Solving problems with pictographs 2

WEBVTT
Kind: captions
Language: en

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- Let's tackle some exercise
with picture graphs,

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and once again, I'm using the Khan Academy

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exercise to do this.

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It says, which towns had fewer sunny days

00:00:09.995 --> 00:00:13.350
than Sparkle City in June?

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All right, so, if we look at
the picture graph down here,

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each picture of a sun
represents six sunny days.

00:00:22.771 --> 00:00:25.755
We want to say which towns had fewer ...

00:00:25.755 --> 00:00:26.941
what did they say?

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Fewer sunny days in Sparkle City in June.

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Sparkle City is this one right over here.

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Sparkle City had, let's see,

00:00:35.751 --> 00:00:37.771
we have one, two, three, four, five

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pictures of a sun.

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Each of those represents six sunny days.

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Five times six ...

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Sparkle City had 30 sunny days in June.

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Which of these had fewer
than 30 sunny days?

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Well, you can just look at
the picture graph itself,

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and all of Sunville, Shinny
Town, and Star Village,

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they don't have as many of
these pictures of the sun.

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They all had fewer sunny days.

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We actually don't even have to calculate

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how many sunny days
each of these represent.

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Although, if you cared, this
would be four times six,

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this would be 24.

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This would be two times six or 12.

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This would be three times
six or 18 sunny days in June.

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All three of them, Sunville,
Shinny Town, and Star Village.

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Sunville, Shinny Town, and Star Village

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all had fewer sunny days
than Sparkle City in June.

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Let's keep going.

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Let's do a couple more of these.

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The graph shows how
many mice a farmer found

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in here field each day for five days.

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Which day did the farmer
find the same amount of mice

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as on Wednesday and Thursday combined?

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All right, let's look at this.

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Each picture of a mouse

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represents two mice.

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See, on Wednesday and Thursday combined,

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there's two ways to think about his.

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On Wednesday and Thursday combined,

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I have one picture of a mouse,

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and then two more pictures of mice.

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That's a total of three pictures of mice.

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What other day do I have
three pictures of mice?

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Well, Tuesday I have
three pictures of mice.

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I could just pick Tuesday.

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Another way to think it is

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on Wednesday, the actual number
of mice that were observed,

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one picture means two mice.

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Two mice on Wednesday,

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four mice on Thursday,

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because I have two pictures
each of them represent two mice.

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Two on Wednesday, four on Thursday,

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so six total.

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You see on Tuesday we have
six mice were observed.

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Once again, each of these
pictures represent two.

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Two, four, six.

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There you go.

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All right, let's keep going.

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Funland had blank
millimeters less rainfall

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than Happyville in August.

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This right over here,

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this is Funland, this is Happyville,

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and each little raindrop picture
represents six millimeters.

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Funville has two raindrop pictures,

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Happyville has four raindrops pictures.

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Funland had two less raindrop pictures.

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I had two less of these raindrops.

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Two less raindrops would be
two times six, it would be 12.

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12 millimeters less
rainfall than Happyville.

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Another way you could
have thought about it

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Funland had 12 millimeters
of rainfall in August.

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Each of these six then 12.

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Each of these represent six millimeters.

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Happyville had six,
12, 18, 24 millimeters.

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12 millimeters verses 24 millimeters.

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Well, Funland's going to
have 12 millimeters less.

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12 millimeters is 12
less than 24 millimeters.


Creating picture and bar graphs 2 exercise examples

WEBVTT
Kind: captions
Language: en

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- [Voiceover] Let's do some examples

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creating picture and bar graphs.

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So it says Mr. Smith
assigned a special project

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about the ocean to the students

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in his Earth Science class.

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To find out if students
who spend more time

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on their projects got better grades,

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he asked the students how much time

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they spent completing their projects.

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Create a bar graph to show how much time

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each student spent
completing the ocean project.

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So James spent 36 minutes.

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So I'm gonna click here

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and I'm gonna move this up to 36.

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Eji spent 54 minutes.

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So I'm gonna move this up to 54 minutes.

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Then Minli spent 36 minutes.

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So I'm gonna move Minli up to 36 minutes.

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Then Simone spent 30 minutes.

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So I'm gonna move Simone up to 30.

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Then Kiran spent 12 minutes.

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So I'll move Kiran up to 12.

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And there you go, I have
constructed the bar graph.

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Let's do a couple more of these.

00:01:02.303 --> 00:01:03.310
All right.

00:01:03.310 --> 00:01:06.085
So on Thursday, Ming went to see a loud

00:01:06.085 --> 00:01:09.207
and exciting performance
by the Dinosaur Orchestra.

00:01:09.207 --> 00:01:10.624
Create a bar graph to show how many

00:01:10.624 --> 00:01:11.901
of each type of dinosaur were

00:01:11.901 --> 00:01:13.921
in the Dinosaur Orchestra.

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So I guess there were 42 Stegosaurus's.

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I don't know if that's a
plural for Stegosaurus.

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So there are 42 Stegosaurus's,

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63 Raptors.

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So we move the Raptor up to 63.

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35 Triceratops.

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Then you had 49 Tyrannosaurus.

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49 of these.

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So fairly straightforward.

00:01:37.731 --> 00:01:39.856
So let's do a couple more of these.

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All right, so now it tells
us Rose's flower shop

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makes bouquets for special occasions.

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Each bouquet comes with

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a different number of flowers.

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Create a picture graph to show the number

00:01:50.699 --> 00:01:51.976
of flowers in each bouquet.

00:01:51.976 --> 00:01:53.659
So this is kind of like a bar graph,

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but instead we're gonna use pictures.

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Each picture shows a certain number.

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So in this case, a picture of a flower

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represents three flowers.

00:02:01.170 --> 00:02:05.988
So the Mother's day
bouquet has 21 flowers.

00:02:05.988 --> 00:02:07.892
So 21 flowers.

00:02:07.892 --> 00:02:11.107
Now you might be tempted
to put 21 pictures

00:02:11.107 --> 00:02:13.186
of flowers here, but you have to remember

00:02:13.186 --> 00:02:16.506
each of these flowers
represent three flowers.

00:02:16.506 --> 00:02:17.388
So one way to think about it,

00:02:17.388 --> 00:02:18.890
you could count by threes.

00:02:18.890 --> 00:02:21.612
Three, six, nine,

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12, 15, 18, 21.

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So that over here, this right over here,

00:02:27.836 --> 00:02:29.429
would represent 21 flowers.

00:02:29.429 --> 00:02:33.145
And you notice I just made
seven of this picture,

00:02:33.145 --> 00:02:34.769
and that makes sense because seven

00:02:34.769 --> 00:02:36.267
of these pictures, and
each of these pictures

00:02:36.267 --> 00:02:39.761
represent three flowers,
seven times three is 21.

00:02:39.761 --> 00:02:43.942
The Mother's Day bouquet
has 21 flowers in it.

00:02:43.942 --> 00:02:46.727
All right, the Anniversary
bouquet has 27 flowers.

00:02:46.727 --> 00:02:48.897
So three, six, nine,

00:02:48.897 --> 00:02:53.897
12, 15, 18, 21, 24, 27.

00:02:53.936 --> 00:02:55.189
I have nine flowers here.

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Nine times three is 27.

00:02:58.289 --> 00:03:00.913
The Birthday bouquet has 18.

00:03:00.913 --> 00:03:05.835
So three, six, nine, 12, 15, 18.

00:03:05.835 --> 00:03:07.438
And I just made six pictures here

00:03:07.438 --> 00:03:09.400
because each of them
represent three flowers.

00:03:09.400 --> 00:03:12.382
Six times three is 18.

00:03:12.382 --> 00:03:14.217
Then finally, the Congratulations bouquet

00:03:14.217 --> 00:03:15.796
has 12 flowers in it.

00:03:15.796 --> 00:03:20.695
Three, six, nine, and 12.

00:03:20.695 --> 00:03:21.704
There you go.

00:03:21.704 --> 00:03:23.136
I think we're done.

00:03:23.136 --> 00:03:24.913
I think we're done.

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Let's do one more of these.

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All right.

00:03:29.043 --> 00:03:31.945
Barry Bee and his bee friends love

00:03:31.945 --> 00:03:33.744
to pollinate flowers.

00:03:33.744 --> 00:03:35.799
They created a chart and a picture graph

00:03:35.799 --> 00:03:37.088
to show how many flowers each

00:03:37.088 --> 00:03:38.830
of them pollinated today.

00:03:38.830 --> 00:03:40.884
Use the information in the chart

00:03:40.884 --> 00:03:43.658
to answer the question
about the picture graph.

00:03:43.658 --> 00:03:45.566
So it says, On the picture graph,

00:03:45.566 --> 00:03:48.085
each flower equals blank flowers,

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or each picture of a flower, I should say,

00:03:50.209 --> 00:03:52.867
equals a blank number of flowers.

00:03:52.867 --> 00:03:56.121
So it says Barry pollinated 27.

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These are impressive bees

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that they sit there making charts.

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Barry pollinated 27 flowers,

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and they only drew three pictures here.

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So these three flower
pictures must represent 27.

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So the way that they would represent 27

00:04:11.840 --> 00:04:13.664
is if each of these represent nine

00:04:13.664 --> 00:04:17.448
because we'd have nine, 18, 27.

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So each of these must be nine flowers.

00:04:19.700 --> 00:04:21.141
But let's see if that works.

00:04:21.141 --> 00:04:23.728
So for Bumbly, 63.

