Strategies for dividing multiples of 10, 100 and 1000

WEBVTT
Kind: captions
Language: en

00:00:00.195 --> 00:00:01.256
- [Instructor] We're
going to do in this video

00:00:01.256 --> 00:00:03.977
is get some practice doing division

00:00:03.977 --> 00:00:08.356
with numbers that are
multiples of 10, 100, 1,000,

00:00:08.356 --> 00:00:09.616
things like that.

00:00:09.616 --> 00:00:11.033
So let's say we wanted to compute

00:00:11.033 --> 00:00:11.866
what 2,400

00:00:14.283 --> 00:00:15.700
divided by 30 is.

00:00:18.335 --> 00:00:19.228
Pause this video,

00:00:19.228 --> 00:00:20.923
and see if you can calculate it

00:00:20.923 --> 00:00:24.895
using whatever strategy
makes sense to you.

00:00:24.895 --> 00:00:26.763
Alright, so let's think
about this together,

00:00:26.763 --> 00:00:29.428
and I'm gonna show you how my
brain likes to handle this.

00:00:29.428 --> 00:00:32.729
We'll do this out on my
little digital blackboard,

00:00:32.729 --> 00:00:34.769
but eventually you'll be
able to do things like this

00:00:34.769 --> 00:00:36.110
in your head.

00:00:36.110 --> 00:00:38.777
So 2,400 or 2,400 divided by 30,

00:00:40.918 --> 00:00:43.501
that is the same thing as 2,400

00:00:48.882 --> 00:00:49.715
over 30.

00:00:53.609 --> 00:00:56.082
So this is just another
way of saying 2,400

00:00:56.082 --> 00:00:57.708
divided by 30.

00:00:57.708 --> 00:00:59.732
Now the reason why I wrote it this way

00:00:59.732 --> 00:01:03.674
is because you can now
write each of these,

00:01:03.674 --> 00:01:05.037
the numerator and the denominator

00:01:05.037 --> 00:01:07.122
as the product of some number

00:01:07.122 --> 00:01:10.239
and either 10 or 100 or 1,000.

00:01:10.239 --> 00:01:14.239
So 2,400, that's the same
thing as 24 times 100,

00:01:19.281 --> 00:01:20.114
and I knew that.

00:01:20.114 --> 00:01:22.180
I was like, okay, I've got
these two zeros at the end,

00:01:22.180 --> 00:01:25.894
so you could view this
literally as 24 hundreds,

00:01:25.894 --> 00:01:28.285
and then 30 you can view as,

00:01:28.285 --> 00:01:29.479
we got one zero here,

00:01:29.479 --> 00:01:31.111
so it's three tens.

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The three is in the tens place.

00:01:33.051 --> 00:01:34.551
So three times 10.

00:01:36.509 --> 00:01:39.605
Now what's valuable about
thinking of it this way

00:01:39.605 --> 00:01:43.739
is you can separately
divide the 24 by the three

00:01:43.739 --> 00:01:45.734
and then the 100 by the 10,

00:01:45.734 --> 00:01:48.394
so this is the same thing as,

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lemme do this this way,

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as that times that.

00:01:52.427 --> 00:01:55.260
And so we have 24 divided by three

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times 100 divided by 10.

00:02:04.857 --> 00:02:06.860
Now 24 divided by three,

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you might already know
that is going to be eight.

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Three times eight is 24.

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So this is going to be equal to eight,

00:02:16.832 --> 00:02:19.415
and what's 100 divided by 10?

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Well, 100 divided by 10
is just going to be 10,

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so our quotient, I guess you could say,

00:02:26.342 --> 00:02:28.077
is going to be eight times 10,

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or it's going to be equal to 80,

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and we're done.

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And you might notice
something interesting here.

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So if I take my 24

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and divide it by my three,

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I'm gonna get this eight,

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and then if I take two zeros

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and if I take away another zero,

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I'm gonna be left with
one zero right over here.

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So you get 80,

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but why did that thing
with the zeros work?

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Because you're really
just taking 2,400 hundreds

00:03:00.804 --> 00:03:02.959
divided by three tens.

00:03:02.959 --> 00:03:05.043
So 100 divided by 10,

00:03:05.043 --> 00:03:06.100
well, you're gonna lose a zero.

00:03:06.100 --> 00:03:07.267
That's gonna be equal to 10,

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which has only one zero.

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Let's do another example
just to hit the point home,

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and try to do this next example

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the way we just did it,

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maybe in your head

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or maybe on a piece of paper.

00:03:16.524 --> 00:03:19.664
So let's say we wanted to calculate 3,500,

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which you could also think of as 3,500,

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and we wanna divide that by,

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lemme write the division symbol

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a little bit nicer than that.

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We wanna divide that by 700.

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Pause this video and see
if you can compute that.

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So as we just did,

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we could view this as 3,500 over 700.

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3,500 we can view as 35

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times 100

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over, this is going to be over.

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Lemme get the right color here,

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over seven times 100.

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Now the one hundreds cancel out,

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and we're just left with 35 over seven.

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Now what's 35 divided by seven?

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Well, that is going to be equal to five,

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and notice, you could just say 35

00:04:22.855 --> 00:04:24.938
divided by seven is five,

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and if you're saying, "How many
zeros do I have left over?"

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Well, I have two zeros here,

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but since I'm dividing by
something with two zeros,

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those two zeros are
going to be canceled out.

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I don't want you to just memorize that.

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The reason why that happens is
because those two zeros here

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represent hundreds, 35 hundreds.

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These two zeros represent hundreds,

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so if you divide 100 by hundreds,

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they're all gonna cancel out.

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So you had two zeros before,

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but you're dividing by
something with the two zeros,

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so you don't have any
zeros after the five here.

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Lemme do one more example

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just to really hit that point home,

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but I want you to appreciate that

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it's not just some magical trick.

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It just makes sense out of things

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that you might already know.

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So if someone, and I'm
gonna give a crazy one,

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let's say we had 42 million

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divided by,

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let's say, 60,000.

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What is that going to be?

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Pause the video and see
if you can think about it

00:05:27.078 --> 00:05:28.870
on your own.

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Well, using the notions
that we just talked about,

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you could say, "Alright, 42 divided by six

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"is going to be seven."

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And then if I, let's see,

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over here I have six zeros,

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so we're talking about millions,

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and I'm gonna divide by
four zeros right over here,

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which is 10 thousands.

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So if you had six zeros,

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or if you have millions with six zeros

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and you divide by 10
thousands with four zeros,

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six minus four is gonna be two,

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so your answer's gonna
have two zeros in it.

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So this is going to be equal to 700.

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Now once again, not a magical trick,

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the way that we got this

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is that this is equal
to 42 times a million.

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We got our six zeros right over there

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divided by

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six 10 thousands,

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six times 10,000.

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So our 42 divided by six,

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that's where we get the seven from,

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and now one way to think about it,

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if we divide the numerator
and the denominator by 10,

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we lose a zero.

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Then we do it again.

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We lose zeros.

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We do it again.

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We lose zeros.

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We do it again.

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We lose zeros,

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and so this thing just all becomes one,

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or another way to think about it,

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if we divide the numerator

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and the denominator by 10,000,

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this becomes one.

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This thing loses four zeros,

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and you're left with,

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42 divided by six is seven hundreds,

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because we have a one
now in the denominator,

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100 divided by one, so 700.


Introduction to dividing by 2 digits

WEBVTT
Kind: captions
Language: en

00:00:00.025 --> 00:00:02.480
- [Instructor] What we're
going to do in this video is

00:00:02.480 --> 00:00:06.861
start trying to divide
by two-digit numbers.

00:00:06.861 --> 00:00:09.207
And as we'll see, this is
a super important skill

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that a lot of the rest of
mathematics will build off of,

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but it's also interesting
'cause it's a bit of an art.

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So let's just start

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by trying to compute what
186 divided by 31 is.

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And of course, we could
also write this as 186

00:00:24.959 --> 00:00:26.126
divided by 31.

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Pause the video, and see
if you can figure it out.

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All right, now let's work
through this together.

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I assumed you've given it a go at it.

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So I don't have my 31
times tables memorized,

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so I can't just immediately
tell you the answer.

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But my brain tries to
approximate these numbers

00:00:43.847 --> 00:00:48.119
so that my times tables
knowledge does come in handy.

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For example, 31 is close to 30.

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And this is why I'm saying
it's a bit of an art,

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but I'm saying, hey, look,
this is pretty close to 30.

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And if I think about multiples of 30,

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well, those are just
the multiples of three

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with an extra zero or the
multiples of three times 10.

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So the multiples of 30 are 30, 60, 90.

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Instead of three times four is 12,

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30 times four is 120,

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150 instead of 15,

00:01:12.972 --> 00:01:15.098
180 instead of 18

00:01:15.098 --> 00:01:16.515
for 30 times six,

00:01:17.707 --> 00:01:20.821
and gee, this looks pretty close to 180.

00:01:20.821 --> 00:01:22.404
So this looks close

00:01:23.660 --> 00:01:24.493
to 30

00:01:25.448 --> 00:01:26.691
times six.

00:01:26.691 --> 00:01:28.337
And if this is close to 30,

00:01:28.337 --> 00:01:31.128
well, maybe, maybe this is,

00:01:31.128 --> 00:01:34.188
maybe this is going to
be six right over here.

00:01:34.188 --> 00:01:35.988
And I'm gonna put a question mark

00:01:35.988 --> 00:01:38.206
because then the natural
thing to do is to actually

00:01:38.206 --> 00:01:39.157
try it out.

00:01:39.157 --> 00:01:41.863
Figure out what is six times 31?

00:01:41.863 --> 00:01:43.617
I'll put the question mark here again.

00:01:43.617 --> 00:01:45.282
Is this equal to six?

00:01:45.282 --> 00:01:47.903
Well, the art part is you've made a good,

00:01:47.903 --> 00:01:49.853
or we've made a good guess here.

00:01:49.853 --> 00:01:51.462
Now let's try to verify that

00:01:51.462 --> 00:01:53.401
maybe it is six, maybe it isn't.

00:01:53.401 --> 00:01:55.324
So let's multiply

00:01:55.324 --> 00:01:56.475
six,

00:01:56.475 --> 00:01:58.994
or let's multiple 31 times six.

00:01:58.994 --> 00:01:59.827
31

00:02:01.230 --> 00:02:02.063
times six,

00:02:03.315 --> 00:02:05.503
one times six is six,

00:02:05.503 --> 00:02:08.208
and then three times six,
which is really 30 times six,

00:02:08.208 --> 00:02:11.075
is gonna be 180 right over here.

00:02:11.075 --> 00:02:12.716
So this is 186.

00:02:12.716 --> 00:02:14.495
So it all works out.

00:02:14.495 --> 00:02:15.912
186 divided by 31

00:02:16.747 --> 00:02:18.627
is indeed six.

00:02:18.627 --> 00:02:22.284
We can get rid of this question mark here.

00:02:22.284 --> 00:02:24.367
Let's do another example.

00:02:25.872 --> 00:02:27.498
So let me delete.

00:02:27.498 --> 00:02:29.248
Let me delete that as well.

00:02:29.248 --> 00:02:31.831
Let's say we want to figure out

00:02:32.703 --> 00:02:33.536
what 336

00:02:36.585 --> 00:02:37.418
divided by

00:02:38.646 --> 00:02:39.896
48 is equal to.

00:02:40.823 --> 00:02:44.990
So pause this video, and see
if you can figure it out.

00:02:46.394 --> 00:02:49.203
So the way I would think about it,

00:02:49.203 --> 00:02:52.361
this thing right over here is close to 50,

00:02:52.361 --> 00:02:53.361
close to 50.

00:02:54.682 --> 00:02:56.449
And this thing, well,

00:02:56.449 --> 00:02:58.412
if you think about the multiples of 50,

00:02:58.412 --> 00:03:01.733
you have things like 300,
which would be 50 times six.

00:03:01.733 --> 00:03:05.900
And then you have 350, which
would be 50 times seven,

00:03:06.756 --> 00:03:09.323
because five times seven is 35.

00:03:09.323 --> 00:03:10.386
And so let's think about this,

00:03:10.386 --> 00:03:12.123
and actually let me
write these things down.

00:03:12.123 --> 00:03:15.060
If I were to say 50 times six,

00:03:15.060 --> 00:03:17.193
that's the same thing as,

00:03:17.193 --> 00:03:21.483
well, that's gonna be five times
six times 10, which is 300.

00:03:21.483 --> 00:03:23.100
If I say 50

00:03:23.100 --> 00:03:24.785
times seven,

00:03:24.785 --> 00:03:26.702
that's going to be 350.

00:03:27.577 --> 00:03:29.130
Five times seven is 35,

00:03:29.130 --> 00:03:31.733
and then you're multiplying that by 10.

00:03:31.733 --> 00:03:35.285
But this number is someplace
in between 300 and 350.

00:03:35.285 --> 00:03:37.883
So my candidates for
what this is going to be,

00:03:37.883 --> 00:03:39.732
well, I'm saying, hey, maybe this is six,

00:03:39.732 --> 00:03:41.129
maybe this is seven.

