639
but we're looking at it another way.

00:02:25.639 --> 00:02:28.018
We're looking at it in
terms of place value

00:02:28.018 --> 00:02:30.477
and multiplying by 10 moved every digit

00:02:30.477 --> 00:02:32.810
one place value to the left.

00:02:35.603 --> 00:02:37.580
So, if we do that with this same question,

00:02:37.580 --> 00:02:39.280
seven 100s,

00:02:39.280 --> 00:02:44.007
seven 100s, if we move 100s
one place value to the left,

00:02:44.007 --> 00:02:45.821
we'll end up with 1,000s.

00:02:45.821 --> 00:02:47.904
So, 700 times 10 is seven

00:02:50.300 --> 00:02:51.133
1,000s.

00:02:53.640 --> 00:02:55.091
Or, as we saw earlier,

00:02:55.091 --> 00:02:55.924
7,000.

00:02:57.765 --> 00:03:01.528
So either one of these
is a correct answer.

00:03:01.528 --> 00:03:03.361
700 times 10 is 7,000.

00:03:07.660 --> 00:03:09.588
And here's an example with division.

00:03:09.588 --> 00:03:11.838
Now we have dividing by 10.

00:03:13.096 --> 00:03:14.339
And as you might predict,

00:03:14.339 --> 00:03:18.055
dividing by 10 is the
opposite of multiplying by 10,

00:03:18.055 --> 00:03:21.886
so our patterns are also the opposite.

00:03:21.886 --> 00:03:25.008
Instead of adding a zero to
the end of a whole number,

00:03:25.008 --> 00:03:27.675
we would drop a zero at the end.

00:03:29.164 --> 00:03:31.514
We would drop a zero at the end.

00:03:31.514 --> 00:03:34.264
So, for an example, if we had 40,

00:03:35.366 --> 00:03:37.319
divided by 10,

00:03:37.319 --> 00:03:40.808
we would drop that zero
and end up with four.

00:03:40.808 --> 00:03:44.089
If you divide 40 into groups of 10,

00:03:44.089 --> 00:03:45.839
you have four groups.

00:03:47.107 --> 00:03:49.190
Let's use that over here.

00:03:50.599 --> 00:03:51.972
212 10s.

00:03:51.972 --> 00:03:53.139
So we have 212

00:03:54.314 --> 00:03:55.941
10s.

00:03:55.941 --> 00:03:58.144
So 212, 10 times.

00:03:58.144 --> 00:04:00.887
That's how we got the zero, there.

00:04:00.887 --> 00:04:03.224
And we divide that by 10,

00:04:03.224 --> 00:04:05.438
we can use this first
pattern we thought of

00:04:05.438 --> 00:04:07.784
and just drop the zero on the end.

00:04:07.784 --> 00:04:09.331
Let's drop that zero,

00:04:09.331 --> 00:04:11.581
and our answer will be 212.

00:04:14.637 --> 00:04:15.619
But we could also,

00:04:15.619 --> 00:04:17.392
we could use the place value pattern.

00:04:17.392 --> 00:04:19.749
We could think in terms of place value.

00:04:19.749 --> 00:04:23.916
And instead of moving one
place value to the left,

00:04:25.556 --> 00:04:26.953
one place value larger,

00:04:26.953 --> 00:04:30.154
we're gonna move one place value smaller.

00:04:30.154 --> 00:04:31.667
Or to the right.

00:04:31.667 --> 00:04:34.526
One place value to the right.

00:04:34.526 --> 00:04:39.126
So what's one place value
smaller than 212 10s?

00:04:39.126 --> 00:04:41.959
If we have 212 10s, divided by 10,

00:04:43.207 --> 00:04:46.631
we wanna move this 10s one
place value to the right,

00:04:46.631 --> 00:04:49.038
or smaller, which is ones.

00:04:49.038 --> 00:04:50.559
So our solution

00:04:50.559 --> 00:04:52.059
would be 212 ones.