00:04:23.728 --> 00:04:28.338
So let's see, nine, 18, 27,

00:04:28.338 --> 00:04:33.086
36, 45, 54, 63.

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Yep, it looks like it works out.

00:04:34.781 --> 00:04:38.205
Betty is one, two, three, four, five, six.

00:04:38.205 --> 00:04:40.597
Six, six times nine is 54.

00:04:40.597 --> 00:04:43.384
That is the number of
flowers she pollinated.

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Bertie, one, two, three, four, five.

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If each of those pictures represent nine,

00:04:47.980 --> 00:04:50.778
then this would be five times nine is 45.

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That is the number of flowers Bertie

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had actually pollinated.


More solving problems with bar graphs

WEBVTT
Kind: captions
Language: en

00:00:00.372 --> 00:00:02.496
- [Voiceover] Lola asked her classmates

00:00:02.496 --> 00:00:05.735
their favorite type of movie
and graphed the results.

00:00:05.735 --> 00:00:09.717
All right so it says that 20 people

00:00:09.717 --> 00:00:12.132
said their favorite type
of movie was comedy.

00:00:12.132 --> 00:00:15.197
Six people said their favorite
type of movie was scary.

00:00:15.197 --> 00:00:18.110
10 people said their favorite
type of movie was adventure.

00:00:18.110 --> 00:00:20.049
10 people also said their favorite

00:00:20.049 --> 00:00:21.814
type of movie is cartoons.

00:00:21.814 --> 00:00:23.671
And then 16 people said their favorite

00:00:23.671 --> 00:00:25.215
type of movie is a mystery.

00:00:25.215 --> 00:00:27.096
All right, so let's
read the questions here.

00:00:27.096 --> 00:00:29.174
So which of the following types of movies

00:00:29.174 --> 00:00:32.018
were picked by fewer than 14 people?

00:00:32.018 --> 00:00:34.607
So fewer than 14 people.

00:00:34.607 --> 00:00:38.194
So more than 14 picked comedy or mystery.

00:00:38.194 --> 00:00:41.212
So this line right over here would be 14.

00:00:41.212 --> 00:00:44.649
So fewer than 14 were
scary, adventure, cartoon.

00:00:44.649 --> 00:00:46.936
This was six people, 10
people, and 10 people.

00:00:46.936 --> 00:00:49.629
Scary, adventure, and cartoon.

00:00:49.629 --> 00:00:54.164
So we wanna pick scary,
adventure, and cartoon.

00:00:54.164 --> 00:00:57.763
These three had less
than 14 people pick them.

00:00:57.763 --> 00:01:00.247
So let's do a couple more of these.

00:01:00.247 --> 00:01:02.261
Let's do a couple more.

00:01:05.444 --> 00:01:08.880
Puppy Party Place graphed
the number of dogs

00:01:08.880 --> 00:01:10.656
that came in each weekday.

00:01:10.656 --> 00:01:13.303
So let's see, 80 dogs came in on Monday,

00:01:13.303 --> 00:01:17.215
160 dogs came in on Tuesday,
80 dogs came in on Wednesday.

00:01:17.215 --> 00:01:19.699
140 dogs came in on Thursday,

00:01:19.699 --> 00:01:21.499
and then Friday was a very popular day,

00:01:21.499 --> 00:01:25.260
180 dogs came in to the
Puppy Party Place on Friday.

00:01:25.260 --> 00:01:27.338
All right, so what are they asking us?

00:01:27.338 --> 00:01:29.741
On which day did the same number of dogs

00:01:29.741 --> 00:01:31.773
come to Puppy Party Place,

00:01:31.773 --> 00:01:35.012
as on Monday and Wednesday combined?

00:01:35.012 --> 00:01:38.448
All right, so let's see,
Monday and Wednesday combined.

00:01:38.448 --> 00:01:43.288
So on Monday we had 80 puppies
come there, or 80 dogs.

00:01:43.288 --> 00:01:45.706
And on Wednesday we had 80 dogs.

00:01:45.706 --> 00:01:47.923
And they're saying which day had the same

00:01:47.923 --> 00:01:50.709
as Monday and Wednesday combined?

00:01:50.709 --> 00:01:53.623
So Monday and Wednesday
combined would be 80

00:01:53.623 --> 00:01:56.711
plus 80, which would be 160.

00:01:56.711 --> 00:01:59.544
So on which of these
days did 160 dogs come?

00:01:59.544 --> 00:02:02.086
Well we see it right over here, 160 dogs,

00:02:02.086 --> 00:02:05.731
that was on Tuesday, and only on Tuesday.

00:02:05.731 --> 00:02:09.667
So Tuesday, let's do a few more of these.

00:02:12.728 --> 00:02:17.329
Dessert Zone asked its customers about

00:02:17.329 --> 00:02:19.233
their favorite ice cream flavor,

00:02:19.233 --> 00:02:20.997
and graphed the results.

00:02:20.997 --> 00:02:25.478
So 175 customers said
vanilla, 225 said chocolate,

00:02:27.693 --> 00:02:31.186
75 said strawberry, and
200 said cookie dough.

00:02:31.186 --> 00:02:33.496
All right, how many more customers picked

00:02:33.496 --> 00:02:36.561
the most popular flavor than
the least popular flavor?

00:02:36.561 --> 00:02:39.417
All right, so the most
popular flavor was chocolate,

00:02:39.417 --> 00:02:43.118
that was 225, and the
least popular flavor...

00:02:44.963 --> 00:02:49.099
To the least popular flavor,
it's a tongue twister, was 75.

00:02:49.099 --> 00:02:51.405
So how many more picked the most popular

00:02:51.405 --> 00:02:52.798
than the least popular?

00:02:52.798 --> 00:02:56.295
Well the most popular was
225, the least popular was 75.

00:02:56.295 --> 00:03:00.137
So what's 225 minus 75?

00:03:00.137 --> 00:03:03.539
Let's see, 225 minus 25 would be 200,

00:03:03.539 --> 00:03:05.884
minus 50 would be 175.

00:03:05.884 --> 00:03:08.635
Minus 75 would be 150.

00:03:08.635 --> 00:03:11.978
So we get 150 customers.

00:03:11.978 --> 00:03:13.522
And once again, we're saying that

00:03:13.522 --> 00:03:16.355
150 more customers picked chocolate,

00:03:16.355 --> 00:03:19.559
the most popular flavor,
than the least popular.

00:03:19.559 --> 00:03:21.080
Another way you could do it is you could

00:03:21.080 --> 00:03:22.659
look at the least popular
and the most popular

00:03:22.659 --> 00:03:23.878
and say well how many
more do I have to add

00:03:23.878 --> 00:03:26.397
to the least popular to
get to the most popular?

00:03:26.397 --> 00:03:30.959
And you see 25, 50, 75,

00:03:30.959 --> 00:03:34.886
100, 125, 150.

00:03:34.886 --> 00:03:38.067
Each of these lines is 25 more.

00:03:38.067 --> 00:03:41.085
So there you have it, 150 more customers

00:03:41.085 --> 00:03:43.988
liked the most popular flavor, chocolate,

00:03:43.988 --> 00:03:46.041
than the least popular flavor.


Telling time problems with number line

WEBVTT
Kind: captions
Language: en

00:00:01.081 --> 00:00:03.066
- Andrey, Andrey?

00:00:03.066 --> 00:00:06.049
Andrey starts working
on his science project

00:00:06.049 --> 00:00:11.049
at 4 o'clock pm, and he
finishes 50 minutes later.

00:00:11.599 --> 00:00:15.283
Which number line below
has a red dot marking

00:00:15.283 --> 00:00:19.087
when Andrey finishes working
on his science project?

00:00:19.087 --> 00:00:21.142
So they tell us that he
starts his science project

00:00:21.142 --> 00:00:23.208
at 4 o'clock pm.

00:00:23.208 --> 00:00:27.834
This first choice over here,
puts the dot at 4 o'clock,

00:00:27.834 --> 00:00:29.356
but they didn't say when
did he start working

00:00:29.356 --> 00:00:30.597
on his science project,

00:00:30.597 --> 00:00:32.036
they say put a red dot marking

00:00:32.036 --> 00:00:35.473
when Andrey finishes working
on his science project.

00:00:35.473 --> 00:00:37.378
So he started at 4:00, and it says

00:00:37.378 --> 00:00:40.812
he finishes 50 minutes later.

00:00:40.812 --> 00:00:43.970
So if you start at four, if
you add 50 minutes to four,

00:00:43.970 --> 00:00:46.489
that's gonna put us at 4:50.

00:00:46.489 --> 00:00:48.567
So where is 4:50 on this number line?

00:00:48.567 --> 00:00:51.887
So, let's see, or on this time
line, I guess I could say.

00:00:51.887 --> 00:00:54.233
So, let's see, this is 4:15,

00:00:54.233 --> 00:00:56.532
so each of these marks
must be five minutes.

00:00:56.532 --> 00:01:01.164
This is 4:05, 4:10, 4:15, 4:20,

00:01:01.164 --> 00:01:05.567
4:25, 4:30, 4:35, 4:40,

00:01:05.567 --> 00:01:09.464
4:45, and then 4:50
would be right over here.

00:01:09.464 --> 00:01:12.371
So which of these choices
has a dot at 4:50?

00:01:12.371 --> 00:01:16.027
This last choice has a dot,
has the red dot, at 4:50.

00:01:16.027 --> 00:01:20.778
Notice this is 50 minutes
after he started at 4 o'clock.

00:01:21.973 --> 00:01:23.959
Let's do a few more of these.