00:03:41.129 --> 00:03:44.023
And what I would do is I
would try out each of them.

00:03:44.023 --> 00:03:46.523
So let's try out 48 times six.

00:03:47.614 --> 00:03:49.327
So let's try that,

00:03:49.327 --> 00:03:51.046
this first candidate out.

00:03:51.046 --> 00:03:52.446
48

00:03:52.446 --> 00:03:53.279
times six,

00:03:54.683 --> 00:03:56.772
so eight times six

00:03:56.772 --> 00:03:58.272
is going to be 48.

00:04:00.473 --> 00:04:02.231
Four times six

00:04:02.231 --> 00:04:03.064
is 24,

00:04:04.110 --> 00:04:05.268
plus four

00:04:05.268 --> 00:04:06.101
is 288.

00:04:07.518 --> 00:04:10.956
So that actually seems a
good bit lower than this.

00:04:10.956 --> 00:04:13.668
It actually seems almost exactly 48 lower.

00:04:13.668 --> 00:04:15.723
So I could probably, I'm
feeling pretty confident

00:04:15.723 --> 00:04:18.042
that I can squeeze another 48 into this.

00:04:18.042 --> 00:04:19.458
So instead of squeezing,

00:04:19.458 --> 00:04:22.119
instead of being able to
divide 6/48 into this,

00:04:22.119 --> 00:04:24.168
I'm feeling pretty good that
maybe seven is the answer,

00:04:24.168 --> 00:04:25.460
but let me try it out.

00:04:25.460 --> 00:04:27.794
So this, so six is not

00:04:27.794 --> 00:04:29.610
going to be my answer, I tried it out.

00:04:29.610 --> 00:04:32.120
Let me try 48 times seven.

00:04:32.120 --> 00:04:33.444
48

00:04:33.444 --> 00:04:34.444
times seven,

00:04:35.346 --> 00:04:37.346
eight times seven is 56,

00:04:38.972 --> 00:04:41.920
four times seven is 28, plus three,

00:04:41.920 --> 00:04:43.334
336.

00:04:43.334 --> 00:04:44.735
That's exactly right.

00:04:44.735 --> 00:04:46.765
So there you have it, with a
little bit of trial and error,

00:04:46.765 --> 00:04:48.727
but it was an informed trial and error,

00:04:48.727 --> 00:04:51.317
we got 336 divided by 48

00:04:51.317 --> 00:04:53.377
is equal to seven.

00:04:53.377 --> 00:04:55.865
This is what I meant,
that it's a bit of an art.


Developing strategies for multiplying two digit decimals

WEBVTT
Kind: captions
Language: en

00:00:00.668 --> 00:00:02.909
- [Instructor] Let's
say I want to multiply

00:00:02.909 --> 00:00:04.909
3.1 or 3 1/10

00:00:06.130 --> 00:00:06.963
times

00:00:08.394 --> 00:00:09.227
times 2.4

00:00:10.420 --> 00:00:11.320
which could also be

00:00:11.320 --> 00:00:14.524
described as 2 4/10ths

00:00:14.524 --> 00:00:16.045
so pause the video if you can do this

00:00:16.045 --> 00:00:16.968
and once again, I'll give you a hint.

00:00:16.968 --> 00:00:18.269
See if you can express these

00:00:18.269 --> 00:00:19.352
as fractions.

00:00:20.933 --> 00:00:23.000
So there's a couple ways you
can express it as a fraction.

00:00:23.000 --> 00:00:26.860
You can express this as 3 1/10th

00:00:26.860 --> 00:00:27.693
times

00:00:28.607 --> 00:00:30.442
2 4/10ths

00:00:30.442 --> 00:00:31.475
two,

00:00:31.475 --> 00:00:33.274
let's get the same color,

00:00:33.274 --> 00:00:35.024
2 4/10ths.

00:00:36.177 --> 00:00:37.137
Now whenever you're multi

00:00:37.137 --> 00:00:39.225
these are mixed numbers
right over here and

00:00:39.225 --> 00:00:43.033
mixed numbers are not the super
straightforward to multiply,

00:00:43.033 --> 00:00:45.587
it's easier if they were written as

00:00:45.587 --> 00:00:47.660
what's often known as improper fractions

00:00:47.660 --> 00:00:49.721
but essentially not as mixed numbers.

00:00:49.721 --> 00:00:52.699
So three is the same thing as 30/10ths.

00:00:52.699 --> 00:00:54.957
So 30/10ths plus 1/10th,

00:00:54.957 --> 00:00:55.790
this is 31

00:00:56.629 --> 00:00:57.895
10ths

00:00:57.895 --> 00:00:59.317
times

00:00:59.317 --> 00:01:01.621
two is the same thing as 20/10ths.

00:01:01.621 --> 00:01:05.424
So 20/10ths plus four is 24/10ths.

00:01:05.424 --> 00:01:06.257
24

00:01:07.276 --> 00:01:08.716
over 10.

00:01:08.716 --> 00:01:11.252
And hopefully this
makes sense too that 3.1

00:01:11.252 --> 00:01:12.924
this three right over here,

00:01:12.924 --> 00:01:14.248
this is

00:01:14.248 --> 00:01:16.576
30/10ths

00:01:16.576 --> 00:01:18.091
or I can write,

00:01:18.091 --> 00:01:19.438
let me write 30/10ths

00:01:19.438 --> 00:01:21.823
and that this is 1/10th.

00:01:21.823 --> 00:01:24.964
So this total is going to be 31/10ths.

00:01:24.964 --> 00:01:26.525
Likewise, this two

00:01:26.525 --> 00:01:28.226
is 20/10ths

00:01:28.226 --> 00:01:31.181
plus 4/10th because it's 24/10ths.

00:01:31.181 --> 00:01:33.526
And now we can multiply.

00:01:33.526 --> 00:01:36.167
So this is going to give us

00:01:36.167 --> 00:01:37.915
our denominator's pretty straightforward.

00:01:37.915 --> 00:01:39.801
10 times 10 is

00:01:39.801 --> 00:01:40.875
100

00:01:40.875 --> 00:01:43.789
and then 31 times 24, we can multiply

00:01:43.789 --> 00:01:45.490
in the traditional way

00:01:45.490 --> 00:01:48.015
that we're used to
multiplying two digit numbers.

00:01:48.015 --> 00:01:48.932
31 times 24

00:01:50.930 --> 00:01:52.847
is going to be equal to

00:01:53.733 --> 00:01:55.620
four times one is four,

00:01:55.620 --> 00:01:57.745
four times three is 12,

00:01:57.745 --> 00:02:00.218
now we're gonna be multiplying
in the tenths place.

00:02:00.218 --> 00:02:01.907
We're going to put a zero here.

00:02:01.907 --> 00:02:04.304
So two times one is two.

00:02:04.304 --> 00:02:06.806
We're really saying 20 times one is 20.

00:02:06.806 --> 00:02:07.834
But you get the idea.

00:02:07.834 --> 00:02:09.581
Two times one is two.

00:02:09.581 --> 00:02:11.816
Two times three is

00:02:11.816 --> 00:02:12.649
six.

00:02:12.649 --> 00:02:15.119
Really 600, because it's 20 times 30.

00:02:15.119 --> 00:02:17.447
But I'm just following the standard multi

00:02:17.447 --> 00:02:19.165
the method for multiplication

00:02:19.165 --> 00:02:20.657
then you add these.

00:02:20.657 --> 00:02:22.694
And you're gonna get four

00:02:22.694 --> 00:02:23.803
four

00:02:23.803 --> 00:02:25.133
seven.

00:02:25.133 --> 00:02:27.391
So when you multiply
these two things together,

00:02:27.391 --> 00:02:29.808
in the numerator, you get 744

00:02:30.717 --> 00:02:32.209
100ths.

00:02:32.209 --> 00:02:34.955
Which can also be expressed as

00:02:34.955 --> 00:02:37.578
this is the same thing as 700ths

00:02:37.578 --> 00:02:39.828
or 700 100ths I should say,

00:02:40.870 --> 00:02:42.953
plus 44/100ths

00:02:43.929 --> 00:02:46.019
and 700/100ths,

00:02:46.019 --> 00:02:48.184
that's just going to be equal to seven.

00:02:48.184 --> 00:02:49.624
So this is seven

00:02:49.624 --> 00:02:51.243
plus 44/100ths

00:02:51.243 --> 00:02:53.368
which we could write as

00:02:53.368 --> 00:02:54.201
.44

00:02:55.446 --> 00:02:58.151
that's our seven and 44/100ths.

00:02:58.151 --> 00:02:59.574
And we would be done.

00:02:59.574 --> 00:03:01.913
And you might already be seeing a pattern.

00:03:01.913 --> 00:03:05.013
If you just took 31 and
multiplied it by 24,

00:03:05.013 --> 00:03:06.013
you get 744.

00:03:07.126 --> 00:03:08.223
And notice,

00:03:08.223 --> 00:03:09.622
I have one

00:03:09.622 --> 00:03:12.397
and two digits behind the decimal point.

00:03:12.397 --> 00:03:14.249
Notice I have one

00:03:14.249 --> 00:03:16.762
and two digits behind the decimal point.

00:03:16.762 --> 00:03:18.910
And so think about
whether that always works.

00:03:18.910 --> 00:03:21.139
Think about and why that might work.

00:03:21.139 --> 00:03:22.539
If you just multiply the numbers

00:03:22.539 --> 00:03:23.911
as if they didn't have decimals,

00:03:23.911 --> 00:03:25.264
so you would've gotten 744

00:03:25.264 --> 00:03:27.551
and you say, I got two
numbers behind the decimal,

00:03:27.551 --> 00:03:29.838
so my product is going to have two numbers

00:03:29.838 --> 00:03:30.697
behind the decimal,

00:03:30.697 --> 00:03:32.009
why does that work?

00:03:32.009 --> 00:03:33.187
Or does it always work?

00:03:33.187 --> 00:03:34.911
And how does it relate to what we did here

00:03:34.911 --> 00:03:37.437
which is converting these things to

00:03:37.437 --> 00:03:39.050
improper fractions

00:03:39.050 --> 00:03:41.800
and then multiplying it that way?


Developing strategies for multiplying decimals

WEBVTT
Kind: captions
Language: en

00:00:00.225 --> 00:00:01.659
- [Instructor] So right
over here we wanna compute

00:00:01.659 --> 00:00:05.826
what three times 0.25 or
three times 25 hundredths is.

00:00:07.342 --> 00:00:09.309
And so I encourage you to pause the video

00:00:09.309 --> 00:00:11.542
and see if you can figure this out.

00:00:11.542 --> 00:00:13.259
Alright, now let's work
through this together.

00:00:13.259 --> 00:00:16.809
And in this video, we're gonna
explore multiple strategies.

00:00:16.809 --> 00:00:19.558
In the future, we're going
to show you what's called

00:00:19.558 --> 00:00:22.525
the standard strategy,
which you might use a lot,

00:00:22.525 --> 00:00:24.039
but the strategies we're
gonna look at in this video

00:00:24.039 --> 00:00:26.139
are actually very
helpful for understanding

00:00:26.139 --> 00:00:28.755
what multiplying decimals actually means,

00:00:28.755 --> 00:00:31.194
how it relates to multiplying fractions,

00:00:31.194 --> 00:00:33.688
as often the way that people, even people

00:00:33.688 --> 00:00:35.101
who have a lot of math behind them,

00:00:35.101 --> 00:00:37.501
how they actually multiply decimals.

00:00:37.501 --> 00:00:40.234
So here, three times 25 hundredths.

00:00:40.234 --> 00:00:42.852
There's a couple of
ways to think about it.

00:00:42.852 --> 00:00:45.208
One way is to say, hey,
this is the same thing

00:00:45.208 --> 00:00:49.534
as three times, and I'm just
gonna write it a different way.

00:00:49.534 --> 00:00:50.701
25 hundredths,

00:00:52.114 --> 00:00:53.031
hundredths.

00:00:54.324 --> 00:00:56.573
If I have three times 25 of something,

00:00:56.573 --> 00:00:58.391
what is it going to be?

00:00:58.391 --> 00:01:00.973
Well, what's three times 25?

00:01:00.973 --> 00:01:01.806
Let's see.

00:01:01.806 --> 00:01:05.627
Two times 25 is 50, three times 25 is

00:01:05.627 --> 00:01:06.960
75.

00:01:06.960 --> 00:01:09.809
So it's going to be 75,
and I'm multiplying,

00:01:09.809 --> 00:01:11.693
not just three times 25, I'm multiplying

00:01:11.693 --> 00:01:13.926
three times 25 hundredths.

00:01:13.926 --> 00:01:17.825
Instead of 25 hundredths,
I'm gonna have 75,

00:01:17.825 --> 00:01:18.992
75 hundredths.

00:01:20.375 --> 00:01:23.359
Written out in words, this
would be 75 hundredths.

00:01:23.359 --> 00:01:25.842
How would we write that as a decimal?

00:01:25.842 --> 00:01:30.230
That is the same thing
as this, 75 hundredths.