00:04:55.616 --> 00:04:58.019
Which is equal to what we already saw,

00:04:58.019 --> 00:04:58.936
simply 212.

00:04:59.973 --> 00:05:02.140
So 212 10s, divided by 10.

00:05:03.318 --> 00:05:06.399
We could write the number
out and drop a zero,

00:05:06.399 --> 00:05:08.428
or we could think about place value

00:05:08.428 --> 00:05:10.381
and move one place value to the right.

00:05:10.381 --> 00:05:13.298
Either way, our answer is 212 ones.


Dividing whole numbers by 10

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.997
- [Voiceover] Dividing by 10,
a lot like multiplying by 10,

00:00:03.997 --> 00:00:06.159
creates a pattern with numbers.

00:00:06.159 --> 00:00:08.312
So let's dig in and look at dividing by 10

00:00:08.312 --> 00:00:10.363
and look at happens when we divide by 10

00:00:10.363 --> 00:00:12.389
and see if we can figure out that pattern

00:00:12.389 --> 00:00:14.318
and maybe even how it relates

00:00:14.318 --> 00:00:16.623
to the pattern for multiplying by 10.

00:00:16.623 --> 00:00:20.426
Let's take a fairly simple one to start.

00:00:20.426 --> 00:00:23.926
Let's say something like 30 divided by 10.

00:00:26.121 --> 00:00:30.103
One way to think about this
is we're taking the number 30

00:00:30.103 --> 00:00:33.064
and we're dividing it into groups of 10.

00:00:33.064 --> 00:00:37.231
So let's see how many groups
of 10 it takes to make 30.

00:00:38.869 --> 00:00:42.187
One group of 10 is 10,
so that's not enough,

00:00:42.187 --> 00:00:46.354
plus a second group is 20,
plus a third group is 30.

00:00:47.280 --> 00:00:51.069
So 30 can be thought of
as 10 plus 10 plus 10,

00:00:51.069 --> 00:00:52.902
or three groups of 10.

00:00:54.607 --> 00:00:58.774
So if we divide 30 by 10,
divide 30 into groups of 10,

00:00:59.937 --> 00:01:02.270
we end up with three groups.

00:01:05.770 --> 00:01:09.844
Let's try another one, maybe
something slightly trickier,

00:01:09.844 --> 00:01:13.011
maybe let's go with 110 divided by 10.

00:01:18.841 --> 00:01:22.265
And again, we're
dividing, we're taking 110

00:01:22.265 --> 00:01:24.919
and dividing it into groups of 10.

00:01:24.919 --> 00:01:28.801
So let's see how many groups
of 10 it takes to get to 110.

00:01:28.801 --> 00:01:31.583
Here's one 10, plus another is 20,

00:01:31.583 --> 00:01:32.500
30, 40, 50,

00:01:37.255 --> 00:01:40.005
another 10 gets us to 60, 70, 80,

00:01:42.885 --> 00:01:46.135
we're getting closer, 90, 100, and 110.

00:01:48.843 --> 00:01:53.238
So this right here is
how many groups of 10

00:01:53.238 --> 00:01:55.405
it takes us to get to 110.

00:01:56.431 --> 00:01:59.040
So let's see how many groups is that.

00:01:59.040 --> 00:02:03.207
One, two, three, four, five,
six, seven, eight, nine, 10,

00:02:04.672 --> 00:02:06.589
11, our solution is 11.

00:02:09.389 --> 00:02:13.384
If we have 110 and we
divide it into groups of 10,

00:02:13.384 --> 00:02:15.467
we end up with 11 groups.

00:02:17.316 --> 00:02:19.653
Let's look at these first two,

00:02:19.653 --> 00:02:22.543
let's pause here and
see if we see a pattern.

00:02:22.543 --> 00:02:26.710
30 divide by 10 was three,
110 divided by 10 was 11,

00:02:28.368 --> 00:02:31.451
so what happened to the 30 in the 110

00:02:32.488 --> 00:02:35.008
to get these quotients?