00:01:23.959 --> 00:01:26.734
Amira starts raking leaves at 2:30 pm,

00:01:26.734 --> 00:01:29.415
and she finishes 25 minutes later.

00:01:29.415 --> 00:01:32.778
Which number line below has a red dot

00:01:32.778 --> 00:01:35.645
marking when Amira
finishes raking the leaves?

00:01:35.645 --> 00:01:39.871
So she starts at 2:30, and
she finishes 25 minutes later.

00:01:39.871 --> 00:01:41.253
So it looks like on this one,

00:01:41.253 --> 00:01:44.793
each of these spaces is five minutes.

00:01:44.793 --> 00:01:49.528
So this is 2:30, so this five, 10,

00:01:49.528 --> 00:01:53.648
15, 20, 25 minutes later.

00:01:53.648 --> 00:01:56.647
And this space right over her is 2:55.

00:01:56.647 --> 00:01:58.692
It looks like this first choice

00:01:58.692 --> 00:02:00.594
is actually the choice we're looking for.

00:02:00.594 --> 00:02:03.694
They put the red dot
25 minutes after 2:30.

00:02:03.694 --> 00:02:06.306
Notice this is 2:30,
five minutes after 2:30,

00:02:06.306 --> 00:02:10.335
10 minutes after 2:30,
15 minutes after 2:30,

00:02:10.335 --> 00:02:15.335
20 minutes after 2:30,
25 minutes after 2:30.

00:02:15.594 --> 00:02:18.345
Let's keep going, this
is actually a lot of fun.

00:02:20.623 --> 00:02:22.341
The number line shows when Scarlet

00:02:22.341 --> 00:02:24.966
starts and finishes art club.

00:02:24.966 --> 00:02:26.371
That's when she starts.

00:02:26.371 --> 00:02:28.136
That's when she finishes.

00:02:28.136 --> 00:02:31.212
What time did Scarlet start art club?

00:02:31.212 --> 00:02:33.267
Well, let's see, this is half way

00:02:33.267 --> 00:02:35.066
between 3 o'clock and 3:30,

00:02:35.066 --> 00:02:36.913
so that's going to be 3:15.

00:02:36.913 --> 00:02:40.013
Each of these marks go up by 15 minutes.

00:02:40.013 --> 00:02:42.927
So this is at 3:15.

00:02:42.927 --> 00:02:45.527
What time did Scarlet finish art club?

00:02:45.527 --> 00:02:48.975
So this is right in
between 4:30 and 5 o'clock,

00:02:48.975 --> 00:02:52.272
or you could say it's 15
minutes more than 4:30,

00:02:52.272 --> 00:02:57.272
so that's going to be 4:45, 4:45.

00:02:57.614 --> 00:03:00.365
How long was Scarlet in art club?

00:03:00.365 --> 00:03:01.735
So let's think about it.

00:03:01.735 --> 00:03:02.850
There's a couple of ways you could do it.

00:03:02.850 --> 00:03:04.208
You could look at the line.

00:03:04.208 --> 00:03:06.170
Let's see, to go from
this point to this point,

00:03:06.170 --> 00:03:11.170
that's 15 minutes, then
30, then 45, then one hour,

00:03:11.601 --> 00:03:14.579
one hour 15 minutes, one hour 30 minutes.

00:03:14.579 --> 00:03:17.272
So you could say one hour 30 minutes,

00:03:17.272 --> 00:03:19.199
or actually they want it all in minutes.

00:03:19.199 --> 00:03:23.401
One hour is 60 minutes plus
30 minutes is 90 minutes.

00:03:23.401 --> 00:03:25.562
So actually let me just do
it all in minutes again.

00:03:25.562 --> 00:03:28.684
So this is, as I move my mouse,

00:03:28.684 --> 00:03:30.763
I'm gonna talk about how
many minutes I'm adding,

00:03:30.763 --> 00:03:32.875
relative to this, or from the start.

00:03:32.875 --> 00:03:37.875
So 15 minutes gets us to
3:30, 30 minutes, 45 minutes,

00:03:38.900 --> 00:03:43.900
60 minutes, 75 minutes, 90 minutes.

00:03:44.474 --> 00:03:46.482
So that's 90 minutes right over there.

00:03:46.482 --> 00:03:48.290
Another way to think about it is

00:03:48.290 --> 00:03:52.438
it would take 45 minutes to
go from 3:15 to 4 o'clock,

00:03:52.438 --> 00:03:55.618
45 minutes to go from 3:15 to 4 o'clock,

00:03:55.618 --> 00:03:57.778
that makes sense, then another 45 minutes

00:03:57.778 --> 00:04:00.762
to go from 4 o'clock to 4:45.

00:04:00.762 --> 00:04:05.762
So 45 plus 45 is going to be 90 minutes.

00:04:07.249 --> 00:04:09.965
Let's do a couple of these.

00:04:09.965 --> 00:04:12.706
So the number line shows
when Anna starts and finishes

00:04:12.706 --> 00:04:15.063
reading a chapter in her book.

00:04:15.063 --> 00:04:17.466
What time did Anna start reading?

00:04:17.466 --> 00:04:21.539
It says right over there she
started reading at 8:10 pm.

00:04:21.539 --> 00:04:23.798
8:10 pm.

00:04:23.798 --> 00:04:25.627
What time did Anna finish reading?

00:04:25.627 --> 00:04:27.612
Let's see, let me make
sure I'm reading this,

00:04:27.612 --> 00:04:31.250
so this is 8:20, this is 8:25,

00:04:31.250 --> 00:04:33.560
and they have one, two,
three, four, five marks,

00:04:33.560 --> 00:04:35.593
so each of these go up a minute.

00:04:35.593 --> 00:04:38.077
So, you could say it's
a minute before 8:25,

00:04:38.077 --> 00:04:40.213
or four minutes after 8:24,

00:04:40.213 --> 00:04:44.694
8:21, 8:22, 8:23, 8:24.

00:04:44.694 --> 00:04:46.787
8:24.

00:04:48.135 --> 00:04:49.593
How long did Anna read?

00:04:49.593 --> 00:04:50.800
Well, she starts reading at 8:10

00:04:50.800 --> 00:04:52.171
and finishes reading at 8:24.

00:04:52.171 --> 00:04:56.037
To go from 10 to 24 that
means she read for 14 minutes.

00:04:56.037 --> 00:04:57.593
And you could even count it over here.

00:04:57.593 --> 00:05:02.593
One, two, three, four, five,
six, seven, eight, nine,

00:05:03.024 --> 00:05:07.575
10, 11, 12, 13, 14.

00:05:09.469 --> 00:05:11.119
Let's do one more.

00:05:12.491 --> 00:05:15.138
Mohamed speaks on the phone for 15 minutes

00:05:15.138 --> 00:05:18.597
and finishes his phone call at 9:20 am.

00:05:18.597 --> 00:05:21.151
Which number line below
has a green dot marking

00:05:21.151 --> 00:05:24.554
when Mohamed starts his phone call?

00:05:24.554 --> 00:05:27.874
Alright, it finishes at
9:20, so it finishes,

00:05:27.874 --> 00:05:29.917
let's see, where's 9:20
on this number line.

00:05:29.917 --> 00:05:33.307
So it looks like each of these
marks go up by five minutes.

00:05:33.307 --> 00:05:35.629
So this is 9:15, and I was
able to figure that out

00:05:35.629 --> 00:05:38.334
because we have three
marks that go to 9:15,

00:05:38.334 --> 00:05:42.572
from 9:00 to 9:15, so
this is 9:05, 9:10, 9:15.

00:05:42.572 --> 00:05:44.650
So this would be 9:20.

00:05:44.650 --> 00:05:46.867
So this is when he finishes, 9:20,

00:05:46.867 --> 00:05:50.625
and he was on the phone for 15 minutes.

00:05:50.625 --> 00:05:52.173
Remember, we don't want
to mark when he finished,

00:05:52.173 --> 00:05:53.369
they tell us that it's 9:20.

00:05:53.369 --> 00:05:55.389
We want to mark when he started.

00:05:55.389 --> 00:05:57.258
So if he's on the phone
call for 15 minutes,

00:05:57.258 --> 00:06:00.279
and he finishes at 9:20,
he's gonna finish 15 minutes,

00:06:00.279 --> 00:06:03.018
or sorry, if he's on the
phone for 15 minutes,

00:06:03.018 --> 00:06:06.602
and he finishes at 9:20,
he's going to start

00:06:06.602 --> 00:06:08.974
15 minutes before 9:20.

00:06:08.974 --> 00:06:11.191
So five, 10, 15.

00:06:11.191 --> 00:06:13.478
He's gonna start at 9:05.

00:06:13.478 --> 00:06:15.720
So that's this choice right over here.

00:06:15.720 --> 00:06:17.171
Another way you could think about it is

00:06:17.171 --> 00:06:22.171
if I'm at 9:20, and I go
15 minutes before 9:20,

00:06:22.420 --> 00:06:24.126
20 minus 15 is five,

00:06:24.126 --> 00:06:27.446
so that's gonna get me to 9:05.

00:06:27.446 --> 00:06:29.246
And we can just make sure
we feel good about it.

00:06:29.246 --> 00:06:32.786
If he starts his phone call at 9:05

00:06:32.786 --> 00:06:34.598
and he speaks for 15 minutes,

00:06:34.598 --> 00:06:38.580
five, 10, 15, he's gonna
finish his phone call

00:06:38.580 --> 00:06:40.298
right over here at 9:20,

00:06:40.298 --> 00:06:42.944
which is exactly what they described.