00:01:30.230 --> 00:01:32.758
Another way to conceptualize
this, to think about

00:01:32.758 --> 00:01:36.841
what this is, is if we
were to write three times,

00:01:37.908 --> 00:01:39.574
we could write it as a fraction.

00:01:39.574 --> 00:01:42.408
We could write 25/100.

00:01:42.408 --> 00:01:45.424
This is another way of
writing 25 hundredths.

00:01:45.424 --> 00:01:47.734
These are all equivalent.

00:01:47.734 --> 00:01:50.901
What is three times 25/100?

00:01:51.907 --> 00:01:52.856
Same idea.

00:01:52.856 --> 00:01:55.738
This is going to be equal to,

00:01:55.738 --> 00:02:00.453
you could say this is 25/100
plus 25/100 plus 25/100.

00:02:00.453 --> 00:02:03.286
This is going to be 75 hundredths,

00:02:04.716 --> 00:02:06.799
which once again is 0.75.

00:02:08.546 --> 00:02:10.309
If you wanted to more formally view it

00:02:10.309 --> 00:02:14.610
as fraction multiplication,
you could view it as 3/1

00:02:14.610 --> 00:02:16.610
times 25/100,

00:02:18.916 --> 00:02:20.666
and you multiply the numerators,

00:02:20.666 --> 00:02:23.935
you get 75, you multiply the
denominators, you get 100.

00:02:23.935 --> 00:02:25.715
Either way, in all of these situations,

00:02:25.715 --> 00:02:28.597
you're gonna get 75 hundredths.

00:02:28.597 --> 00:02:30.330
Or, another way to think about it,

00:02:30.330 --> 00:02:33.296
is hey look, this thing right over here,

00:02:33.296 --> 00:02:37.463
this 25/100, this is
the same thing as 1/4.

00:02:38.632 --> 00:02:41.381
So you could view this as three times 1/4.

00:02:41.381 --> 00:02:43.230
In fact, this is a decimal
that it's good to recognize

00:02:43.230 --> 00:02:45.497
that this is the same thing as 1/4.

00:02:45.497 --> 00:02:49.638
So you could view this as three times 1/4,

00:02:49.638 --> 00:02:51.621
or 3/4,

00:02:51.621 --> 00:02:53.591
this is a fourth right
here, 1/4 could be viewed

00:02:53.591 --> 00:02:55.904
as a fourth, so this is going to be equal

00:02:55.904 --> 00:02:58.821
to 3/4, three over four,

00:03:01.711 --> 00:03:03.077
3/4.

00:03:03.077 --> 00:03:04.826
All of these are equivalent.

00:03:04.826 --> 00:03:06.692
If someone wanted it
written out as a decimal,

00:03:06.692 --> 00:03:09.577
you could, you might know that 3/4

00:03:09.577 --> 00:03:12.276
can be expressed as 75 hundredths,

00:03:12.276 --> 00:03:14.659
which in general, is a good thing to know.

00:03:14.659 --> 00:03:19.058
Now let's tackle slightly
more complicated examples.

00:03:19.058 --> 00:03:21.891
Let's say we wanted to figure out,

00:03:22.942 --> 00:03:25.609
we wanted to figure out what 0.4

00:03:27.761 --> 00:03:28.594
times

00:03:29.878 --> 00:03:31.060
zero,

00:03:31.060 --> 00:03:32.810
let me just do this in a new color,

00:03:32.810 --> 00:03:35.643
times 0.3 is going to be equal to.

00:03:36.492 --> 00:03:38.576
Pause the video and see
if you can compute this,

00:03:38.576 --> 00:03:39.959
and I'll give you a hint, see if you

00:03:39.959 --> 00:03:42.542
can express these as fractions.

00:03:44.743 --> 00:03:46.809
What we have here in
white, we could read this

00:03:46.809 --> 00:03:48.059
as four tenths,

00:03:50.445 --> 00:03:51.528
and we could write it as a fraction,

00:03:51.528 --> 00:03:54.661
as 4/10, and we're gonna multiply

00:03:54.661 --> 00:03:57.361
that by what we have over here.

00:03:57.361 --> 00:03:59.111
This is three tenths,

00:04:00.244 --> 00:04:01.327
three tenths,

00:04:02.297 --> 00:04:06.287
which we could write
as a fraction as 3/10,

00:04:06.287 --> 00:04:08.585
and so you could view this as 4/10 of 3/10

00:04:08.585 --> 00:04:11.219
or 3/10 of 4/10, but we're
multiplying these fractions,

00:04:11.219 --> 00:04:13.969
which we've seen before in other videos.

00:04:13.969 --> 00:04:15.285
What's going to happen?

00:04:15.285 --> 00:04:18.085
Well, if we multiply
the numerator we get 12,

00:04:18.085 --> 00:04:19.385
or the numerators.

00:04:19.385 --> 00:04:21.709
We multiply the denominators, you get 100.

00:04:21.709 --> 00:04:23.856
So you get 12 hundredths.

00:04:23.856 --> 00:04:25.372
If you wanted to write that as a decimal,

00:04:25.372 --> 00:04:26.789
it would be 0.12,

00:04:28.011 --> 00:04:29.178
12 hundredths.

00:04:30.127 --> 00:04:32.028
You might notice something
interesting here,

00:04:32.028 --> 00:04:33.844
and you'll see this more and more

00:04:33.844 --> 00:04:36.661
as you learn the standard method.

00:04:36.661 --> 00:04:39.078
12 is four times three is 12,

00:04:40.900 --> 00:04:43.294
but now I have two digits
behind the decimal,

00:04:43.294 --> 00:04:45.353
but notice, I have one digit
behind the decimal here,

00:04:45.353 --> 00:04:47.119
one digit behind the decimal here,

00:04:47.119 --> 00:04:50.151
for a total of two digits
behind the decimal.

00:04:50.151 --> 00:04:51.452
I'm giving you a little bit of a hint

00:04:51.452 --> 00:04:53.786
about where we're going,
but the important thing

00:04:53.786 --> 00:04:55.035
for this video is to recognize

00:04:55.035 --> 00:04:58.451
that you can re-express
each of these as fractions,

00:04:58.451 --> 00:05:00.527
and then multiply the
fractions to get something

00:05:00.527 --> 00:05:02.262
expressed in terms of hundredths,

00:05:02.262 --> 00:05:05.179
and then express that as a decimal.


Strategies for multiplying multiples of 10, 100 and 1000

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:00.833
- [Instructor] What we're
gonna do in this video

00:00:00.833 --> 00:00:02.938
is think about multiplying, or strategies

00:00:02.938 --> 00:00:05.680
for multiplying numbers that are expressed

00:00:05.680 --> 00:00:09.533
in terms of hundreds,
or thousands, or tens.

00:00:09.533 --> 00:00:11.184
And so we see an example right over here.

00:00:11.184 --> 00:00:13.017
We have 800 times 400.

00:00:14.317 --> 00:00:17.192
Now like always, I encourage
you to pause this video

00:00:17.192 --> 00:00:20.928
and see if you could work
this out on your own.

00:00:20.928 --> 00:00:23.589
Now let's work this through together,

00:00:23.589 --> 00:00:25.067
and I'm going to work it out in a way

00:00:25.067 --> 00:00:27.501
that at least my head likes to tackle it.

00:00:27.501 --> 00:00:29.504
Once you get enough practice,
you might even be able

00:00:29.504 --> 00:00:32.192
to do these types of
multiplication problems

00:00:32.192 --> 00:00:35.419
without even needing to use paper.

00:00:35.419 --> 00:00:37.820
So the key realization
here is to say, well look,

00:00:37.820 --> 00:00:40.168
this is eight 100s.

00:00:40.168 --> 00:00:43.835
So that's the same thing
as eight times 100.

00:00:45.229 --> 00:00:47.896
And this over here is four 100s.

00:00:49.966 --> 00:00:52.133
So this is four times 100.

00:00:53.732 --> 00:00:57.925
And so it's eight times
100, times four times 100.

00:00:57.925 --> 00:01:00.805
And if you're multiplying a
bunch of numbers like this,

00:01:00.805 --> 00:01:02.146
you can switch the order in which

00:01:02.146 --> 00:01:03.841
you're doing the multiplication.

00:01:03.841 --> 00:01:07.258
So you can view this as eight times four.

00:01:09.180 --> 00:01:12.347
Eight times four, times 100 times 100.

00:01:14.711 --> 00:01:16.378
Times 100 times 100.

00:01:19.799 --> 00:01:20.632
Times 100.

00:01:21.608 --> 00:01:23.490
Now why is this easier?

00:01:23.490 --> 00:01:26.921
Well what is eight times four going to be?

00:01:26.921 --> 00:01:31.821
Well eight times four, if we
know our times tables, is 32.

00:01:31.821 --> 00:01:34.758
And so it's going to be 32 times,

00:01:34.758 --> 00:01:38.081
what's 100 times 100 going to be?

00:01:38.081 --> 00:01:40.733
Now there's multiple ways
that you can think about this,

00:01:40.733 --> 00:01:42.220
and I want you to really think it through,

00:01:42.220 --> 00:01:44.937
but we'll soon see that
there's a fairly fast way

00:01:44.937 --> 00:01:47.606
of making sure we got it right.

00:01:47.606 --> 00:01:49.678
But one way to think about it is,

00:01:49.678 --> 00:01:51.553
well let me do it over here.

00:01:51.553 --> 00:01:54.136
10 times 100 is equal to 1,000.

00:01:56.367 --> 00:02:00.836
And so 100 times 100 is
going to be 10 times that,

00:02:00.836 --> 00:02:04.079
or it's going to be equal to 10,000.

00:02:04.079 --> 00:02:08.162
So this stuff right over
here is equal to 10,000.

00:02:12.679 --> 00:02:15.128
Now you might notice
something interesting here.

00:02:15.128 --> 00:02:18.663
I have two zeroes, and
then another two zeroes.

00:02:18.663 --> 00:02:20.434
So I have a total of four zeroes.

00:02:20.434 --> 00:02:22.593
And then I have four zeroes here.

00:02:22.593 --> 00:02:25.792
Because every time you multiply by 10

00:02:25.792 --> 00:02:27.232
you're gonna add another zero.

00:02:27.232 --> 00:02:29.403
So if you're multiplying by 100
you're gonna add two zeroes.

00:02:29.403 --> 00:02:30.587
If you're multiplying by 1,000,

00:02:30.587 --> 00:02:32.872
you're gonna add three
zeroes, and you see that here.

00:02:32.872 --> 00:02:37.039
So you have 32 times 10,000,
which is going to be what?

00:02:39.376 --> 00:02:41.387
Well let's see.

00:02:41.387 --> 00:02:43.970
32 times 1,000 would be 32,000.

00:02:45.578 --> 00:02:48.045
But this is 32 times 10,000.

00:02:48.045 --> 00:02:50.378
So it's going to be 320,000.

00:02:52.747 --> 00:02:56.239
Now you might already notice
an interesting pattern here.

00:02:56.239 --> 00:02:59.353
32 times one followed by four zeroes

00:02:59.353 --> 00:03:01.809
is 32 followed by four zeroes.

00:03:01.809 --> 00:03:04.892
This is 32 10,000s, which is 320,000.

00:03:07.219 --> 00:03:08.756
Now another was you
could've thought about it

00:03:08.756 --> 00:03:11.756
is eight times four gives us our 32.

00:03:14.765 --> 00:03:19.398
And then we have two zeroes
there, two zeroes there

00:03:19.398 --> 00:03:20.988
for a total of four zeroes,

00:03:20.988 --> 00:03:23.885
and we have our four
zeroes right over there.

00:03:23.885 --> 00:03:25.766
Now I don't want you
to just memorize that.

00:03:25.766 --> 00:03:28.760
It works because this is eight 100s

00:03:28.760 --> 00:03:30.000
times four 100s.

00:03:30.000 --> 00:03:32.154
Eight times four gives us the 32.

00:03:32.154 --> 00:03:34.187
And then the 100 times the 100s,

00:03:34.187 --> 00:03:36.868
that's where these four zeroes come from.

00:03:36.868 --> 00:03:38.951
Let's do another example.

00:03:40.018 --> 00:03:42.685
So let's do, let me delete this.

00:03:44.360 --> 00:03:47.527
And let us do, let me get my pen back.

00:03:49.242 --> 00:03:51.242
So let's do 30 times 70,

00:03:54.682 --> 00:03:56.436
or let's do 30 times 700.

00:03:56.436 --> 00:03:58.976
Pause the video and see if
you can figure this out.

00:03:58.976 --> 00:04:00.473
So we can do it like we did before,

00:04:00.473 --> 00:04:02.223
30 is three times 10.

00:04:03.374 --> 00:04:04.874
700, so times 700,

00:04:06.846 --> 00:04:08.929
which is seven times 100.

00:04:10.835 --> 00:04:15.002
And so if you say three times
seven, is going to be 21

00:04:18.671 --> 00:04:22.088
times 10 times 100, is going to be 1,000.

00:04:25.190 --> 00:04:27.437
So what's 21 times 1,000?

00:04:27.437 --> 00:04:30.020
Well that's going to be 21,000.