00:02:35.008 --> 00:02:37.508
And what happened is the zero,

00:02:38.617 --> 00:02:41.199
the zero on the end was taken off.

00:02:41.199 --> 00:02:43.159
Our solution is the same,

00:02:43.159 --> 00:02:45.958
but with the zero taken off the end.

00:02:45.958 --> 00:02:48.584
Here again, the solution is the same

00:02:48.584 --> 00:02:50.930
with a zero taken off the end.

00:02:50.930 --> 00:02:54.929
And if we remember for
multiplication, it was the opposite.

00:02:54.929 --> 00:02:59.059
If we had two times 10
instead of dividing,

00:02:59.059 --> 00:03:01.559
times 10, our solution was 20,

00:03:03.698 --> 00:03:07.865
or two, our original number,
with a zero added to the end.

00:03:11.134 --> 00:03:15.301
Remember, in another one,
something like 13 times 10,

00:03:16.361 --> 00:03:19.546
our product, our solution is a 13,

00:03:19.546 --> 00:03:23.667
the original number, with
a zero added to the end.

00:03:23.667 --> 00:03:27.779
So in multiplication,
when we multiply by 10,

00:03:27.779 --> 00:03:31.335
we add a zero to our
whole number at the end,

00:03:31.335 --> 00:03:34.634
and when we divide, we
do the opposite by 10,

00:03:34.634 --> 00:03:38.801
we take off a zero from the
end of our whole number.

00:03:39.987 --> 00:03:42.712
So knowing that pattern,
let's try one more,

00:03:42.712 --> 00:03:45.716
maybe one where we don't
work out all the 10s,

00:03:45.716 --> 00:03:48.988
but just try to use the
pattern to solve it.

00:03:48.988 --> 00:03:51.062
If we had somethig like, say,

00:03:51.062 --> 00:03:52.729
7,000 divided by 10,

00:03:55.868 --> 00:03:59.118
well, our solution is going to be 7,000

00:04:00.008 --> 00:04:03.557
but with a zero taken off of the end

00:04:03.557 --> 00:04:05.707
because we're dividing by 10,

00:04:05.707 --> 00:04:08.874
so instead of 7,000 we would have 700.

00:04:11.135 --> 00:04:16.060
7,000 divided into groups of
10 would be 700 groups of 10,

00:04:16.060 --> 00:04:17.977
so our solution is 700.

00:04:18.883 --> 00:04:21.924
Let's take this all a step
further and let's think

00:04:21.924 --> 00:04:25.399
about what dividing by 10
is doing to these numbers,

00:04:25.399 --> 00:04:30.354
to 30, to 110, to 7,000, in
terms of their place value.

00:04:30.354 --> 00:04:32.808
So here's a place value chart.

00:04:32.808 --> 00:04:35.223
Let's use it to look at one of the numbers

00:04:35.223 --> 00:04:38.223
we already tried, something like 30.

00:04:39.519 --> 00:04:41.936
And when we divided 30 by 10,

00:04:43.592 --> 00:04:46.088
remember what happened to the three,

00:04:46.088 --> 00:04:50.255
instead of being three 10s,
our solution was three ones.

00:04:51.595 --> 00:04:55.247
The three moved one
place value to the right,

00:04:55.247 --> 00:04:59.245
and the zero really did too,
it would move after a decimal,

00:04:59.245 --> 00:05:03.162
which would be 3.0, which
is the same as three,

00:05:04.498 --> 00:05:06.873
which is the reason we didn't
need to write that zero,

00:05:06.873 --> 00:05:09.527
the reason that we could cross it off.

00:05:09.527 --> 00:05:12.067
So our number, instead of being three 10s,

00:05:12.067 --> 00:05:15.288
when we divided by 10, became three ones.

00:05:15.288 --> 00:05:17.782
Let's look at a little
bit trickier of one.