Comparing fractions of different wholes

WEBVTT
Kind: captions
Language: en

00:00:00.368 --> 00:00:04.230
- Amir ate 2/3 of a piece of red licorice.

00:00:04.230 --> 00:00:07.248
So, let's draw a piece
of red licorice over here

00:00:07.248 --> 00:00:11.567
and let's draw it into thirds,
so, or split it into thirds.

00:00:11.567 --> 00:00:14.144
Three equal sections, as
best as I can draw that,

00:00:14.144 --> 00:00:16.934
and he ate 2/3 of it, so
that's 1/3 right over here

00:00:16.934 --> 00:00:18.875
and then, this is a second third,

00:00:18.875 --> 00:00:20.629
So, that's 2/3, what I shaded in.

00:00:20.629 --> 00:00:23.542
This is how much of that red
licorice he would have eaten.

00:00:23.542 --> 00:00:26.944
Then, they tell us Nikko
ate 2/3 of a longer,

00:00:26.944 --> 00:00:30.727
but equally thick, piece of red licorice.

00:00:30.727 --> 00:00:33.459
So, it's gonna be equally
thick, but it's longer.

00:00:33.459 --> 00:00:35.507
So, I'm just gonna draw
something that is longer.

00:00:35.507 --> 00:00:38.912
So, that's longer, but equally
thick and he also ate 2/3

00:00:38.912 --> 00:00:41.867
of this, but this is a longer
piece and it's equally thick,

00:00:41.867 --> 00:00:43.627
so it's actually gonna
be just a larger piece.

00:00:43.627 --> 00:00:45.061
It's gonna have more licorice in it.

00:00:45.061 --> 00:00:48.997
So, 2/3 of that, let me see if
I can split this into thirds

00:00:48.997 --> 00:00:52.664
and this is 1/3, this is a second third.

00:00:52.664 --> 00:00:56.820
Well, 2/3 of a larger piece
is going to be more than 2/3

00:00:56.820 --> 00:00:58.376
of a smaller piece.

00:00:58.376 --> 00:01:00.710
This right over here,
this amount that he ate,

00:01:00.710 --> 00:01:03.136
it has the same width, but it's longer

00:01:03.136 --> 00:01:05.154
than this right over here.

00:01:05.154 --> 00:01:09.148
So, Nikko, because this is a
longer, but equally thick piece

00:01:09.148 --> 00:01:12.607
of red licorice, Nikko
ate more red licorice.

00:01:12.607 --> 00:01:15.307
Nikko for sure.

00:01:15.307 --> 00:01:17.338
Let's do another one.

00:01:17.338 --> 00:01:20.657
My unicorn, that's
interesting to have a unicorn.

00:01:20.657 --> 00:01:25.570
My unicorn, ate 2/6 of a
pizza from Store A, alright.

00:01:26.977 --> 00:01:30.974
I ate 2/6 of a different
pizza from Store B.

00:01:30.974 --> 00:01:32.974
Who ate more pizza?

00:01:32.974 --> 00:01:35.133
Well, it would depends.

00:01:35.133 --> 00:01:37.614
You know Store A's pizza
might look like this.

00:01:37.614 --> 00:01:40.609
Store B's pizza might look like this.

00:01:40.609 --> 00:01:43.152
So, if this was the case,
so if this is Store A

00:01:43.152 --> 00:01:45.864
and this is Store B, you eat
2/6 of this, let me divide

00:01:45.864 --> 00:01:50.864
this into sixths, so that's
halves, and that would be,

00:01:50.996 --> 00:01:53.376
and then sixths.

00:01:53.376 --> 00:01:56.360
Woops, I don't wanna do
eighths, I wanna do sixths.

00:01:56.360 --> 00:02:01.360
So, I wanna do something,
so ah that's close enough.

00:02:01.654 --> 00:02:02.596
You get the idea.

00:02:02.596 --> 00:02:06.520
So 2/6 would be like this,
one sixth, two sixths

00:02:06.520 --> 00:02:10.989
and 2/6 of this would
be, would be like this.

00:02:10.989 --> 00:02:13.926
Let me do my best shot at drawing this.

00:02:13.926 --> 00:02:17.024
I'm trying to do six equal
pieces, it's hard to hand draw,

00:02:17.024 --> 00:02:18.707
but this gets us close.

00:02:18.707 --> 00:02:22.290
2/6 here would be that and that

00:02:22.290 --> 00:02:26.040
and if so, Store B's pizza is
bigger than Store A's pizza,

00:02:26.040 --> 00:02:29.015
then I would have eaten
more pizza than my unicorn.

00:02:29.015 --> 00:02:30.431
But, it might have been
the other way around.

00:02:30.431 --> 00:02:32.700
Maybe Store B's pizza's like this

00:02:32.700 --> 00:02:35.718
and Store A's pizza's like
this and if this was the case,

00:02:35.718 --> 00:02:39.399
my unicorn ate this 2/6
and the unicorn ate more.

00:02:39.399 --> 00:02:41.279
Or, maybe the pizzas were both this size,

00:02:41.279 --> 00:02:43.276
in which case, we would've
eaten the same amount.

00:02:43.276 --> 00:02:45.261
So, just based on what
they told us, we don't know

00:02:45.261 --> 00:02:48.314
how Store B's pizza
compares to Store A's pizza.

00:02:48.314 --> 00:02:53.097
We don't know, We don't know whether I

00:02:53.097 --> 00:02:57.630
or my unicorn got more, got more pizza.

00:02:57.630 --> 00:03:00.319
Let's do one more of these, these are fun.

00:03:00.319 --> 00:03:05.311
It took Hiro 1/3 of an hour to
run from his house to school.

00:03:05.691 --> 00:03:09.803
It took Fred 1/3 of an hour to
run from his house to school.

00:03:09.803 --> 00:03:12.262
Who took more time running to school?

00:03:12.262 --> 00:03:14.192
Now, this is a good
one, this is a good one,

00:03:14.192 --> 00:03:15.748
'cause at first you
might say, OK, ya know,

00:03:15.748 --> 00:03:18.964
Hiro might live here, that's Hiro's house.

00:03:18.964 --> 00:03:20.949
I'll put H for Hiro here.

00:03:20.949 --> 00:03:24.602
Maybe this is the school,
I'll just try to draw larger,

00:03:24.602 --> 00:03:28.824
a larger building right
here, this is the school.

00:03:28.824 --> 00:03:31.252
And, you might say, OK
well maybe Fred's house,

00:03:31.252 --> 00:03:32.563
who knows where Fred's house is.

00:03:32.563 --> 00:03:34.362
Fred's house could be here.

00:03:34.362 --> 00:03:38.792
It could be there, it could
be over here some place.

00:03:38.792 --> 00:03:41.067
It could be over here some place.

00:03:41.067 --> 00:03:43.633
We don't know where Fred's
house is, we don't know

00:03:43.633 --> 00:03:46.496
if it's closer or further
away than Hiro's house.

00:03:46.496 --> 00:03:49.004
So, you might be saying oh, we don't know.

00:03:49.004 --> 00:03:51.917
Well, remember, they're not
saying who's house is closer

00:03:51.917 --> 00:03:55.238
or further away, or even who ran faster.

00:03:55.238 --> 00:03:58.813
They're telling us who took
more time running to school

00:03:58.813 --> 00:04:01.901
and they directly tell us
the amount of time they took.

00:04:01.901 --> 00:04:06.739
Hiro took 1/3 of an hour to run to school,

00:04:06.739 --> 00:04:08.074
from his house to school

00:04:08.074 --> 00:04:11.115
and Fred took exactly 1/3 of an hour.

00:04:11.115 --> 00:04:12.799
I don't know who ran faster or slower,

00:04:12.799 --> 00:04:15.922
or who went further distance
or shorter distance,

00:04:15.922 --> 00:04:18.894
but I know that they both
took the same amount of time.

00:04:18.894 --> 00:04:23.235
They both took 1/3 of an
hour, so this is the same.

00:04:23.235 --> 00:04:26.997
They both took the same, same time.

00:04:26.997 --> 00:04:29.945
This questions a little bit
like the famous brain teaser

00:04:29.945 --> 00:04:32.144
that some people might ask you,

00:04:32.144 --> 00:04:35.239
what weighs more, a pound of gold or a

00:04:35.239 --> 00:04:37.538
or, what would you rather
have, or actually no.

00:04:37.538 --> 00:04:39.546
What would, I know which
one you'd rather have.

00:04:39.546 --> 00:04:44.201
Which one weighs more, a pound
of gold or a pound of cotton?

00:04:44.201 --> 00:04:46.153
And people are like oh,
gold is heavier than cotton,

00:04:46.153 --> 00:04:49.334
maybe gold would make, but
we're saying a pound of gold

00:04:49.334 --> 00:04:51.144
versus a pound of cotton.

00:04:51.144 --> 00:04:53.128
Well they're both a pound,
they would weigh the same.

00:04:53.128 --> 00:04:54.647
That's kind of what we're
doing in this question

00:04:54.647 --> 00:04:56.781
right over here.


Clarification: Comparing fractions of different wholes

WEBVTT
Kind: captions
Language: en

00:00:00.650 --> 00:00:02.180
I want to make a
quick clarification

00:00:02.180 --> 00:00:03.180
based on the last video.

00:00:03.180 --> 00:00:05.340
In the last video, we
compared fractions.

00:00:05.340 --> 00:00:09.090
For example, we
compared 4/7 to 3/7.