00:04:32.690 --> 00:04:36.087
Now just like we saw before,
once you get a hang of it,

00:04:36.087 --> 00:04:38.758
and I always want you to
understand where it's coming from,

00:04:38.758 --> 00:04:41.091
three times seven is the 21,

00:04:42.100 --> 00:04:46.449
and then you're gonna multiply
that times 10 and then 100.

00:04:46.449 --> 00:04:48.673
So you have one, two, three zeroes.

00:04:48.673 --> 00:04:50.590
One, two, three zeroes.

00:04:51.469 --> 00:04:53.746
Let's do one more of these.

00:04:53.746 --> 00:04:57.913
So let's say we wanted to
multiply 2,000 times 8,000.

00:05:01.801 --> 00:05:04.021
Pause the video and see if you
can figure out what this is.

00:05:04.021 --> 00:05:04.884
Maybe in your head.

00:05:04.884 --> 00:05:06.436
Try to do this one in your head.

00:05:06.436 --> 00:05:08.449
Or on paper, don't feel bad
if you need to use paper.

00:05:08.449 --> 00:05:10.685
That's always prudent.

00:05:10.685 --> 00:05:12.508
Well you might get the hang of it now.

00:05:12.508 --> 00:05:14.284
You might be able to
do this quite quickly.

00:05:14.284 --> 00:05:17.407
You might be able to say
hey, two times eight,

00:05:17.407 --> 00:05:20.268
well that's going to be equal to 16.

00:05:20.268 --> 00:05:21.518
And then I have

00:05:24.066 --> 00:05:26.066
three plus three zeroes,

00:05:27.640 --> 00:05:28.965
so that's gonna be six zeroes.

00:05:28.965 --> 00:05:32.042
One, two, three, four, five, six,

00:05:32.042 --> 00:05:34.671
which gives me 16 million.

00:05:34.671 --> 00:05:37.214
You would absolutely be correct.

00:05:37.214 --> 00:05:40.006
Now I want to reinforce what you're doing

00:05:40.006 --> 00:05:42.680
when you're just counting
zeroes like that.

00:05:42.680 --> 00:05:43.788
What you're doing, you're just saying hey,

00:05:43.788 --> 00:05:47.288
this is the same thing as two times 1,000,

00:05:48.603 --> 00:05:50.603
times eight times 1,000.

00:05:51.761 --> 00:05:53.261
Eight times 1,000.

00:05:55.067 --> 00:05:57.468
And then you're just changing
the order of multiplication.

00:05:57.468 --> 00:06:01.107
You're saying hey, let me
multiply the two and the eight.

00:06:01.107 --> 00:06:05.297
You multiply the two times
the eight, and you get 16.

00:06:05.297 --> 00:06:08.536
And then you multiply the
times 1,000 times 1,000.

00:06:08.536 --> 00:06:10.786
So times 1,000 times 1,000.

00:06:12.833 --> 00:06:16.488
And 1,000 1,000s, that's one million.

00:06:16.488 --> 00:06:18.876
This is one million right over here.

00:06:18.876 --> 00:06:20.326
And notice you see it there too.

00:06:20.326 --> 00:06:22.833
1,000 times 1,000, you have
three zeroes, three zeroes,

00:06:22.833 --> 00:06:23.712
you get six zeroes.

00:06:23.712 --> 00:06:25.807
1,000 1,000s is a million.

00:06:25.807 --> 00:06:28.557
16 times a million is 16 million.

00:06:30.148 --> 00:06:31.113
So hopefully that helps and makes you

00:06:31.113 --> 00:06:34.247
a little more comfortable
multiplying these numbers

00:06:34.247 --> 00:06:36.262
that are multiples of ten, hundred,

00:06:36.262 --> 00:06:38.345
thousands, even millions.


Strategies for subtracting more complex decimals with tenths

WEBVTT
Kind: captions
Language: en

00:00:00.154 --> 00:00:01.861
- [Instructor] Do some more examples

00:00:01.861 --> 00:00:03.723
subtracting decimals.

00:00:03.723 --> 00:00:05.447
So let's say we wanna figure out

00:00:05.447 --> 00:00:07.280
what two minus 1.2 is.

00:00:09.813 --> 00:00:10.646
Pause this video

00:00:10.646 --> 00:00:13.506
and see if you can calculate this.

00:00:13.506 --> 00:00:16.501
So there is multiple ways to tackle this.

00:00:16.501 --> 00:00:18.765
One way is you could say,
"Look, this is the same thing

00:00:18.765 --> 00:00:20.182
"as two minus one

00:00:24.512 --> 00:00:26.069
"minus 2/10."

00:00:26.069 --> 00:00:28.781
This is two minus one and 2/10.

00:00:28.781 --> 00:00:30.094
So we're subtracting one,

00:00:30.094 --> 00:00:33.056
and we're subtracting 2/10.

00:00:33.056 --> 00:00:36.290
Now two minus one is pretty
straightforward to compute.

00:00:36.290 --> 00:00:38.413
Two minus one is going to be one,

00:00:38.413 --> 00:00:41.601
and then we need to
subtract 2/10 from that.

00:00:41.601 --> 00:00:44.258
So one is the same thing as 10/10.

00:00:44.258 --> 00:00:47.425
We could say this is 10/10.

00:00:48.961 --> 00:00:51.243
10, write it this way.

00:00:51.243 --> 00:00:55.446
10/10, and we're gonna subtract 2/10.

00:00:55.446 --> 00:00:56.989
What is that gonna give us?

00:00:56.989 --> 00:00:58.555
Well, that's going to give us,

00:00:58.555 --> 00:00:59.434
if we have 10/10,

00:00:59.434 --> 00:01:00.883
and we take away 2/10,

00:01:00.883 --> 00:01:03.675
that's going to give us 8/10.

00:01:03.675 --> 00:01:04.763
Lemme write it down here.

00:01:04.763 --> 00:01:08.096
8/10, which is the same thing

00:01:09.314 --> 00:01:11.564
as 0.8, or 8/10.

00:01:13.265 --> 00:01:14.875
One way to think about this

00:01:14.875 --> 00:01:18.042
is if you're subtracting 0.2 from one,

00:01:19.774 --> 00:01:22.274
if you view this one as a 1.0,

00:01:24.981 --> 00:01:29.109
instead of expressing this
as one, one, and 0/10,

00:01:29.109 --> 00:01:30.861
we are thinking about this

00:01:30.861 --> 00:01:33.694
as zero ones and 10/10.

00:01:35.968 --> 00:01:37.810
And when you think about it as zero ones

00:01:37.810 --> 00:01:39.430
and 10/10,

00:01:39.430 --> 00:01:41.346
well, 10/10 minus 2/10,

00:01:41.346 --> 00:01:43.591
it's easier to then think about, well,

00:01:43.591 --> 00:01:45.270
10 of something minus two of something

00:01:45.270 --> 00:01:46.441
is gonna be eight of something.

00:01:46.441 --> 00:01:48.167
It's gonna be 8/10.

00:01:48.167 --> 00:01:51.787
Now we can also visualize
this on a number line,

00:01:51.787 --> 00:01:56.288
so for example, let me
draw a number line here,

00:01:56.288 --> 00:01:59.126
and so zero, one, two, three, four, five,

00:01:59.126 --> 00:02:01.336
six, seven, eight, nine.

00:02:01.336 --> 00:02:04.531
That's one, one, two,
three, four, five, six,

00:02:04.531 --> 00:02:06.463
seven, eight, nine.

00:02:06.463 --> 00:02:07.758
That is two,

00:02:07.758 --> 00:02:09.825
so we're starting at two,

00:02:09.825 --> 00:02:13.262
and we're subtracting one and 2/10.

00:02:13.262 --> 00:02:14.521
So one way to think about it is

00:02:14.521 --> 00:02:16.785
we first subtracted one.

00:02:16.785 --> 00:02:18.356
We first subtracted one,

00:02:18.356 --> 00:02:21.277
and then we subtracted 2/10,

00:02:21.277 --> 00:02:25.444
and that got us to the point
8/10 on the number line.

00:02:27.704 --> 00:02:29.897
Another way to think about this,

00:02:29.897 --> 00:02:32.203
and the whole point here is
to see multiple strategies

00:02:32.203 --> 00:02:34.447
and for you to think about
what strategy you like the most

00:02:34.447 --> 00:02:36.287
and to realize they all
get you to the same place.

00:02:36.287 --> 00:02:38.586
If you're thinking about
it in a reasonable way,

00:02:38.586 --> 00:02:39.419
is you could use,

00:02:39.419 --> 00:02:42.068
what's the difference between two and 1.2?

00:02:42.068 --> 00:02:45.341
So 1.2 sits here on the number line,

00:02:45.341 --> 00:02:46.948
so what's the difference between two

00:02:46.948 --> 00:02:49.276
and one and 2/10?

00:02:49.276 --> 00:02:50.820
Another way to think about it is

00:02:50.820 --> 00:02:53.713
how many tenths do you have to add

00:02:53.713 --> 00:02:56.482
to one and 2/10 to get to two?

00:02:56.482 --> 00:02:58.183
Well, if you've already got 2/10,

00:02:58.183 --> 00:02:59.484
you need to add another 8/10

00:02:59.484 --> 00:03:01.020
to get to the next whole.

00:03:01.020 --> 00:03:02.559
So you have to add 8/10,

00:03:02.559 --> 00:03:04.476
or you have to add 0.8.

00:03:05.335 --> 00:03:09.100
So the difference between two and 1.2,

00:03:09.100 --> 00:03:11.854
the difference between two and 1.2

00:03:11.854 --> 00:03:13.187
is equal to 0.8.

00:03:15.267 --> 00:03:16.597
Let's do a few more examples

00:03:16.597 --> 00:03:19.284
that get a little bit more involved.

00:03:19.284 --> 00:03:20.659
So let's say we wanna calculate

00:03:20.659 --> 00:03:22.492
what 3.8 minus 1.5 is.

00:03:25.531 --> 00:03:28.582
Pause the video and see
if you can calculate this.

00:03:28.582 --> 00:03:29.818
Well, just like before,

00:03:29.818 --> 00:03:33.594
we could view this as three minus one,

00:03:33.594 --> 00:03:35.946
so we're subtracting the ones

00:03:35.946 --> 00:03:37.613
plus 8/10

00:03:39.464 --> 00:03:41.297
minus 5/10.

00:03:48.135 --> 00:03:50.935
Notice we have three and 8/10

00:03:50.935 --> 00:03:52.485
minus one and 5/10,

00:03:52.485 --> 00:03:55.677
minus one and minus 5/10.

00:03:55.677 --> 00:03:57.158
And so now we can figure out,

00:03:57.158 --> 00:03:59.414
okay, three minus one,

00:03:59.414 --> 00:04:01.390
that's just going to be equal to two,

00:04:01.390 --> 00:04:05.046
and then 8/10 minus 5/10,

00:04:05.046 --> 00:04:07.709
well, that is 3/10,

00:04:07.709 --> 00:04:11.216
and so this is going to be two and 3/10,

00:04:11.216 --> 00:04:14.383
which of course we could write as 2.3.

00:04:16.377 --> 00:04:17.595
That seemed pretty straightforward.

00:04:17.595 --> 00:04:21.144
Let's do one that's a
little bit more involved.

00:04:21.144 --> 00:04:25.920
Let's say we wanna calculate
four and 5/10 or 4.5,

00:04:25.920 --> 00:04:29.003
minus two and 8/10 or 2.8.

00:04:30.786 --> 00:04:34.342
Pause the video and see
if you can calculate this.

00:04:34.342 --> 00:04:36.653
So you might wanna do
the exact same thing.

00:04:36.653 --> 00:04:37.957
You might say, "Okay, well,
this is the same thing.

00:04:37.957 --> 00:04:39.142
"Let's think about the ones."

00:04:39.142 --> 00:04:40.975
This is four minus two

00:04:43.014 --> 00:04:44.681
plus 5/10

00:04:49.474 --> 00:04:51.307
minus 8/10.

00:04:53.806 --> 00:04:55.806
Four and 5/10

00:04:57.569 --> 00:04:59.767
minus two and minus 8/10,

00:04:59.767 --> 00:05:01.758
minus two and 8/10.

00:05:01.758 --> 00:05:03.808
That's exactly what we have up here.

00:05:03.808 --> 00:05:06.889
Then you would say,
"Alright, four minus two,

00:05:06.889 --> 00:05:08.403
"that is two."

00:05:08.403 --> 00:05:11.406
But then you get to 5/10 minus 8/10,

00:05:11.406 --> 00:05:13.473
and there's multiple ways to tackle this,

00:05:13.473 --> 00:05:15.346
but you might say, "Oh,
how do I take away 8/10

00:05:15.346 --> 00:05:17.943
"if I've only got 5/10 here?"

00:05:17.943 --> 00:05:19.514
And there's a bunch of strategies

00:05:19.514 --> 00:05:21.058
that you could think about.

00:05:21.058 --> 00:05:22.569
You could say, "Hey, what if I can get

00:05:22.569 --> 00:05:24.206
"some more tenths here?"