00:05:17.782 --> 00:05:22.143
We also tried 7,000, so that
would be seven thousands,

00:05:22.143 --> 00:05:25.149
zero hundreds, zero 10s, and zero ones,

00:05:25.149 --> 00:05:27.316
and when we divided by 10,

00:05:28.829 --> 00:05:32.978
our seven in our thousands
place became seven hundreds,

00:05:32.978 --> 00:05:36.518
and the zero hundreds became zero 10s,

00:05:36.518 --> 00:05:39.452
and zero 10s became zero ones.

00:05:39.452 --> 00:05:43.098
And that last zero we
were able to cross off

00:05:43.098 --> 00:05:45.444
and move to after the decimal.

00:05:45.444 --> 00:05:48.027
So 7,000 divided by 10 was 700.

00:05:50.112 --> 00:05:54.813
Again, everything moved one
place value to the right.

00:05:54.813 --> 00:05:58.460
So there's two ways to
think about dividing by 10.

00:05:58.460 --> 00:06:01.827
We could either say you
drop a zero off the end,

00:06:01.827 --> 00:06:03.950
or we could say that you move

00:06:03.950 --> 00:06:07.367
every digit one place value to the right.

00:06:08.755 --> 00:06:11.094
Let's think about it again
in terms of place value

00:06:11.094 --> 00:06:15.094
with a new number, let's
try something like 630.

00:06:20.691 --> 00:06:24.858
If we divide 630 by 10, we're
going to move everything

00:06:26.801 --> 00:06:29.716
one place value to the
right, so the six hundreds

00:06:29.716 --> 00:06:33.883
will become six 10s, three
10s will become three ones,

00:06:35.832 --> 00:06:39.567
and the zero ones will
move after the decimal.

00:06:39.567 --> 00:06:42.567
So we can say that 630 divided by 10

00:06:46.088 --> 00:06:49.588
is equal to 63, or six 10s and three ones.

00:06:53.393 --> 00:06:58.283
So again, two ways to
think about dividing by 10.

00:06:58.283 --> 00:07:02.450
Either we can cross off a
zero, or we move every digit,

00:07:04.583 --> 00:07:07.916
each digit one place value to the right.


Multiplying whole numbers by 10

WEBVTT
Kind: captions
Language: en

00:00:01.214 --> 00:00:02.756
- [Voiceover] Multiplying by 10 creates

00:00:02.756 --> 00:00:05.130
a really neat pattern with numbers,

00:00:05.130 --> 00:00:06.471
so let's try a few out and see

00:00:06.471 --> 00:00:07.975
if we can discover the pattern.

00:00:07.975 --> 00:00:09.897
Let's try to figure it out.

00:00:09.897 --> 00:00:11.813
We'll start with one that
maybe we already know,

00:00:11.813 --> 00:00:15.146
let's start something like two times 10.

00:00:17.190 --> 00:00:19.068
And maybe we know the
solution but let's think about

00:00:19.068 --> 00:00:20.404
more than just the solution,

00:00:20.404 --> 00:00:22.153
let's think about what it really means

00:00:22.153 --> 00:00:24.533
to multiply two times 10.

00:00:24.533 --> 00:00:27.450
Two times 10 means we have two 10s.

00:00:29.836 --> 00:00:32.669
Or, we have a 10, plus another 10.

00:00:34.791 --> 00:00:38.958
Which is equal 10 plus
another 10, is equal to 20.

00:00:41.756 --> 00:00:44.376
And again, maybe we didn't
need this middle part,

00:00:44.376 --> 00:00:46.553
maybe we already knew two times 10 is 20,

00:00:46.553 --> 00:00:49.177
but it'll be helpful to think about what

00:00:49.177 --> 00:00:50.887
two times 10 means because it will help us

00:00:50.887 --> 00:00:54.271
when we get to much trickier ones.

00:00:54.271 --> 00:00:56.560
Let's try one that's maybe
just a little bit trickier,

00:00:56.560 --> 00:00:58.560
let's try five times 10.

00:01:00.603 --> 00:01:03.770
Five times 10 is going to be five 10s,

00:01:06.779 --> 00:01:10.279
or, one 10 plus another 10 plus a third 10

00:01:11.691 --> 00:01:15.858
plus a fourth 10 plus a fifth
10, so we have five 10s,

00:01:16.959 --> 00:01:20.292
we have one, two, three, four, five 10s.