00:00:09.090 --> 00:00:12.190
And we saw, clearly,
4/7 is a larger

00:00:12.190 --> 00:00:15.700
fraction of the
whole than 3/7 was.

00:00:15.700 --> 00:00:18.550
But you might say, hey, but
what if my whole was bigger?

00:00:18.550 --> 00:00:20.860
What if I took 3/7 of
this big thing here?

00:00:20.860 --> 00:00:23.230
Then 3/7 would look like this.

00:00:23.230 --> 00:00:30.420
So it would be 1, 2, 3/7.

00:00:30.420 --> 00:00:32.770
And so this 3/7--
this looks like I

00:00:32.770 --> 00:00:38.580
have filled in more than I would
have over here for the 4/7.

00:00:38.580 --> 00:00:42.460
So doesn't it matter which whole
you're taking the fraction of?

00:00:42.460 --> 00:00:44.110
And the answer is yes.

00:00:44.110 --> 00:00:45.200
It does matter.

00:00:45.200 --> 00:00:47.390
And when you compare
fractions, you

00:00:47.390 --> 00:00:50.880
assume that you're taking
fractions of the same whole.

00:00:50.880 --> 00:00:53.720
So you can only make this
comparison right over here.

00:00:53.720 --> 00:00:57.100
So it has to be-- let
me make this very clear.

00:00:57.100 --> 00:00:59.190
It has to be the same.

00:00:59.190 --> 00:01:04.150
It has to be the same whole that
you're making the comparison.

00:01:04.150 --> 00:01:08.760
You can't compare 4/7 of a
mouse to 3/7 of an elephant.

00:01:08.760 --> 00:01:10.470
Those are two different things.

00:01:10.470 --> 00:01:12.290
You cannot make that comparison.

00:01:12.290 --> 00:01:16.860
You could compare 4/7 of a
mouse to 3/7 of that same mouse,

00:01:16.860 --> 00:01:18.560
or a mouse the same size.

00:01:18.560 --> 00:01:20.700
Then you could make
the same comparison.

00:01:20.700 --> 00:01:25.010
When we talk about fractions
as just pure numbers,

00:01:25.010 --> 00:01:27.600
then we automatically
go to the number line.

00:01:27.600 --> 00:01:30.700
The whole that we talk about
when we're on the number line

00:01:30.700 --> 00:01:34.710
is the section of our
number line between 0 and 1.

00:01:37.240 --> 00:01:40.250
So if this is 0 and
then this is 1 here,

00:01:40.250 --> 00:01:42.440
when we talk about fractions
as just pure numbers,

00:01:42.440 --> 00:01:46.090
we're not saying 4/7 of a
mouse or 4/7 of an elephant.

00:01:46.090 --> 00:01:48.730
We're just talking about a
number on the number line.

00:01:48.730 --> 00:01:50.520
And so we would split
this into sevenths.

00:01:50.520 --> 00:01:52.240
Let me see if I could do that.

00:01:52.240 --> 00:02:01.070
Let me draw-- so that's
1/7, 2/7, 3/7, 4, 5, 6,

00:02:01.070 --> 00:02:03.760
and that's 7/7 right
over there, or 1.

00:02:03.760 --> 00:02:07.310
So this is 7/7, or 1.

00:02:07.310 --> 00:02:19.056
And this right over here is 1/7,
2/7, 3/7, 4/7, 5/7, and 6/7.

00:02:19.056 --> 00:02:20.930
And so when you look at
the number line here,

00:02:20.930 --> 00:02:23.940
it's clear that 3/7, which
is three jumps from 0,

00:02:23.940 --> 00:02:27.810
three jumps of a
seventh each-- 1, 2, 3--

00:02:27.810 --> 00:02:31.880
3/7 puts you right there,
while 4/7 is a larger number.

00:02:31.880 --> 00:02:33.190
It's to the right of 3/7.

00:02:33.190 --> 00:02:35.940
You have to make
four jumps-- 1, 2,

00:02:35.940 --> 00:02:39.720
3, 4-- four jumps of a seventh
to get right over there.

00:02:39.720 --> 00:02:41.520
So you can make this
comparison as long

00:02:41.520 --> 00:02:44.280
as you're looking at the
fraction of the same whole.

00:02:44.280 --> 00:02:46.150
Here, the same
whole is the region

00:02:46.150 --> 00:02:48.430
of our number line
between 0 and 1.

00:02:48.430 --> 00:02:51.230
In the previous video, the
same whole was this yellow bar.

00:02:51.230 --> 00:02:53.830
You can't compare 4/7
of this yellow bar

00:02:53.830 --> 00:02:58.650
to 3/7 of this much
larger blue bar.


Equivalent fraction models

WEBVTT
Kind: captions
Language: en

00:00:00.556 --> 00:00:02.331
- So this hexagon right over here,

00:00:02.331 --> 00:00:05.088
the whole thing is filled
in with this pink color.

00:00:05.088 --> 00:00:07.997
So we'll say that this
represents one whole.

00:00:07.997 --> 00:00:10.077
The whole thing is filled in.

00:00:10.077 --> 00:00:12.498
Now, what I want you to think about is,

00:00:12.498 --> 00:00:17.498
which of these other
hexagons have 2/3 filled in?

00:00:17.749 --> 00:00:20.974
So, our goal is to identify the hexagons

00:00:20.974 --> 00:00:24.197
that are 2/3 filled in.

00:00:24.197 --> 00:00:26.865
So, pause the video now.

00:00:26.865 --> 00:00:30.076
So, I assume you have given
a go at it, you have tried

00:00:30.076 --> 00:00:31.847
to determine which of
these are 2/3 filled in.

00:00:31.847 --> 00:00:33.946
Now let's work on this together.

00:00:33.946 --> 00:00:36.332
So, when you're thinking in
terms of thirds, and here we're

00:00:36.332 --> 00:00:40.474
thinking in terms of 2/3,
literally two thirds,

00:00:40.474 --> 00:00:41.831
what we think about is dividing

00:00:41.831 --> 00:00:43.569
things into three equal sections.

00:00:43.569 --> 00:00:47.513
Let me see if I can draw
a hexagon fairly well.

00:00:47.513 --> 00:00:51.197
So, let me draw the hexagon.

00:00:51.197 --> 00:00:52.498
And I'm going to try to split it up

00:00:52.498 --> 00:00:55.635
into three equal sections.

00:00:55.635 --> 00:00:57.714
Whoops, I'm going to try to split it up

00:00:57.714 --> 00:00:59.803
into three equal sections.

00:00:59.803 --> 00:01:02.714
So, this is the center of
the hexagon right over here.

00:01:02.714 --> 00:01:06.907
And so, maybe that's one
of the equal sections.

00:01:06.907 --> 00:01:09.069
And then if I do one
more line, I split it up

00:01:09.069 --> 00:01:12.770
into three equal
sections, one, two, three.

00:01:12.770 --> 00:01:14.436
It's actually kind of
neat the way it's drawn.

00:01:14.436 --> 00:01:15.672
It looks like a three dimensional cube.

00:01:15.672 --> 00:01:17.053
But that was not my intent.

00:01:17.053 --> 00:01:19.537
My intent was to draw a hexagon.

00:01:19.537 --> 00:01:23.568
So each of these is a third,
actually I could write this.

00:01:23.568 --> 00:01:27.719
That's one third, that's one
third, and this is one third.

00:01:27.719 --> 00:01:29.938
But what we care about is two thirds,

00:01:29.938 --> 00:01:31.970
so two of these one thirds.

00:01:31.970 --> 00:01:35.354
And so, let me clean this up a little bit.

00:01:35.354 --> 00:01:40.354
So, I would fill in one of the one thirds

00:01:41.220 --> 00:01:43.926
and then two of the one thirds.

00:01:43.926 --> 00:01:46.236
And this right over here,
this hexagon that I've just

00:01:46.236 --> 00:01:49.543
drawn, now has 2/3 of it filled in.

00:01:49.543 --> 00:01:50.609
Now, I know what you're thinking.

00:01:50.609 --> 00:01:52.543
"All right, Sal, that would
have been pretty straightforward

00:01:52.543 --> 00:01:54.379
"if these were divided into thirds."

00:01:54.379 --> 00:01:55.992
"But these are not divided into thirds.

00:01:55.992 --> 00:01:57.996
"Each of these are divided into one, two

00:01:57.996 --> 00:02:00.375
"three, four, five, six equal pieces.

00:02:00.375 --> 00:02:03.009
"This is divided into sixths.

00:02:03.009 --> 00:02:04.426
"How do we figure out how many of the

00:02:04.426 --> 00:02:06.176
"sixths should be filled in, in order

00:02:06.176 --> 00:02:08.991
"to have the same thing as 2/3?"

00:02:08.991 --> 00:02:12.975
Well, I would tell you,
"You, don't worry too much."

00:02:12.975 --> 00:02:15.724
All we have to do, is we can redraw this

00:02:15.724 --> 00:02:18.860
or we can do a little bit
of work here to split this

00:02:18.860 --> 00:02:20.459
into, instead of three equal sections,

00:02:20.459 --> 00:02:22.625
we can split it into six equal sections.

00:02:22.625 --> 00:02:24.025
Well, how would we do that?

00:02:24.025 --> 00:02:26.259
We take each of those three equal sections

00:02:26.259 --> 00:02:28.642
and then split them
into two equal sections.

00:02:28.642 --> 00:02:30.037
So, this one right over here, I can split

00:02:30.037 --> 00:02:32.074
this into two equal sections.