00:05:24.206 --> 00:05:26.373
So this is 5/10

00:05:28.612 --> 00:05:30.445
minus 8/10.

00:05:32.275 --> 00:05:33.834
What if I could get some more tenths here?

00:05:33.834 --> 00:05:35.329
The best way I can think of it is like

00:05:35.329 --> 00:05:37.329
what if I were to break up these ones

00:05:37.329 --> 00:05:39.849
because one is 10/10?

00:05:39.849 --> 00:05:41.599
So I could view a two

00:05:42.736 --> 00:05:44.069
as one plus one,

00:05:45.698 --> 00:05:49.865
or I could view this as one plus 10/10.

00:05:53.626 --> 00:05:56.395
So if you view a two as one and 10/10,

00:05:56.395 --> 00:05:58.129
you can then just add those.

00:05:58.129 --> 00:06:00.911
You could then figure out what is 10/10

00:06:00.911 --> 00:06:02.578
plus 5/10

00:06:06.159 --> 00:06:07.992
minus 8/10?

00:06:12.740 --> 00:06:15.116
What is that going to be?

00:06:15.116 --> 00:06:17.572
Well, this is a little
bit more straightforward.

00:06:17.572 --> 00:06:21.739
10/10 plus 5/10 is going to be 15/10,

00:06:24.623 --> 00:06:25.751
and if you have 15/10

00:06:25.751 --> 00:06:27.597
and you take away eight of them,

00:06:27.597 --> 00:06:30.063
you're going to be left with 7/10.

00:06:30.063 --> 00:06:32.303
So this gets us to

00:06:32.303 --> 00:06:34.386
one plus 7/10,

00:06:36.176 --> 00:06:38.139
so all of this

00:06:38.139 --> 00:06:39.223
when you compute it,

00:06:39.223 --> 00:06:41.093
that is 7/10,

00:06:41.093 --> 00:06:43.653
which I could write as 0.7,

00:06:43.653 --> 00:06:45.850
which is equal to,

00:06:45.850 --> 00:06:49.517
so this is equal to one and 7/10.

00:06:52.544 --> 00:06:55.389
Now there's other strategies
that you could do here.

00:06:55.389 --> 00:06:56.351
One strategy that,

00:06:56.351 --> 00:06:58.854
and this is the one that I
typically do in my head is

00:06:58.854 --> 00:07:00.437
I write this as 4.5

00:07:03.452 --> 00:07:04.285
minus 2.5

00:07:07.825 --> 00:07:08.658
minus 0.3,

00:07:10.412 --> 00:07:11.606
or four and 5/10

00:07:11.606 --> 00:07:13.230
minus two and 5/10

00:07:13.230 --> 00:07:14.742
minus 3/10.

00:07:14.742 --> 00:07:16.792
Now why did I write it this way?

00:07:16.792 --> 00:07:20.686
Because I find this pretty
straightforward to compute,

00:07:20.686 --> 00:07:22.022
and then once I get that answer,

00:07:22.022 --> 00:07:23.983
I just have to take away 3/10.

00:07:23.983 --> 00:07:25.423
So for example,

00:07:25.423 --> 00:07:27.347
well, if I have 5/10 here,

00:07:27.347 --> 00:07:29.123
and I'm taking away 5/10,

00:07:29.123 --> 00:07:30.848
those are gonna knock each other out,

00:07:30.848 --> 00:07:33.841
and so I'm just gonna be
left with four minus two,

00:07:33.841 --> 00:07:35.225
which is gonna be two,

00:07:35.225 --> 00:07:39.691
and then I have to take away the 3/10.

00:07:39.691 --> 00:07:41.320
This is a pretty straightforward way

00:07:41.320 --> 00:07:42.888
of doing it in your head.

00:07:42.888 --> 00:07:45.577
So what's 3/10 less than two?

00:07:45.577 --> 00:07:48.068
Well, you can visualize a
number line in your head.

00:07:48.068 --> 00:07:51.841
Well, that's gonna be one and 7/10,

00:07:51.841 --> 00:07:53.841
one and 7/10,

00:07:55.200 --> 00:07:57.853
and if this feels strange how I got,

00:07:57.853 --> 00:07:59.196
oh, one, I wrote 7/100,

00:07:59.196 --> 00:08:00.926
one and 7/10.

00:08:00.926 --> 00:08:03.689
And if this seems strange
how I got there that fast,

00:08:03.689 --> 00:08:05.262
just think about this.

00:08:05.262 --> 00:08:08.261
This is the same thing as one plus one

00:08:08.261 --> 00:08:10.094
minus 3/10,

00:08:11.727 --> 00:08:13.232
and this one right over here

00:08:13.232 --> 00:08:17.110
is the same thing as 10/10,

00:08:17.110 --> 00:08:19.600
and so 10/10 minus 3/10.

00:08:19.600 --> 00:08:22.381
That over there is going to be,

00:08:22.381 --> 00:08:25.277
that is going to be 7/10,

00:08:25.277 --> 00:08:27.558
so it's going to be one and 7/10,

00:08:27.558 --> 00:08:29.142
which is what we got before.

00:08:29.142 --> 00:08:30.877
So the whole point here is to appreciate

00:08:30.877 --> 00:08:34.054
there's multiple strategies
for subtracting decimals,

00:08:34.054 --> 00:08:36.166
some that you can do a little
bit more automatically,

00:08:36.166 --> 00:08:37.425
but it's really good to think about

00:08:37.425 --> 00:08:38.559
what's going on in your head.

00:08:38.559 --> 00:08:41.212
And some strategies are
actually better in your head

00:08:41.212 --> 00:08:42.422
than on paper,

00:08:42.422 --> 00:08:44.860
or at least more easy in your head.


More advanced subtraction strategies with hundredths

WEBVTT
Kind: captions
Language: en

00:00:00.565 --> 00:00:02.642
- [Sal] Let's say we wanted to compute

00:00:02.642 --> 00:00:04.559
eight and 38 hundredths

00:00:06.303 --> 00:00:08.720
minus four and 54 hundredths.

00:00:12.282 --> 00:00:14.474
See if you can pause this video,

00:00:14.474 --> 00:00:17.437
and figure it out on your own.

00:00:17.437 --> 00:00:20.407
There are multiple
strategies for doing this.

00:00:20.407 --> 00:00:23.736
I'll tell you the way that
my head likes to do this.

00:00:23.736 --> 00:00:25.274
I would view this as the same thing

00:00:25.274 --> 00:00:27.524
as eight and 38 hundredths,

00:00:28.941 --> 00:00:33.360
and then I would subtract
four and 38 hundredths.

00:00:33.360 --> 00:00:36.610
The reason why I pick 38
hundredths is that will cancel out,

00:00:36.610 --> 00:00:38.639
it'll take away these 38 hundredths.

00:00:38.639 --> 00:00:40.713
And then I still have to
subtract a little bit more.

00:00:40.713 --> 00:00:43.028
If I also subtracted 38 hundredths,

00:00:43.028 --> 00:00:45.919
I have to subtract a
total of 54 hundredths.

00:00:45.919 --> 00:00:49.127
Let's see, 54 is how much more than 38?

00:00:49.127 --> 00:00:51.969
I am doing this in my head as I speak.

00:00:51.969 --> 00:00:55.969
To go from 38 to 48, I
need six, I need 10 more.

00:00:59.036 --> 00:01:01.599
I need to subtract another 16 hundredths.

00:01:01.599 --> 00:01:03.145
How did I think about that?

00:01:03.145 --> 00:01:04.478
54 is 38 and 16.

00:01:06.188 --> 00:01:08.864
If I'm subtracting 54,
I could break that up.

00:01:08.864 --> 00:01:11.061
I could subtract 38 hundredths,

00:01:11.061 --> 00:01:13.460
and then I could subtract 16 hundredths.

00:01:13.460 --> 00:01:14.840
Why did I pick 38 hundredths?

00:01:14.840 --> 00:01:16.584
Because it matches up with this.

00:01:16.584 --> 00:01:20.751
And so, if I say eight minus
four is going to be four,

00:01:23.985 --> 00:01:27.883
and then I have 38 hundredths
minus 38 hundredths,

00:01:27.883 --> 00:01:30.119
those are just gonna
cancel out with each other.

00:01:30.119 --> 00:01:32.396
So this minus that is just gonna be four.

00:01:32.396 --> 00:01:35.896
And then I'd say four minus 16 hundredths.

00:01:37.354 --> 00:01:39.674
So how do we think about that?

00:01:39.674 --> 00:01:41.502
Well, you might be able to do this

00:01:41.502 --> 00:01:42.760
in your head at this point.

00:01:42.760 --> 00:01:45.284
You might say: "OK, I
have to go 16 hundredths

00:01:45.284 --> 00:01:50.240
"less than four, that's gonna
be three and 84 hundredths."

00:01:50.240 --> 00:01:52.234
Or, you might wanna just break it up.

00:01:52.234 --> 00:01:55.921
You could say: "OK, four
is the same thing as

00:01:55.921 --> 00:01:58.254
"three plus 100 hundredths."

00:02:00.379 --> 00:02:01.296
Hundredths.

00:02:02.611 --> 00:02:06.528
And then I wanna take
away minus 16 hundredths.

00:02:08.826 --> 00:02:10.409
100 minus 16 is 84.

00:02:13.087 --> 00:02:16.286
This part right over
here is 84 hundredths.

00:02:16.286 --> 00:02:17.790
I'll write it out.

00:02:17.790 --> 00:02:18.707
Hundredths.

00:02:20.152 --> 00:02:22.319
Which I can write as 0.84.

00:02:24.007 --> 00:02:27.007
Three plus 0.84, that's going to be,

00:02:28.111 --> 00:02:29.614
this is going to be equal to,

00:02:29.614 --> 00:02:33.349
we figured it out already multiple times,

00:02:33.349 --> 00:02:35.349
three and 84 hundredths.

00:02:36.757 --> 00:02:38.589
Now, as I said, there's multiple ways

00:02:38.589 --> 00:02:40.619
that we can try to tackle this.

00:02:40.619 --> 00:02:43.613
For example, another way that I could do

00:02:43.613 --> 00:02:46.753
this one right over here is I could say,

00:02:46.753 --> 00:02:49.170
all right, lemme do the ones.

00:02:51.104 --> 00:02:53.820
I'd say, eight minus four.

00:02:53.820 --> 00:02:55.237
Eight minus four.

00:02:56.503 --> 00:02:57.642
Plus.

00:02:57.642 --> 00:02:59.715
Let me try to do the tenths.

00:02:59.715 --> 00:03:03.715
So, I could have three
tenths minus five tenths.

00:03:05.036 --> 00:03:06.203
0.3 minus 0.5.

00:03:09.257 --> 00:03:12.223
And then, I would have the hundredths.

00:03:12.223 --> 00:03:15.234
So, eight hundredths
minus four hundredths.

00:03:15.234 --> 00:03:18.901
Plus eight hundredths
minus four hundredths.

00:03:20.761 --> 00:03:22.589
Now, this is pretty easy to compute,

00:03:22.589 --> 00:03:24.663
this is pretty easy to
compute, but what about this?

00:03:24.663 --> 00:03:27.952
I don't have five tenths to take away.

00:03:27.952 --> 00:03:32.380
What I could do is, instead
of having an eight here,

00:03:32.380 --> 00:03:36.612
I could take one away from
it, and make that a seven.

00:03:36.612 --> 00:03:40.141
And so, I have one that I can
regroup someplace over here.

00:03:40.141 --> 00:03:41.933
I can reorganize it.

00:03:41.933 --> 00:03:45.766
So, I could view this
as seven plus 10 tenths.

00:03:47.547 --> 00:03:50.497
And so, I can take those 10 tenths,

00:03:50.497 --> 00:03:53.586
I could take those 10 tenths,
and add 'em right over here.

00:03:53.586 --> 00:03:54.482
Lemme rewrite this.

00:03:54.482 --> 00:03:57.614
I could rewrite this as seven minus four,

00:03:57.614 --> 00:03:58.864
plus 10 tenths,

00:04:02.594 --> 00:04:04.094
plus three tenths.

00:04:04.959 --> 00:04:08.069
Actually, lemme just write
it all as plus three tenths.

00:04:08.069 --> 00:04:10.461
I'm mixing different ways
of writing it this way,

00:04:10.461 --> 00:04:11.438
but that might be good.

00:04:11.438 --> 00:04:12.938
Minus five tenths.

00:04:14.472 --> 00:04:16.216
And then this part I could just compute.

00:04:16.216 --> 00:04:19.351
This is plus four hundredths.

00:04:19.351 --> 00:04:20.979
Zero point zero.

00:04:20.979 --> 00:04:22.429
Color.

00:04:22.429 --> 00:04:23.718
Plus four hundredths.

00:04:23.718 --> 00:04:27.198
This right here is gonna
be four hundredths.

00:04:27.198 --> 00:04:28.539
Now what is this going to be?

00:04:28.539 --> 00:04:31.706
Seven minus four is going to be three.

00:04:33.177 --> 00:04:35.783
10 tenths plus three tenths.

00:04:35.783 --> 00:04:37.802
The right color.

00:04:37.802 --> 00:04:40.587
This is going to be three.