00:01:21.401 --> 00:01:23.991
And we can solve that, we
can add those together,

00:01:23.991 --> 00:01:25.574
10, 20, 30, 40, 50.

00:01:29.967 --> 00:01:32.300
So our solution here, is 50.

00:01:35.211 --> 00:01:38.461
Five 10s is 50, or five times 10 is 50.

00:01:39.945 --> 00:01:42.030
Let's go to one more, maybe
one that we don't know

00:01:42.030 --> 00:01:43.662
the answer to off the top of our head,

00:01:43.662 --> 00:01:46.745
let's try something like 13 times 10.

00:01:48.131 --> 00:01:50.463
Maybe we don't know the
answer to 13 times 10

00:01:50.463 --> 00:01:53.963
but we do know that 13 times 10 is 13 10s.

00:01:56.216 --> 00:01:58.305
And we can count 13 tens.

00:01:58.305 --> 00:02:02.770
We have a 10, plus another 10,
plus another, there's three,

00:02:02.770 --> 00:02:06.437
four, five, six 10s,
seven, eight, nine, 10,

00:02:12.722 --> 00:02:15.639
we're almost there, 11 10s, 12 10s,

00:02:16.893 --> 00:02:18.806
and finally a thirteenth 10.

00:02:18.806 --> 00:02:20.389
Let's count to make sure.

00:02:20.389 --> 00:02:24.520
One, two, three, four, five,
six, seven, eight, nine, 10,

00:02:24.520 --> 00:02:26.020
11, 12, 13, great.

00:02:27.602 --> 00:02:30.161
So we have 13 10s, so let's count those,

00:02:30.161 --> 00:02:31.669
let's see how much that is.

00:02:31.669 --> 00:02:34.919
We have 10, 20, 30, 40, 50, 60, 70, 80,

00:02:38.756 --> 00:02:40.673
90, 100, 110, 120, 130.

00:02:44.431 --> 00:02:46.348
So our solution is 130.

00:02:49.493 --> 00:02:51.628
I think we can pause
here and look at the ones

00:02:51.628 --> 00:02:55.296
we've done so far and see if
we can figure out this pattern.

00:02:55.296 --> 00:02:58.463
Two times 10 is 20, five times 10, 50,

00:03:00.636 --> 00:03:02.053
13 times 10, 130.

00:03:04.134 --> 00:03:08.301
In every case we took the
number that we started with,

00:03:09.723 --> 00:03:11.896
and we kept that, that
was part of our answer,

00:03:11.896 --> 00:03:13.524
and then we added one new thing,

00:03:13.524 --> 00:03:16.237
which was a zero at the end.

00:03:16.237 --> 00:03:18.995
Any time we multiply a whole number by 10

00:03:18.995 --> 00:03:21.804
we're gonna keep the original number

00:03:21.804 --> 00:03:25.060
and simply add a zero to the end.

00:03:25.060 --> 00:03:28.834
So let's try some without
all this middle stuff.

00:03:28.834 --> 00:03:33.001
What if we had something
like, a little bit tougher,

00:03:35.834 --> 00:03:37.751
maybe like 49 times 10.

00:03:41.095 --> 00:03:43.611
Well 49 times 10, you may guess is,

00:03:43.611 --> 00:03:47.444
is gonna be a 49 with
what at the end, a zero.

00:03:49.200 --> 00:03:52.283
Or 490, because this would be 49 10s,

00:03:54.585 --> 00:03:58.335
and if we counted 49
10s we would get to 490.

00:04:00.305 --> 00:04:01.976
Let's go even tougher than that.

00:04:01.976 --> 00:04:05.559
What if we had something
like 723 times 10?