00:02:32.074 --> 00:02:33.425
This one right over here, I can

00:02:33.425 --> 00:02:35.370
split into two equal sections.

00:02:35.370 --> 00:02:36.474
This one right over here, I can

00:02:36.474 --> 00:02:38.074
split into two equal sections.

00:02:38.074 --> 00:02:39.809
So, I had three equal sections before,

00:02:39.809 --> 00:02:41.710
now each of them have been split into two,

00:02:41.710 --> 00:02:43.809
so now I have six equal sections.

00:02:43.809 --> 00:02:47.309
So now, they way I've drawn
it, I'm dealing with sixths.

00:02:47.309 --> 00:02:49.659
And how many sixths represent the

00:02:49.659 --> 00:02:54.275
same fraction as the 2/3 did?

00:02:54.275 --> 00:02:55.759
I still have my shaded area.

00:02:55.759 --> 00:03:00.759
I have one, two, three, four sixths.

00:03:00.793 --> 00:03:05.404
So, 4/6 is the same thing as 2/3.

00:03:05.404 --> 00:03:07.676
Or, another way to think
about it, any of these

00:03:07.676 --> 00:03:09.891
that have four out of
the six equal sections

00:03:09.891 --> 00:03:12.416
filled in, that means that 2/3

00:03:12.416 --> 00:03:14.242
of the sections are filled in.

00:03:14.242 --> 00:03:19.242
Or I could say 2/3 of
the hexagon is filled in.

00:03:19.837 --> 00:03:21.241
So, let's just look at these.

00:03:21.241 --> 00:03:24.409
This one, we have one, well
let me do it in a color

00:03:24.409 --> 00:03:25.625
that has a little more contrast.

00:03:25.625 --> 00:03:28.759
So we have one, two, three, four

00:03:28.759 --> 00:03:30.510
out of the six is filled in.

00:03:30.510 --> 00:03:33.344
4/6 are filled in, that's
the same thing as 2/3.

00:03:33.344 --> 00:03:36.642
So, this one represents 2/3.

00:03:36.642 --> 00:03:39.209
This one only has two
of the sixths filled in,

00:03:39.209 --> 00:03:44.209
so it's not 4/6, which has
to be 2/3, this is 2/6.

00:03:44.293 --> 00:03:46.126
We want 2/3.

00:03:46.126 --> 00:03:50.376
This one is one, two, three, four.

00:03:50.376 --> 00:03:52.260
Four of the sixths are filled in.

00:03:52.260 --> 00:03:54.176
So this is 2/3.

00:03:54.176 --> 00:03:57.292
So I will put a square around that one.

00:03:57.292 --> 00:04:00.558
And this one has one, two, three, four

00:04:00.558 --> 00:04:03.074
of the sixths filled in, so this is 4/6,

00:04:03.074 --> 00:04:04.876
which we've already figured out

00:04:04.876 --> 00:04:09.542
is the same thing as 2/3.

00:04:09.542 --> 00:04:11.054
And we're done.


Equivalent fractions with visuals

WEBVTT
Kind: captions
Language: en

00:00:00.463 --> 00:00:02.405
- [Voiceover] So if
this bar right over here

00:00:02.405 --> 00:00:04.287
represents one whole,

00:00:04.287 --> 00:00:07.217
so the whole thing is shaded
in with the purple color,

00:00:07.217 --> 00:00:10.541
my question to you is,
which of these other bars,

00:00:10.541 --> 00:00:15.386
and there might be more than
one of them, represent 1/2?

00:00:15.386 --> 00:00:20.386
So our goal, our goal is to see 1/2.

00:00:22.994 --> 00:00:24.417
So once again, like always,

00:00:24.417 --> 00:00:27.252
pause the video and try it on your own.

00:00:27.252 --> 00:00:30.362
Okay, so you've tried it on
your own, let's work through it.

00:00:30.362 --> 00:00:32.569
If we're thinking about halves,

00:00:32.569 --> 00:00:34.971
and we just have one of them,

00:00:34.971 --> 00:00:38.633
let me just try to draw another bar here,

00:00:38.633 --> 00:00:41.687
it would look something like this.

00:00:41.687 --> 00:00:42.875
I'll try to draw it pretty close

00:00:42.875 --> 00:00:45.526
to these other bars here.

00:00:45.526 --> 00:00:50.526
I would divide it into two equal sections,

00:00:50.737 --> 00:00:52.917
and I would only care or I would really

00:00:52.917 --> 00:00:56.105
fill in one of them, that
would be 1/2 of this figure.

00:00:56.105 --> 00:00:58.554
Actually, these sections
don't look quite equal,

00:00:58.554 --> 00:01:01.135
that looks a little bit off...

00:01:01.135 --> 00:01:02.839
It's pretty good, I
think you get the idea,

00:01:02.839 --> 00:01:06.865
that my intent is to
draw these to be equal.

00:01:06.865 --> 00:01:11.865
Then, this right over here would be 1/2.

00:01:12.658 --> 00:01:15.290
Now, none of these are
divided into halves.

00:01:15.290 --> 00:01:19.660
This one over here is
divided into fourths,

00:01:19.660 --> 00:01:20.651
this one over here is divided into

00:01:20.651 --> 00:01:24.934
one, two, three, four, five,
so it's divided into fifths,

00:01:24.934 --> 00:01:25.886
this one over here is divided into

00:01:25.886 --> 00:01:27.832
one, two, three, four, five, six,

00:01:27.832 --> 00:01:32.575
so it's divided into sixths,
this is divided into thirds.

00:01:32.575 --> 00:01:35.806
We're going to have to really relate 1/2

00:01:35.806 --> 00:01:39.894
to other - to breaking up your whole

00:01:39.894 --> 00:01:42.695
into different amounts,
not just breaking it up

00:01:42.695 --> 00:01:44.224
into two equal sections,
breaking it up into

00:01:44.224 --> 00:01:45.928
four equal sections, five equal sections,

00:01:45.928 --> 00:01:47.507
six equal sections, and
three equal sections.

00:01:47.507 --> 00:01:49.041
How do we do that?

00:01:49.041 --> 00:01:50.360
The easiest thing might be to just

00:01:50.360 --> 00:01:53.088
break this one up into
four equal sections.

00:01:53.088 --> 00:01:54.541
You break this up into
four equal sections,

00:01:54.541 --> 00:01:55.878
that's just taking each of these two

00:01:55.878 --> 00:01:58.309
and then breaking those up into two.

00:01:58.309 --> 00:02:01.024
That's one equal section, and another,

00:02:01.024 --> 00:02:05.651
let me use that blue color
actually, 'cause that's my...

00:02:05.651 --> 00:02:07.569
That's an equal section over here,

00:02:07.569 --> 00:02:09.250
and this is an equal section,

00:02:09.250 --> 00:02:12.530
so this is the same thing as 1/2.

00:02:12.530 --> 00:02:14.523
Notice I didn't change
how much I shaded in,

00:02:14.523 --> 00:02:16.531
I just divided it into more sections.

00:02:16.531 --> 00:02:18.701
So we see that 1/2 is the exact

00:02:18.701 --> 00:02:23.467
same thing as two out of four.

00:02:23.467 --> 00:02:25.093
Well, how many do we have right over here?

00:02:25.093 --> 00:02:30.093
We have one, two out of
four, so this is one, two

00:02:30.247 --> 00:02:33.895
out of four, and this
is one, two out of four,

00:02:33.895 --> 00:02:38.362
so 2/4 and 1/2 are the same,
these two are equivalent.

00:02:38.362 --> 00:02:39.854
Now this might not be obvious,

00:02:39.854 --> 00:02:42.138
but if you took this
block right over here,

00:02:42.138 --> 00:02:44.629
and if you were to move this one over,

00:02:44.629 --> 00:02:46.733
and so this one is painted
and this one isn't,

00:02:46.733 --> 00:02:48.734
they would look the same,
so maybe that would help

00:02:48.734 --> 00:02:53.734
to see that this also has
1/2 of the block filled in.

00:02:54.831 --> 00:02:56.964
So this one is definitely 1/2.

00:02:56.964 --> 00:03:01.549
Now let's think about fifths.

00:03:01.549 --> 00:03:05.696
So let me, well there's
two ways I could do it.

00:03:05.696 --> 00:03:10.423
Let me draw fifths, and
this right over here is 3/5,

00:03:10.423 --> 00:03:11.638
so might as well just write it down.

00:03:11.638 --> 00:03:16.638
This is 3/5, this is 3/6, and this is 1/3.

00:03:17.585 --> 00:03:22.585
Let me draw 3/5 right below this.

00:03:23.065 --> 00:03:27.012
Let me draw, I keep wanting
to change the color around,

00:03:27.012 --> 00:03:30.450
I'm using a new art tool
and color changing isn't

00:03:30.450 --> 00:03:32.971
coming as naturally as my old one.

00:03:32.971 --> 00:03:37.462
This right over here, let
me divide it into fifths

00:03:37.462 --> 00:03:41.972
the best I can, so one,
two, three, four, five,

00:03:41.972 --> 00:03:42.932
and we're going to assume that these are

00:03:42.932 --> 00:03:46.697
equal sections, I know
my drawing isn't perfect,

00:03:46.697 --> 00:03:49.300
but if we have 3/5, where
are we going to get to?

00:03:49.300 --> 00:03:53.831
We're going to get to one, two, three.