00:04:40.587 --> 00:04:44.754
And then, 10 tenths plus
three tenths is 13 tenths,

00:04:46.734 --> 00:04:49.625
minus five tenths is eight tenths,

00:04:49.625 --> 00:04:51.537
and then I have four hundredths.

00:04:51.537 --> 00:04:53.447
Once again, 3.84.

00:04:53.447 --> 00:04:57.141
Three ones, eight tenths, four hundredths.

00:04:57.141 --> 00:04:59.474
Or, three and 84 hundredths.


Subtraction strategies with hundredths

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:02.532
- [Instructor] About some
strategies subtracting decimals

00:00:02.532 --> 00:00:04.287
that involve hundredths.

00:00:04.287 --> 00:00:08.454
For example, if I have 0.69, or 69/100,

00:00:10.615 --> 00:00:14.782
and from that I want to
subtract 0.34, or 34/100,

00:00:17.155 --> 00:00:18.176
what is that going to be?

00:00:18.176 --> 00:00:21.742
Pause this video and see
if you can compute this.

00:00:21.742 --> 00:00:24.697
There's a bunch of ways to think about it.

00:00:24.697 --> 00:00:28.819
One way to think about
it is this is 69/100.

00:00:28.819 --> 00:00:30.555
Hundredths.

00:00:30.555 --> 00:00:35.390
And from that we are subtracting 34/100.

00:00:35.390 --> 00:00:36.307
Hundredths.

00:00:37.608 --> 00:00:40.743
And so this boils down to,
I have 69 of something,

00:00:40.743 --> 00:00:43.469
in this case hundredths,
in this case hundredths,

00:00:43.469 --> 00:00:45.514
and I'm gonna take away 34 of them.

00:00:45.514 --> 00:00:47.207
So what am I left with?

00:00:47.207 --> 00:00:49.207
Well what's 69 minus 34?

00:00:50.216 --> 00:00:54.309
Well nine ones minus, or I
should say nine minus four

00:00:54.309 --> 00:00:56.119
is gonna be five.

00:00:56.119 --> 00:00:58.952
And 60 minus 30 is going to be 30.

00:01:01.194 --> 00:01:04.555
So I'm left with 35/100.

00:01:04.555 --> 00:01:05.472
Hundredths.

00:01:06.952 --> 00:01:09.119
Which I can write as 0.35.

00:01:11.269 --> 00:01:12.716
Now another way I could think about it

00:01:12.716 --> 00:01:14.988
is I could break up the tenths,

00:01:14.988 --> 00:01:17.542
and then the leftover hundredths.

00:01:17.542 --> 00:01:21.082
So I could view this as 6/10,

00:01:21.082 --> 00:01:22.767
let me circle that a little bit better,

00:01:22.767 --> 00:01:25.669
6/10 minus 3/10.

00:01:25.669 --> 00:01:29.002
So 6/10 minus 3/10

00:01:31.549 --> 00:01:32.382
plus...

00:01:36.100 --> 00:01:39.850
Plus 9/100 minus 4/100.

00:01:41.116 --> 00:01:43.116
So plus 9/100

00:01:45.196 --> 00:01:47.113
minus 4/100.

00:01:49.232 --> 00:01:50.885
And we're gonna get the same answer,

00:01:50.885 --> 00:01:53.551
so that is 6/10 and I
take away three of them.

00:01:53.551 --> 00:01:56.041
That's gonna give me 3/10,

00:01:56.041 --> 00:01:59.011
or I could just write that as 0.3.

00:01:59.011 --> 00:02:03.178
And then two that I
would have to add 9/100

00:02:05.439 --> 00:02:09.390
minus 4/100 is 5/100.

00:02:09.390 --> 00:02:10.223
So 0.05.

00:02:11.468 --> 00:02:15.635
So 3/10 and 5/100 is going to be 35/100,

00:02:16.771 --> 00:02:18.204
or we could just write it this way.

00:02:18.204 --> 00:02:20.677
We could write it as 3/10.

00:02:20.677 --> 00:02:22.361
We have a three in the tenth's place.

00:02:22.361 --> 00:02:24.445
And 5/100.

00:02:24.445 --> 00:02:26.436
Let me do that blue color.

00:02:26.436 --> 00:02:28.677
And 5/100.

00:02:28.677 --> 00:02:31.561
Or we could view that as 35/100.

00:02:31.561 --> 00:02:33.213
However way, these are different ways

00:02:33.213 --> 00:02:37.130
of thinking about
subtracting these hundredths.

00:02:38.039 --> 00:02:40.122
Let's do another example.

00:02:42.156 --> 00:02:44.573
Let's say we want to compute.

00:02:46.533 --> 00:02:49.714
We would like to compute,
and this actually

00:02:49.714 --> 00:02:51.971
will probably be a little
bit more straightforward,

00:02:51.971 --> 00:02:55.221
three and 43/100, minus two.

00:02:57.377 --> 00:02:58.751
What is this going to be equal to?

00:02:58.751 --> 00:03:01.554
Pause the video and see
if you can figure it out.

00:03:01.554 --> 00:03:04.758
Well it might jump out at you
that this is the same thing

00:03:04.758 --> 00:03:08.341
as three plus 43/100, minus two.

00:03:11.091 --> 00:03:12.504
And so you can just look at the ones.

00:03:12.504 --> 00:03:13.337
You could look at the wholes.

00:03:13.337 --> 00:03:16.446
We have three wholes, and we're
gonna take away two of them.

00:03:16.446 --> 00:03:18.019
So we're gonna be left with one whole,

00:03:18.019 --> 00:03:20.404
and we still have this 43/100.

00:03:20.404 --> 00:03:22.988
So we still have this 43/100,

00:03:22.988 --> 00:03:25.175
so it's gonna be one and 43/100,

00:03:25.175 --> 00:03:27.758
or we could write that as 1.43.

00:03:30.958 --> 00:03:34.580
That one maybe was a little
bit more straightforward.

00:03:34.580 --> 00:03:36.647
Now let's kind of combine the ideas

00:03:36.647 --> 00:03:37.760
of these last two examples,

00:03:37.760 --> 00:03:40.809
and do one that might seem
a little bit more daunting.

00:03:40.809 --> 00:03:43.611
Let's say that we want to subtract,

00:03:43.611 --> 00:03:46.278
we want to figure out what 65.79

00:03:47.781 --> 00:03:49.031
minus 42.58 is.

00:03:54.060 --> 00:03:57.673
Pause the video and see if
you can figure this out.

00:03:57.673 --> 00:03:59.652
Multiple ways to do this.

00:03:59.652 --> 00:04:02.590
You could separate the whole numbers,

00:04:02.590 --> 00:04:06.135
so you could say this is 65 minus 42.

00:04:06.135 --> 00:04:07.635
65 minus 42, plus,

00:04:11.146 --> 00:04:12.998
and then think about the,

00:04:12.998 --> 00:04:14.827
and then think about the hundredths.

00:04:14.827 --> 00:04:18.577
Plus 79/100, so 79/100,

00:04:20.545 --> 00:04:22.545
minus 58/100.

00:04:23.494 --> 00:04:25.807
Minus 58/100.

00:04:25.807 --> 00:04:28.833
And I just, I'll rewrite this
in words just to reinforce.

00:04:28.833 --> 00:04:31.583
This is 79 of something, 79/100.

00:04:31.583 --> 00:04:34.006
You could say it's 7/10 and 9/100,

00:04:34.006 --> 00:04:37.756
but it's the same thing as 79/100.

00:04:39.293 --> 00:04:40.126
Hundredths.

00:04:40.126 --> 00:04:43.126
This is 58/100.

00:04:43.126 --> 00:04:44.752
Hundredths.

00:04:44.752 --> 00:04:46.335
And so 65 minus 42.

00:04:48.293 --> 00:04:50.794
Five minus two go in the ones.

00:04:50.794 --> 00:04:52.135
We're gonna get three.

00:04:52.135 --> 00:04:55.634
And then 60 minus 40 is equal to 20.

00:04:55.634 --> 00:04:57.384
So we have 23 plus...

00:05:00.338 --> 00:05:04.349
Now 79/100 minus 58/100,

00:05:04.349 --> 00:05:05.849
70 minus 50 is 20.

00:05:08.941 --> 00:05:11.362
And nine minus eight is one.

00:05:11.362 --> 00:05:15.291
So this is gonna be 21/100,

00:05:15.291 --> 00:05:19.124
which we can write as 0.21, 21/100.

00:05:20.232 --> 00:05:23.860
And so when we compute this it'll be 23

00:05:23.860 --> 00:05:25.693
and 21/100.

00:05:28.997 --> 00:05:30.669
This is just one way to tackle it.

00:05:30.669 --> 00:05:34.611
There are multiple ways
that you could try to tackle

00:05:34.611 --> 00:05:37.278
a subtraction problem like this.


Strategies for subtracting basic decimals

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.194
- [Instructor] What we're
gonna do in this video

00:00:01.194 --> 00:00:04.894
is begin to practice subtracting decimals.

00:00:04.894 --> 00:00:06.482
And we're gonna build up slowly,

00:00:06.482 --> 00:00:07.727
and in future videos we're gonna learn

00:00:07.727 --> 00:00:10.040
to do this faster and faster and doing it

00:00:10.040 --> 00:00:12.792
for more and more complex situations.

00:00:12.792 --> 00:00:16.658
So let's say we have 3/10 minus 2/10.

00:00:16.658 --> 00:00:18.741
What is this going to be?

00:00:19.624 --> 00:00:21.673
Well there's a bunch of
ways you could tackle it,

00:00:21.673 --> 00:00:23.212
and I encourage you to pause the video

00:00:23.212 --> 00:00:24.295
and try to do it on your own

00:00:24.295 --> 00:00:26.965
before I work through it with you.

00:00:26.965 --> 00:00:30.566
But I'm assuming you did
that, so let's do it together.

00:00:30.566 --> 00:00:33.968
You could view this as 3/10,

00:00:33.968 --> 00:00:38.175
and then we're going to take away 2/10.

00:00:38.175 --> 00:00:41.119
If I have three of something
and I take away two of them,

00:00:41.119 --> 00:00:42.824
well what am I gonna be left with?

00:00:42.824 --> 00:00:45.647
Well I'm going to be left with one,

00:00:45.647 --> 00:00:47.585
I'm going to be left with 1/10.

00:00:47.585 --> 00:00:49.871
And we can visualize this.

00:00:49.871 --> 00:00:52.293
Let me put a whole there,

00:00:52.293 --> 00:00:54.818
and this whole is divided into tenths,

00:00:54.818 --> 00:00:57.460
and we see that three of the
tenths are already highlighted.

00:00:57.460 --> 00:01:01.536
So these three green bars
you can visualize as 3/10.

00:01:01.536 --> 00:01:04.036
Now we want to take away 2.10.

00:01:05.024 --> 00:01:09.191
We want to take away,
we're gonna take away 1/10,

00:01:10.702 --> 00:01:13.591
and then we take away 2/10.

00:01:13.591 --> 00:01:16.807
And so what are we left with?

00:01:16.807 --> 00:01:21.691
Well we're going to be left
with this 1/10 right over here.

00:01:21.691 --> 00:01:25.858
That's the only tenth that
is left of these 3/10.

00:01:26.899 --> 00:01:29.031
Now let's build on that idea

00:01:29.031 --> 00:01:32.531
and try to tackle more complex situations.

00:01:33.490 --> 00:01:35.823
Let me delete this and this,

00:01:37.585 --> 00:01:40.585
and let's say we want to tackle 1.5,

00:01:42.332 --> 00:01:44.683
or one and 5/10,

00:01:44.683 --> 00:01:47.850
and from that we want to subtract 0.7,

00:01:49.861 --> 00:01:51.524
or 7/10.

00:01:51.524 --> 00:01:55.691
Pause the video and see if
you can figure this out.

00:01:58.038 --> 00:02:00.193
There's a couple of ways
you could think about this,

00:02:00.193 --> 00:02:02.748
and I'll tell you the way
that I do it in my head.

00:02:02.748 --> 00:02:05.351
You could view this as,
so let me rewrite this.

00:02:05.351 --> 00:02:09.812
You could view this as one plus 5/10,

00:02:09.812 --> 00:02:14.696
must 7/10, minus let me do
it in that same blue color.

00:02:14.696 --> 00:02:16.529
Minus 7/10.

00:02:18.205 --> 00:02:21.047
And so there's a couple of
ways that you could view it.

00:02:21.047 --> 00:02:23.369
You could view this as 10/10.

00:02:23.369 --> 00:02:28.042
One whole is 10/10, so this is 10/10

00:02:28.042 --> 00:02:29.792
plus 5/10,

00:02:31.850 --> 00:02:33.821
minus 7/10.

00:02:33.821 --> 00:02:35.654
Minus 7/10.

00:02:37.618 --> 00:02:41.080
And so you could say this is 15/10.

00:02:41.080 --> 00:02:42.106
If you're doing it in your head

00:02:42.106 --> 00:02:43.384
you might get to this faster.