00:04:09.764 --> 00:04:12.810
Well our solution, and
maybe you've guessed it,

00:04:12.810 --> 00:04:16.310
is going to be 723 with a zero on the end,

00:04:18.791 --> 00:04:21.291
or, 7000 200 and 30 is the way

00:04:22.973 --> 00:04:24.808
we would actually read that answer.

00:04:24.808 --> 00:04:28.280
But looking at it, it quite
simply is the original number,

00:04:28.280 --> 00:04:30.613
723, with a zero on the end.

00:04:33.805 --> 00:04:35.931
Let's take this one step
further and let's think about it

00:04:35.931 --> 00:04:37.147
in terms of place value.

00:04:37.147 --> 00:04:39.455
Let's think about what
multiplying by 10 did

00:04:39.455 --> 00:04:43.455
to these numbers in terms
of their place values.

00:04:45.010 --> 00:04:46.856
So here we have a place value chart,

00:04:46.856 --> 00:04:48.861
and let's start back with one
of the simpler ones we did,

00:04:48.861 --> 00:04:50.275
like two.

00:04:50.275 --> 00:04:51.608
Two is two ones.

00:04:54.708 --> 00:04:57.635
And when we multiply that two times 10,

00:04:57.635 --> 00:05:00.218
the two moved up a place value.

00:05:02.815 --> 00:05:05.153
And then we had to fill
in this empty place value

00:05:05.153 --> 00:05:06.778
with a zero.

00:05:06.778 --> 00:05:10.974
So two times 10 was 20,
and what happened in terms

00:05:10.974 --> 00:05:13.698
of place value, was the two
moved up one place value,

00:05:13.698 --> 00:05:15.865
it went from ones to tens,

00:05:17.111 --> 00:05:20.574
it moved to the left one place value.

00:05:20.574 --> 00:05:24.419
Let's look at another one,
maybe one of the tougher ones,

00:05:24.419 --> 00:05:26.002
something like 723.

00:05:29.469 --> 00:05:31.969
When we multiply 723 times 10,

00:05:33.226 --> 00:05:35.396
we multiplied this one times 10,

00:05:35.396 --> 00:05:38.569
the seven moved one
place value to the left

00:05:38.569 --> 00:05:43.151
to the thousands, the two
moved up to the hundreds,

00:05:43.151 --> 00:05:45.608
and the three moved up to the tens.

00:05:45.608 --> 00:05:48.479
And then again, we simply added a zero

00:05:48.479 --> 00:05:50.816
in the empty place value in the end.

00:05:50.816 --> 00:05:54.504
So multiplying by 10, one
way to describe the pattern,

00:05:54.504 --> 00:05:58.030
is that it adds a zero to
the end of a whole number.

00:05:58.030 --> 00:06:00.323
But another way to describe the pattern,

00:06:00.323 --> 00:06:04.333
is that it moves every
place value, every number,

00:06:04.333 --> 00:06:06.666
one place value to the left.

00:06:08.084 --> 00:06:10.294
So if we tried one looking at it this way,

00:06:10.294 --> 00:06:14.461
let's say we tried something
like, 20, let's do 27.

00:06:20.210 --> 00:06:22.460
If we multiply 27 times 10,

00:06:23.787 --> 00:06:27.089
well the two's gonna move
one place value over,

00:06:27.089 --> 00:06:29.052
so it will now be in the hundreds,

00:06:29.052 --> 00:06:31.896
and the seven's gonna
move over a place value,

00:06:31.896 --> 00:06:34.143
so it will be in the tens,

00:06:34.143 --> 00:06:35.485
and then we'll have to fill in

00:06:35.485 --> 00:06:37.948
that empty place value with a zero.

00:06:37.948 --> 00:06:41.865
So we can say that 27
times 10 is equal to 270.

00:06:47.870 --> 00:06:50.123
So whether we think about
it as adding the zero

00:06:50.123 --> 00:06:52.873
to the end or moving the
place value to the left,

00:06:52.873 --> 00:06:55.807
multiplying by 10 creates
a really neat pattern,

00:06:55.807 --> 00:06:59.859
that we can use to help us
to solve these problems.