00:03:53.831 --> 00:03:55.372
One way to think about it,
this, what I just drew,

00:03:55.372 --> 00:03:56.419
is just a rearrangement of this,

00:03:56.419 --> 00:03:57.825
I just took the three filled in sections

00:03:57.825 --> 00:03:59.534
and put them all to the left.

00:03:59.534 --> 00:04:03.211
So I have one, two,
three, and when you look

00:04:03.211 --> 00:04:06.830
at it this way, it's clear
that 3/5 is more than 1/2.

00:04:06.830 --> 00:04:10.400
If we were to try to put the
3/5 onto this one right here,

00:04:10.400 --> 00:04:12.680
it would get us about this far,

00:04:12.680 --> 00:04:14.747
so 3/5 would go all the way over there.

00:04:14.747 --> 00:04:19.747
So 3/5 is definitely not
the same thing as 1/2.

00:04:20.375 --> 00:04:24.264
Now what about 3/6?

00:04:24.264 --> 00:04:25.944
Let's think about that a little bit.

00:04:25.944 --> 00:04:30.944
Can we take - let me draw
another one of these things

00:04:33.520 --> 00:04:36.525
that I have to keep drawing
over and over again.

00:04:36.525 --> 00:04:39.963
We already know that if I split this

00:04:39.963 --> 00:04:44.881
into two equal pieces, I shade
in one of them, that's 1/2.

00:04:44.881 --> 00:04:48.563
This right over here is 1/2.

00:04:48.563 --> 00:04:50.628
Could I turn this into sixths?

00:04:50.628 --> 00:04:52.827
If I take each of these
two and I split them

00:04:52.827 --> 00:04:54.502
into three equal pieces,
then I'm going to have

00:04:54.502 --> 00:04:58.509
two times six pieces, so
I'm going to have sixths.

00:04:58.509 --> 00:05:03.509
Let me do that, so I'm
going to use my blue color,

00:05:04.134 --> 00:05:06.480
there you go, and then there you go,

00:05:06.480 --> 00:05:08.137
I took each of the two and I split them

00:05:08.137 --> 00:05:10.223
into three, and now I have six pieces.

00:05:10.223 --> 00:05:14.428
I haven't changed how much
I shaded in, I have now -

00:05:14.428 --> 00:05:16.105
it was 1/2 of the entire bar, but now,

00:05:16.105 --> 00:05:17.705
when I think in terms of sixths,

00:05:17.705 --> 00:05:22.705
it's one, two, 3/6, 3/6 is
the exact same thing as 1/2.

00:05:23.868 --> 00:05:26.558
We have one, two, 3/6, and once again,

00:05:26.558 --> 00:05:28.735
if you took these two and
shifted them over here,

00:05:28.735 --> 00:05:29.809
you would get something that looks

00:05:29.809 --> 00:05:31.880
very much like that or like this.

00:05:31.880 --> 00:05:36.880
This right over here is
the same thing as 1/2.

00:05:37.089 --> 00:05:40.915
Now what about 1/3?

00:05:40.915 --> 00:05:43.278
All right, I think you
see where this is going.

00:05:43.278 --> 00:05:45.169
And always, you should just feel free

00:05:45.169 --> 00:05:47.188
to pause the video and try
to work it out on your own,

00:05:47.188 --> 00:05:48.849
or frankly, if you get
what's going on in the video,

00:05:48.849 --> 00:05:51.393
you don't have to watch it! (laughs)

00:05:51.393 --> 00:05:56.393
All right, so let's divide it into thirds,

00:05:56.771 --> 00:05:58.764
and we're talking about 1/3.

00:05:58.764 --> 00:06:03.764
We're talking about 1/3 right over here,

00:06:03.920 --> 00:06:08.920
and very clearly you see
that 1/3 is less than 3/6,

00:06:09.667 --> 00:06:11.862
and 3/6 is the same thing as 1/2.

00:06:11.862 --> 00:06:13.978
1/2 would take you about this far,

00:06:13.978 --> 00:06:18.228
would take you that far,
1/3 is less than that.

00:06:18.228 --> 00:06:21.480
So 1/3 is not equal to 1/2.

00:06:21.480 --> 00:06:24.058
Hopefully you found that fun.


Fractions on the number line widget

WEBVTT
Kind: captions
Language: en

00:00:00.190 --> 00:00:01.188
- [Voiceover] We're on the fractions

00:00:01.188 --> 00:00:04.485
on the number line
exercise on Khan Academy,

00:00:04.485 --> 00:00:06.970
and they ask us to move the orange dot

00:00:06.970 --> 00:00:09.965
to three-fourths on the number line.

00:00:09.965 --> 00:00:11.799
Change the number of divisions

00:00:11.799 --> 00:00:14.562
to create tick marks on the number line.

00:00:14.562 --> 00:00:16.002
Let's see what's going on here.

00:00:16.002 --> 00:00:19.020
I have the space from zero
to one on the number line.

00:00:19.020 --> 00:00:20.738
If I want to move it to three-fourths,

00:00:20.738 --> 00:00:22.178
what I would first want to do

00:00:22.178 --> 00:00:25.127
is divide the space between
zero and one into fourths,

00:00:25.127 --> 00:00:27.031
into four equal sections.

00:00:27.031 --> 00:00:29.492
I would want to have four divisions here.

00:00:29.492 --> 00:00:31.767
And there you have it, four divisions.

00:00:31.767 --> 00:00:34.391
I typed in the number four
and have four equal divisions.

00:00:34.391 --> 00:00:36.342
One, two, three, four.

00:00:36.342 --> 00:00:39.639
This is going to be a fourth,
that's another fourth,

00:00:39.639 --> 00:00:41.612
that's another fourth,
and that's another fourth.

00:00:41.612 --> 00:00:44.375
What we care about is three-fourths.

00:00:44.375 --> 00:00:45.861
Once again, that's one-fourth,

00:00:45.861 --> 00:00:47.092
this would be another fourth,

00:00:47.092 --> 00:00:48.753
getting us to two-fourths,

00:00:48.753 --> 00:00:49.971
and then this would be another fourth,

00:00:49.971 --> 00:00:51.573
getting us to three-fourths.

00:00:51.573 --> 00:00:52.920
So, there you have it.

00:00:52.920 --> 00:00:56.862
That is three-fourths on the number line.


Running distance in a week

WEBVTT
Kind: captions
Language: en

00:00:00.750 --> 00:00:04.290
Abe went running 4
days this past week.

00:00:04.290 --> 00:00:07.540
He ran 9 kilometers on each day.

00:00:07.540 --> 00:00:13.184
In that same week, Beth ran
15 fewer kilometers than Abe.

00:00:13.184 --> 00:00:17.520
How many kilometers
did Beth run that week?

00:00:17.520 --> 00:00:19.792
So I encourage you
to pause this video

00:00:19.792 --> 00:00:21.750
and to try this on your
own, try to figure out,

00:00:21.750 --> 00:00:25.960
how many kilometers
did Beth run that week?

00:00:25.960 --> 00:00:27.500
So there's a couple
of ways to think

00:00:27.500 --> 00:00:29.860
about it or a couple of
ways to visualize it.

00:00:29.860 --> 00:00:31.470
The first thing we
might want to do--

00:00:31.470 --> 00:00:33.595
in fact, the first thing
we definitely want to do--

00:00:33.595 --> 00:00:37.600
is to figure out, well, how
far did Abe run in that week?

00:00:37.600 --> 00:00:41.620
Well, he went 4 days, and each
day, he went 9 kilometers.

00:00:41.620 --> 00:00:45.015
So we could say
that he went-- let

00:00:45.015 --> 00:00:50.720
me do that blue color-- 4 days
times 9 kilometers per day.

00:00:50.720 --> 00:00:52.440
And we could visualize that.

00:00:52.440 --> 00:00:54.830
So this is how much
he went in one day.

00:00:54.830 --> 00:00:57.370
This is how much he
went in two days.

00:00:57.370 --> 00:00:59.910
This is how much he'd
go in three days.

00:00:59.910 --> 00:01:03.600
This is how much he
would go in four days.

00:01:03.600 --> 00:01:04.440
So what is this?

00:01:04.440 --> 00:01:10.690
What is 4 times 9 kilometers?

00:01:10.690 --> 00:01:15.030
Well, this is essentially
9 plus 9 plus 9 plus 9.

00:01:15.030 --> 00:01:16.460
So we could just add up the 9's.

00:01:16.460 --> 00:01:22.850
9 plus 9 is 18, plus
9 is 27, plus 9 is 36.

00:01:22.850 --> 00:01:25.986
So he ran a total
of 36 kilometers.

00:01:29.580 --> 00:01:31.450
Now, that's not what
they're asking us for.

00:01:31.450 --> 00:01:33.840
They're asking us for
the number of kilometers

00:01:33.840 --> 00:01:35.060
Beth ran that week.

00:01:35.060 --> 00:01:39.730
And they tell us that she ran
15 fewer kilometers than Abe.

00:01:39.730 --> 00:01:43.130
So this right over here,
Abe's total distance--

00:01:43.130 --> 00:01:44.760
if we start from
here, and we were

00:01:44.760 --> 00:01:50.600
to go all the way over the
week, all the way to here,

00:01:50.600 --> 00:01:53.600
he ran 36 total kilometers.

00:01:53.600 --> 00:01:56.930
Beth ran 15 fewer
kilometers than Abe.

00:01:56.930 --> 00:01:59.345
So let's go back 15 kilometers.

00:02:02.390 --> 00:02:09.139
So Beth ran 15 fewer
kilometers than Abe.

00:02:09.139 --> 00:02:12.960
So that's 15 fewer kilometers.