00:02:43.384 --> 00:02:45.625
You might say hey, 1.5, one and 5/10

00:02:45.625 --> 00:02:50.072
is the same thing as 15/10, minus 7/10.

00:02:50.072 --> 00:02:52.434
Minus 7/10.

00:02:52.434 --> 00:02:54.826
So 15 of something minus seven of it,

00:02:54.826 --> 00:02:57.177
well 15 minus seven is going to be eight.

00:02:57.177 --> 00:03:01.403
So this is going to be equal to 8/10.

00:03:01.403 --> 00:03:03.000
The way I just did it I
just thought of everything

00:03:03.000 --> 00:03:04.015
in terms of tenths.

00:03:04.015 --> 00:03:06.941
Instead of thinking of it in one and 5/10,

00:03:06.941 --> 00:03:10.865
you could view this as if
you could somehow put a 15

00:03:10.865 --> 00:03:15.219
in the tenth's place, and
instead call this zero ones,

00:03:15.219 --> 00:03:18.911
and 15/10, and then you subtract 7/10

00:03:18.911 --> 00:03:23.137
from those 15/10 to get the 8/10,

00:03:23.137 --> 00:03:26.387
which would be 0.8, or 8/10.

00:03:27.955 --> 00:03:30.074
Now another way that you
could've thought about it,

00:03:30.074 --> 00:03:32.518
let's go back to this
step right over here,

00:03:32.518 --> 00:03:34.425
I could've said well look.

00:03:34.425 --> 00:03:38.906
I can think about what one
minus 7/10 is going to be.

00:03:38.906 --> 00:03:43.102
I could view this as one minus 7/10,

00:03:43.102 --> 00:03:47.782
and then I'm going to add 5/10 to that.

00:03:47.782 --> 00:03:50.052
Then I'm going to add 5/10 to that.

00:03:50.052 --> 00:03:54.133
One minus 7/10, one is 10/10.

00:03:54.133 --> 00:03:58.295
If I take 7 of them away,
I'm gonna be left with 3/10.

00:03:58.295 --> 00:04:02.399
So you could say that's
going to be 3/10 plus 5/10.

00:04:02.399 --> 00:04:04.046
Plus 5/10.

00:04:04.046 --> 00:04:08.477
Which is once again, it is equal to 8/10.

00:04:08.477 --> 00:04:10.618
Now another way that
you could tackle this,

00:04:10.618 --> 00:04:12.697
and once again, I'm showing
as many ways as possible

00:04:12.697 --> 00:04:15.250
just so you appreciate that
these are just different ways

00:04:15.250 --> 00:04:16.668
of tackling the same idea.

00:04:16.668 --> 00:04:19.168
Let's draw a number line here.

00:04:21.010 --> 00:04:24.903
Let's say this is zero,
and then one, two, three,

00:04:24.903 --> 00:04:28.666
four, five, six, seven, eight, nine, 10.

00:04:28.666 --> 00:04:30.078
That is one.

00:04:30.078 --> 00:04:32.990
One, two, three, four, five.

00:04:32.990 --> 00:04:33.990
That is 1.5.

00:04:35.044 --> 00:04:38.565
We're gonna start at 1.5 right over here.

00:04:38.565 --> 00:04:39.482
That's 1.5.

00:04:40.364 --> 00:04:43.186
We're gonna take away 7/10.

00:04:43.186 --> 00:04:46.046
So one way that you might
do it is you say okay,

00:04:46.046 --> 00:04:50.213
we could take away, we
could take away 5/10,

00:04:51.474 --> 00:04:52.830
which would take us to one,

00:04:52.830 --> 00:04:55.308
and then we have to take
two more tenths away,

00:04:55.308 --> 00:05:00.182
which is gonna take us to 8/10, or 0.8.

00:05:00.182 --> 00:05:02.004
So the way that I just
thought about it just now

00:05:02.004 --> 00:05:03.669
is I said hey, this is the same thing

00:05:03.669 --> 00:05:06.086
as 1.5 minus 5/10.

00:05:08.587 --> 00:05:10.989
Minus 5/10.

00:05:10.989 --> 00:05:12.782
Minus 2/10.

00:05:12.782 --> 00:05:15.268
The reason why I broke
it up like this is look,

00:05:15.268 --> 00:05:19.100
okay 1.5, or one and 5/10 minus 5/10,

00:05:19.100 --> 00:05:21.979
that's pretty straightforward to compute.

00:05:21.979 --> 00:05:23.442
You could say that right over there

00:05:23.442 --> 00:05:25.048
is just going to be one.

00:05:25.048 --> 00:05:27.041
I'm taking away the 5/10.

00:05:27.041 --> 00:05:29.877
And then I have 2/10
leftover to take away.

00:05:29.877 --> 00:05:34.336
One minus these 2/10, and once again,

00:05:34.336 --> 00:05:36.902
you are left with 8/10.

00:05:36.902 --> 00:05:39.800
These are all perfectly legitimate ways

00:05:39.800 --> 00:05:41.710
to tackle this problem.

00:05:41.710 --> 00:05:44.618
And this is a way that many
people, including myself,

00:05:44.618 --> 00:05:46.879
would try to do it in their head.


Andding decimals with hundredths

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:01.147
- [Instructor] Let's get some practice

00:00:01.147 --> 00:00:04.270
adding numbers that involve hundredths.

00:00:04.270 --> 00:00:07.422
Pause this video and see if
you can add these two numbers.

00:00:07.422 --> 00:00:08.844
See what you get.

00:00:08.844 --> 00:00:10.497
Alright, now let's work
through this together.

00:00:10.497 --> 00:00:14.039
Now there is many different
ways to add decimals.

00:00:14.039 --> 00:00:15.833
And you'll learn more systematic,

00:00:15.833 --> 00:00:17.946
faster ways of doing it in the future,

00:00:17.946 --> 00:00:20.179
but I'll show you a few ways

00:00:20.179 --> 00:00:22.730
that my brain might think about it.

00:00:22.730 --> 00:00:24.674
One way to think about it is you could say

00:00:24.674 --> 00:00:27.418
that this is 53/100.

00:00:27.418 --> 00:00:32.230
You could read this as either
5/10 and 3/100, or 53/100.

00:00:32.230 --> 00:00:36.263
You could say this is 53/100.

00:00:36.263 --> 00:00:37.180
Hundredths.

00:00:38.711 --> 00:00:43.452
And to that you're going to add 42/100.

00:00:43.452 --> 00:00:44.952
42/100.

00:00:47.783 --> 00:00:50.632
And so if I have 53 of
something and I'm gonna add 42

00:00:50.632 --> 00:00:54.024
of that same something to
it, what am I going to get?

00:00:54.024 --> 00:00:55.941
Well what's 53 plus 42?

00:00:56.884 --> 00:01:00.804
Well in my head I say
well 50 plus 40 is 90,

00:01:00.804 --> 00:01:03.463
and three plus two is five.

00:01:03.463 --> 00:01:06.380
It's going to be 95/100.

00:01:07.332 --> 00:01:08.981
95/100.

00:01:08.981 --> 00:01:11.531
And if I wanted to write
that as a pure number,

00:01:11.531 --> 00:01:13.781
I would write that as 0.95,

00:01:15.186 --> 00:01:18.390
which I could write as 95/100, hundredths,

00:01:18.390 --> 00:01:21.219
or 9/10 and 5/100.

00:01:21.219 --> 00:01:22.896
Now the other way we
could've thought about it

00:01:22.896 --> 00:01:25.265
is we could've broken these numbers up.

00:01:25.265 --> 00:01:27.193
We could've said that this first number

00:01:27.193 --> 00:01:31.360
is 5/10 plus 3/100, hundredths.

00:01:33.236 --> 00:01:35.541
And then the second number,
we could've rewritten

00:01:35.541 --> 00:01:38.958
as 4/10 plus 2/100.

00:01:41.148 --> 00:01:42.617
Let me make sure of my decimals.

00:01:42.617 --> 00:01:44.651
Plus 2/100.

00:01:44.651 --> 00:01:46.910
And then we could've separately added

00:01:46.910 --> 00:01:49.070
the tenths and the hundredths.

00:01:49.070 --> 00:01:53.153
So you have 5/10 plus 4/10,

00:01:54.319 --> 00:01:58.064
so 5/10 plus 4/10,

00:01:58.064 --> 00:02:02.231
and then you could separately
add 3/100 plus 2/100.

00:02:03.178 --> 00:02:06.783
So 3/100, I have a little
trouble saying that,

00:02:06.783 --> 00:02:10.450
plus 2/100, and so what do I get?

00:02:11.287 --> 00:02:15.925
Well 5/10 and 4/10, and we've
done this in previous videos,

00:02:15.925 --> 00:02:17.482
if I have five of something
and I add four of it,

00:02:17.482 --> 00:02:19.180
that's gonna be 9/10.

00:02:19.180 --> 00:02:23.347
So it's gonna be 9/10, and
then the 3/100 plus 2/100.

00:02:24.819 --> 00:02:27.547
Well that's going to be 5/100.

00:02:27.547 --> 00:02:28.630
So plus 0.05.

00:02:30.154 --> 00:02:34.066
And then 9/10 plus 5/100 is gonna be,

00:02:34.066 --> 00:02:35.916
I know I'm saying
hundredths kinda strange,

00:02:35.916 --> 00:02:40.243
is going to be 9/10 and 5/100,

00:02:40.243 --> 00:02:44.076
which you could also say as 95/100.

00:02:46.493 --> 00:02:49.049
Let's do another example.

00:02:49.049 --> 00:02:52.497
One that's a little bit more involved.

00:02:52.497 --> 00:02:55.914
Let's say I want to add 68/100

00:02:59.005 --> 00:03:00.755
to 33/100.

00:03:04.148 --> 00:03:06.841
What is this going to be?

00:03:06.841 --> 00:03:09.320
And like always, pause the video and see

00:03:09.320 --> 00:03:11.804
if you can figure it out on your own.

00:03:11.804 --> 00:03:14.858
Well there's a couple of
ways to think about it.

00:03:14.858 --> 00:03:17.817
One way we could split up the
tenths and the hundredths,

00:03:17.817 --> 00:03:20.508
actually let's do it that way.

00:03:20.508 --> 00:03:24.675
We could rewrite this first
number as 6/10 plus 8/100,

00:03:27.370 --> 00:03:31.537
and the second number we could
write as 3/10 plus 3/100.

00:03:34.844 --> 00:03:37.519
Let me do that in that orange color.

00:03:37.519 --> 00:03:39.436
3/10 plus...

00:03:41.948 --> 00:03:45.531
Plus 3/10 plus 3/100.

00:03:49.648 --> 00:03:53.514
So if I add the 6/10 and the 3/10,

00:03:53.514 --> 00:03:54.798
so let me just do that.

00:03:54.798 --> 00:03:56.102
I'm gonna write every step here.

00:03:56.102 --> 00:03:57.096
If you're doing this in your head

00:03:57.096 --> 00:03:58.024
or if you're doing this on paper

00:03:58.024 --> 00:04:00.323
you wouldn't necessarily
write every step here.

00:04:00.323 --> 00:04:01.751
Those are the tenths.

00:04:01.751 --> 00:04:04.530
And then separately I'm
gonna add the hundredths.

00:04:04.530 --> 00:04:08.280
Plus 8/100, plus 3/100.

00:04:09.835 --> 00:04:11.668
Plus 3/100.

00:04:13.737 --> 00:04:16.988
6/10 plus 3/10, we've done
this in previous videos,

00:04:16.988 --> 00:04:19.151
that's hopefully pretty
straightforward by this point.

00:04:19.151 --> 00:04:20.638
If it's not, I encourage you to review

00:04:20.638 --> 00:04:22.924
some of those earlier videos.

00:04:22.924 --> 00:04:26.169
That's going to be 9/10.

00:04:26.169 --> 00:04:27.938
If I have six of something
and then I add three of them,

00:04:27.938 --> 00:04:29.327
in this case we're talking about tenths,

00:04:29.327 --> 00:04:31.839
I'm gonna get nine of them, so 9/10.

00:04:31.839 --> 00:04:33.669
And so what's this going to be?

00:04:33.669 --> 00:04:36.784
Well you could view this is as 8/100.

00:04:36.784 --> 00:04:40.034
8/100 plus 3/100.

00:04:42.841 --> 00:04:45.131
If I have eight of something
and I add three of something,

00:04:45.131 --> 00:04:47.421
that's gonna get 11 of that something.

00:04:47.421 --> 00:04:48.921
11/100.

00:04:50.809 --> 00:04:55.558
How do we write 11/100 as a decimal?

00:04:55.558 --> 00:05:00.247
Well one way to write it, you
could just view this as 0.11.

00:05:00.247 --> 00:05:02.298
This is 11/100.

00:05:02.298 --> 00:05:04.577
Many people would read this as 11/100.

00:05:04.577 --> 00:05:09.141
Or you could view this as equaling 10/100,

00:05:09.141 --> 00:05:12.474
10/100 plus 1/100.

00:05:13.991 --> 00:05:15.464
Hundredth.

00:05:15.464 --> 00:05:19.773
And 10/100 right over here is 1/10.

00:05:19.773 --> 00:05:22.940
You could view this as 1/10

00:05:24.769 --> 00:05:26.193
and 1/100.

00:05:26.193 --> 00:05:28.858
1/10 and 1/100.

00:05:28.858 --> 00:05:31.679
When you add everything
together, what do you get?

00:05:31.679 --> 00:05:35.846
Well you get 9/10, plus 1/10, plus 1/100.

00:05:37.639 --> 00:05:40.287
Well now this is gonna get
interesting still, so let's see.

00:05:40.287 --> 00:05:41.663
Let me actually rewrite this.

00:05:41.663 --> 00:05:45.042
It's gonna be 9/10, and
this one let me write it

00:05:45.042 --> 00:05:46.792
plus 1/10,

00:05:48.758 --> 00:05:52.561
plus that 1/100 leftover.

00:05:52.561 --> 00:05:54.557
Plus that 1/100.

00:05:54.557 --> 00:05:56.049
What is this going to be?

00:05:56.049 --> 00:06:00.216
9/10 and 1/10, that's going to be,

00:06:02.371 --> 00:06:05.935
9/10 and 1/10 is going to be 10/10.

00:06:05.935 --> 00:06:10.850
10/10, which is the
same thing as one whole.

00:06:10.850 --> 00:06:13.382
This is just going to be equal to one.

00:06:13.382 --> 00:06:16.498
It's going to be one plus 1/100.

00:06:16.498 --> 00:06:20.665
It's going to be one and
1/100, and we are done.

00:06:22.212 --> 00:06:24.191
As I keep mentioning in future videos

00:06:24.191 --> 00:06:27.118
we're gonna learn maybe
faster ways of doing this.

00:06:27.118 --> 00:06:28.403
Maybe ways that you might be able to do it

00:06:28.403 --> 00:06:29.596
a little bit more automatically.

00:06:29.596 --> 00:06:31.694
But it's really important to think about

00:06:31.694 --> 00:06:34.212
what we just went here and
how we were able to think,

00:06:34.212 --> 00:06:38.225
okay 11/100 is the same thing
as a tenth and a hundredth,

00:06:38.225 --> 00:06:41.109
and then taking that tenth,
and then adding it to the 9/10

00:06:41.109 --> 00:06:43.113
that we already had and
say, hey that's whole.

00:06:43.113 --> 00:06:44.680
In the future, we're gonna be doing things

00:06:44.680 --> 00:06:47.500
like carrying with decimals,
but this is essentially

00:06:47.500 --> 00:06:49.789
what is happening underneath conceptually.

00:06:49.789 --> 00:06:51.907
It's really important
you get a sense of that

00:06:51.907 --> 00:06:54.990
before you learn the faster methods.


Introduction to adding decimals tenths

WEBVTT
Kind: captions
Language: en

00:00:00.020 --> 00:00:01.739
- [Instructor] In this video
we're going to introduce

00:00:01.739 --> 00:00:05.871
ourselves to the idea of adding decimals.

00:00:05.871 --> 00:00:08.624
And I encourage you as we
work through these problems

00:00:08.624 --> 00:00:10.005
to keep pausing the video

00:00:10.005 --> 00:00:12.188
and seeing if you can
think about it on your own

00:00:12.188 --> 00:00:13.916
before we work through it together.

00:00:13.916 --> 00:00:16.321
Now we're going to build up
slowly, and in future videos

00:00:16.321 --> 00:00:18.718
we're gonna find out
faster ways of doing it.

00:00:18.718 --> 00:00:21.672
But the way we're learning it
in this video in the next view

00:00:21.672 --> 00:00:24.634
is to really make sure we
understand what is happening.

00:00:24.634 --> 00:00:28.587
So let's say we wanted to add 0.1 to 0.8.

00:00:28.587 --> 00:00:31.878
Or you could say we're
adding 1/10 to 8/10.

00:00:31.878 --> 00:00:35.547
Pause this video and see
if you can figure that out.

00:00:35.547 --> 00:00:38.682
Well there's a couple of
ways to think about it.

00:00:38.682 --> 00:00:42.849
You could say, hey look 0.1, that is 1/10,

00:00:44.027 --> 00:00:46.777
and 0.8, that is 8/10.

00:00:49.572 --> 00:00:51.081
And so if I have one of something

00:00:51.081 --> 00:00:53.426
and I add eight more of that something,

00:00:53.426 --> 00:00:56.155
so I have 1/10, and I'm
gonna add eight more tenths,

00:00:56.155 --> 00:00:59.658
well I'm gonna end up with
nine of that something,

00:00:59.658 --> 00:01:01.743
in this case we're talking about tenths.

00:01:01.743 --> 00:01:05.420
So that is going to be equal to 9/10.

00:01:05.420 --> 00:01:07.067
That's one way to think about it.

00:01:07.067 --> 00:01:09.755
Another way, we could
think about it visually.

00:01:09.755 --> 00:01:12.780
So let's say we take a whole,
and we were to divide it

00:01:12.780 --> 00:01:15.027
into tenths, which we
have right over here.

00:01:15.027 --> 00:01:16.865
So if we say this whole square is a whole,

00:01:16.865 --> 00:01:19.384
we divide it into 10 equal sections.

00:01:19.384 --> 00:01:22.507
So each of these white bars
you can view as a tenth.

00:01:22.507 --> 00:01:26.890
So we have 1/10, so let me fill that in.

00:01:26.890 --> 00:01:30.442
So 1/10, woops that's
not what I wanted to do.

00:01:30.442 --> 00:01:32.267
We have 1/10 right over there.

00:01:32.267 --> 00:01:34.437
And to that we want to add 8/10.

00:01:34.437 --> 00:01:36.520
So one, two, three, four,

00:01:37.979 --> 00:01:39.979
five, six, seven, eight.

00:01:41.988 --> 00:01:45.571
And so how many total
tenths do I now have?

00:01:46.616 --> 00:01:48.415
Well let's just count 'em up.

00:01:48.415 --> 00:01:49.964
We have this one here.

00:01:49.964 --> 00:01:52.297
One, two, three, four, five,

00:01:53.316 --> 00:01:55.924
six, seven, eight, nine.

00:01:55.924 --> 00:01:57.357
These are really saying the same thing.

00:01:57.357 --> 00:01:59.962
All of this together, is going to be,

00:01:59.962 --> 00:02:00.795
let me do that a little neater.

00:02:00.795 --> 00:02:05.174
All of this together is going to be 9/10.

00:02:05.174 --> 00:02:09.333
Now in either case, how do we
write 9/10 in decimal form?

00:02:09.333 --> 00:02:11.922
Well we go to the tenth's place,

00:02:11.922 --> 00:02:15.736
which is one space on the
right side of the decimal.

00:02:15.736 --> 00:02:17.936
We say hey we have 9/10.

00:02:17.936 --> 00:02:20.030
This is the tenth's space right over here.

00:02:20.030 --> 00:02:21.813
So that's just saying we have 9/10.

00:02:21.813 --> 00:02:25.563
We have nine of these
tenths right over here.

00:02:26.528 --> 00:02:28.445
So let's keep building.

00:02:29.651 --> 00:02:32.539
Let's do another example.

00:02:32.539 --> 00:02:36.706
So let's say that we, let
me clear all of this out.

00:02:38.544 --> 00:02:42.089
So let's say that we want to add,

00:02:42.089 --> 00:02:44.597
do these with different colors.

00:02:44.597 --> 00:02:46.930
So let's say we want to add,

00:02:48.417 --> 00:02:51.152
I have trouble because
my pen isn't working.

00:02:51.152 --> 00:02:51.985
Let's see.

00:02:53.097 --> 00:02:55.347
Let's say we want to add...

00:02:58.229 --> 00:03:00.139
My pen is, oh here we go.

00:03:00.139 --> 00:03:04.620
Let's say we want to
add 3/10, and to that,

00:03:04.620 --> 00:03:07.203
we want to add 9/10.

00:03:09.304 --> 00:03:11.387
What is that going to be?

00:03:12.555 --> 00:03:14.796
Well you could use the same idea.

00:03:14.796 --> 00:03:17.918
If you say this is 3/10,

00:03:17.918 --> 00:03:22.085
and this is 9/10, plus 9/10,

00:03:23.114 --> 00:03:24.232
well if I have three of something

00:03:24.232 --> 00:03:27.225
and I add nine of them,
well that's going to be 12.

00:03:27.225 --> 00:03:28.400
Three plus nine is 12.

00:03:28.400 --> 00:03:33.173
So we could say this is
going to be equal to 12/10.

00:03:33.173 --> 00:03:35.653
Now this one might be a
little bit counterintuitive.

00:03:35.653 --> 00:03:38.884
12/10, what does that mean?

00:03:38.884 --> 00:03:40.233
Well one way to think about it,

00:03:40.233 --> 00:03:42.316
this is 10/10,

00:03:44.958 --> 00:03:46.708
plus 2/10.

00:03:48.434 --> 00:03:51.124
And what are 10/10?

00:03:51.124 --> 00:03:55.878
Well if I have 10/10, this
right over here is one whole.

00:03:55.878 --> 00:03:57.620
So that is going to be one.

00:03:57.620 --> 00:04:00.151
So we have one and 2/10.

00:04:00.151 --> 00:04:03.703
So how do we write one and 2/10?

00:04:03.703 --> 00:04:06.478
Well we could write it
as in the one's place,

00:04:06.478 --> 00:04:08.051
we just write a one.

00:04:08.051 --> 00:04:13.013
And then in the tenth's
place, we write our 2/10.

00:04:13.013 --> 00:04:15.871
So you could say it's equal to 1.2,

00:04:15.871 --> 00:04:19.458
or you could say it's
equal to one and 2/10,

00:04:19.458 --> 00:04:22.974
which is the same thing as 12/10.

00:04:22.974 --> 00:04:24.532
Now if we want to see that visually,

00:04:24.532 --> 00:04:27.565
let's get our diagram out again.

00:04:27.565 --> 00:04:29.569
So actually I'm gonna
put two of these here.

00:04:29.569 --> 00:04:32.069
So one, and then a second one.

00:04:33.604 --> 00:04:38.318
And we want to add, so
let's start with the 3/10.

00:04:38.318 --> 00:04:42.178
So let me color these in really fast.

00:04:42.178 --> 00:04:44.237
Use that light blue color.

00:04:44.237 --> 00:04:46.237
That is 1/10.

00:04:47.929 --> 00:04:50.531
This is 2/10.

00:04:50.531 --> 00:04:52.390
Just coloring 'em in really fast.

00:04:52.390 --> 00:04:55.019
And this is 3/10.

00:04:55.019 --> 00:04:58.837
And then to that we're gonna add 9/10.

00:04:58.837 --> 00:05:01.420
So to that we're gonna add one,

00:05:04.046 --> 00:05:04.879
two,

00:05:07.168 --> 00:05:08.001
three.

00:05:09.408 --> 00:05:11.047
I'm not coloring them in fully.

00:05:11.047 --> 00:05:12.964
Four, you get the idea.

00:05:14.371 --> 00:05:15.954
Five, almost there.

00:05:17.223 --> 00:05:18.056
Six.

00:05:19.104 --> 00:05:20.066
I need to color faster.

00:05:20.066 --> 00:05:20.899
Seven.

00:05:22.766 --> 00:05:23.599
Seven.

00:05:24.590 --> 00:05:25.423
Eight.

00:05:28.894 --> 00:05:30.217
Nine.

00:05:30.217 --> 00:05:31.050
So there you have it.

00:05:31.050 --> 00:05:32.967
I have added 9/10.

00:05:32.967 --> 00:05:35.202
You notice I've colored in nine,

00:05:35.202 --> 00:05:37.782
I've colored in yellow,
nine of the tenths,

00:05:37.782 --> 00:05:40.794
and before I had three
of the tenths colored in.

00:05:40.794 --> 00:05:42.843
And when you add 'em all
together, what happens?

00:05:42.843 --> 00:05:46.495
Well the 3/10 plus the
7/10 right over here,

00:05:46.495 --> 00:05:48.259
they made a whole.

00:05:48.259 --> 00:05:51.176
So this right over here is our one.

00:05:52.236 --> 00:05:56.082
And then we also have
another 2/10 left over.

00:05:56.082 --> 00:06:00.249
And so this is where,
this is our 0.2, or 2/10.

00:06:01.687 --> 00:06:05.854
So it's gonna be one
plus 2/10, which is 1.2.

00:06:06.893 --> 00:06:08.107
So hopefully this gives you a good sense

00:06:08.107 --> 00:06:10.104
of how we think about adding decimals.

00:06:10.104 --> 00:06:11.184
And even though in the future

00:06:11.184 --> 00:06:13.350
we're gonna figure out
faster ways of doing it,

00:06:13.350 --> 00:06:15.666
or more systematic ways of doing it,

00:06:15.666 --> 00:06:18.055
this is still the way that
I still do it in my head

00:06:18.055 --> 00:06:19.378
if someone walks up to me on the street

00:06:19.378 --> 00:06:21.839
and says hey, add 0.3 to 0.9.

00:06:21.839 --> 00:06:24.256
That's how I think about it.