00:02:12.960 --> 00:02:16.560
And so the number of
kilometers that Beth ran

00:02:16.560 --> 00:02:18.710
would be this distance.

00:02:18.710 --> 00:02:22.830
It would be this
distance right over here.

00:02:22.830 --> 00:02:25.110
So this is kilometers Beth ran.

00:02:28.210 --> 00:02:33.490
Let me write it like this--
Beth's distance in the week.

00:02:33.490 --> 00:02:37.220
Beth's distance would be this
distance right over here.

00:02:37.220 --> 00:02:39.176
So how do we figure that out?

00:02:39.176 --> 00:02:40.800
Well, if we say Beth's
distance-- let's

00:02:40.800 --> 00:02:43.200
just use the letter
B for shorthand.

00:02:43.200 --> 00:02:51.300
So Beth's distance
plus 15 kilometers

00:02:51.300 --> 00:02:53.860
is going to be equal
to Abe's distance, is

00:02:53.860 --> 00:02:57.420
going to be equal
to 36 kilometers.

00:02:57.420 --> 00:03:02.970
Or another way of thinking
about it-- Beth's distance

00:03:02.970 --> 00:03:13.540
is going to be equal to Abe's
distance, so 36 kilometers,

00:03:13.540 --> 00:03:15.550
minus 15.

00:03:15.550 --> 00:03:19.640
So what is Beth's distance
going to be equal to?

00:03:19.640 --> 00:03:23.090
Well, 36 minus 15--
6 minus 5 is 1.

00:03:23.090 --> 00:03:24.590
30 minus 10 is 20.

00:03:24.590 --> 00:03:26.280
So it's going to be 21.

00:03:26.280 --> 00:03:30.732
So Beth's distance
is 21 kilometers.


Marbles for friends

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:04.780
Bill has 198 marbles
in this collection.

00:00:04.780 --> 00:00:07.350
He then buys another 44.

00:00:07.350 --> 00:00:10.410
A year later, he decides he
has had enough of marbles

00:00:10.410 --> 00:00:13.660
and decides to split them
as evenly as possible

00:00:13.660 --> 00:00:17.600
between the other 31
students in his math class.

00:00:17.600 --> 00:00:22.897
Roughly how many marbles will
each of his classmates get?

00:00:22.897 --> 00:00:24.730
And the fact that we
have the word "roughly"

00:00:24.730 --> 00:00:27.260
here means we don't need
to get the exact answer.

00:00:27.260 --> 00:00:29.080
If it said roughly
or estimate how many

00:00:29.080 --> 00:00:31.750
marbles each of his classmates
will get, that says, hey,

00:00:31.750 --> 00:00:34.280
maybe we can round these
numbers a little bit

00:00:34.280 --> 00:00:36.700
to make our calculations
a little bit easier.

00:00:36.700 --> 00:00:38.550
So let's give a go at that.

00:00:38.550 --> 00:00:41.130
So we start with 198 marbles.

00:00:41.130 --> 00:00:43.130
Well, let's round everything
to the nearest ten,

00:00:43.130 --> 00:00:45.250
and maybe that'll
simplify things.

00:00:45.250 --> 00:00:49.570
So 198, if we were to round
it to the nearest ten,

00:00:49.570 --> 00:00:51.780
well, we'd want to
look at the ones place.

00:00:51.780 --> 00:00:53.970
The ones place we have an 8.

00:00:53.970 --> 00:00:57.594
If you have a ones place
that's 5 or greater,

00:00:57.594 --> 00:00:59.260
then you're going to
round up, if you're

00:00:59.260 --> 00:01:01.170
going to round to
the nearest ten.

00:01:01.170 --> 00:01:06.790
So the nearest ten, if you round
up from 198 is actually 200.

00:01:06.790 --> 00:01:08.150
We'll just go up to 200.

00:01:08.150 --> 00:01:10.056
That's also the nearest hundred.

00:01:10.056 --> 00:01:14.710
So this is approximately
equal to 200.

00:01:14.710 --> 00:01:16.740
And this little
squiggly equal sign,

00:01:16.740 --> 00:01:21.100
that means roughly equal to
or approximately equal to.

00:01:21.100 --> 00:01:23.120
And so this is what
he starts off with.

00:01:23.120 --> 00:01:25.370
Then he buys another 44.

00:01:25.370 --> 00:01:30.010
44 is approximately equal to--
if we round to the nearest ten,

00:01:30.010 --> 00:01:31.580
we look at our ones place.

00:01:31.580 --> 00:01:35.960
It's less than 5, so we're going
to round to the ten below 44.

00:01:35.960 --> 00:01:39.880
The ten below 44 is 40.

00:01:39.880 --> 00:01:43.690
If we go to the nearest
ten going down, we get 240.

00:01:43.690 --> 00:01:45.520
So how many total
marbles did he have

00:01:45.520 --> 00:01:46.970
before he distributes them?

00:01:46.970 --> 00:01:51.570
Well, if we take our two rough
estimates and if we add them,

00:01:51.570 --> 00:01:58.080
200 plus 40-- he has roughly
240 marbles before he

00:01:58.080 --> 00:01:59.044
distributes them.

00:01:59.044 --> 00:02:00.460
Now, how many
students is he going

00:02:00.460 --> 00:02:02.070
to distribute them between?

00:02:02.070 --> 00:02:05.010
Well, there's a
total of 31 students.

00:02:05.010 --> 00:02:08.220
There's 31 students, but
once again, let's round this.

00:02:08.220 --> 00:02:10.949
If we round this
to the nearest ten

00:02:10.949 --> 00:02:13.871
we're going to round down,
because our ones place has a 1

00:02:13.871 --> 00:02:14.370
in it.

00:02:14.370 --> 00:02:16.030
It's less than 5.

00:02:16.030 --> 00:02:18.650
So we're going to round
to the ten below 31.

00:02:18.650 --> 00:02:21.530
So that is going to be 30.

00:02:21.530 --> 00:02:24.560
So if you have
roughly 240 marbles

00:02:24.560 --> 00:02:28.380
and you're going to distribute
them amongst roughly 30 folks,

00:02:28.380 --> 00:02:30.550
then how many are each
of them going to get?

00:02:30.550 --> 00:02:36.810
Well, each of them are going
to get 240 divided by 30.

00:02:36.810 --> 00:02:40.470
Once again this is just a rough
estimate-- roughly 240 marbles

00:02:40.470 --> 00:02:42.650
divided by 30 folks.

00:02:42.650 --> 00:02:47.900
Well, what's 240 divided by 30?

00:02:47.900 --> 00:02:53.250
Well, if we say that this
is equal to the marbles

00:02:53.250 --> 00:02:57.690
per student, so let's say
that this is M-- M for marbles

00:02:57.690 --> 00:03:06.470
per student-- this is another
way of saying that M times 30

00:03:06.470 --> 00:03:12.220
is equal to 240, or that
240 is equal to M times 30.

00:03:12.220 --> 00:03:13.550
Let me write it that way.

00:03:13.550 --> 00:03:15.150
So that's the same
thing as saying

00:03:15.150 --> 00:03:19.937
that 240 is equal
to M times 30, where

00:03:19.937 --> 00:03:21.520
M is what we're
trying to figure out--

00:03:21.520 --> 00:03:24.830
the rough number of
marbles per student.

00:03:24.830 --> 00:03:26.150
So let's think about what M is.

00:03:26.150 --> 00:03:28.140
And there's a bunch of
ways we could do it.

00:03:28.140 --> 00:03:34.080
We could just look at our
multiples of 30, so 30, 60, 90.

00:03:34.080 --> 00:03:36.560
Notice, this is very similar
taking to multiples of 3,

00:03:36.560 --> 00:03:37.970
but we just have a 0 now.

00:03:37.970 --> 00:03:42.470
The multiples of 3 are
now in the tens place,

00:03:42.470 --> 00:03:44.460
and now we have a 0
in the ones place.

00:03:44.460 --> 00:03:56.934
90, 120, which is just a 12
with a 0, 150, 180, 210, 240,

00:03:56.934 --> 00:03:57.600
so what is this?

00:03:57.600 --> 00:04:01.807
This is 30 times one, two,
three, four, five, six, seven,

00:04:01.807 --> 00:04:03.130
eight.

00:04:03.130 --> 00:04:07.320
So we know that 240 is
equal to 30 times 8.

00:04:07.320 --> 00:04:12.150
So we could write 240 is
equal to-- and 30 times 8

00:04:12.150 --> 00:04:17.610
is the same thing as 8 times
30, is equal to 8 times 30.

00:04:20.180 --> 00:04:23.010
Or another way we could say
it is the number of marbles

00:04:23.010 --> 00:04:25.780
each of his friends is
going to get is roughly 8.

00:04:25.780 --> 00:04:29.770
So this is going to be 8.

00:04:29.770 --> 00:04:34.750
So each of his classmates is
going to get roughly 8 marbles.

00:04:34.750 --> 00:04:36.260
Once again, this is an estimate.

00:04:36.260 --> 00:04:38.064
It's not an exact answer.

00:04:38.064 --> 00:04:40.730
Now, you might have tried to get
a slightly more precise answer.

00:04:40.730 --> 00:04:44.070
If you didn't want
to round 198 and 44,

00:04:44.070 --> 00:04:45.950
you could have
just added the two.

00:04:45.950 --> 00:04:53.270
8 plus 4 is 12, and then
1 plus 9 plus 4 is 14.

00:04:53.270 --> 00:04:54.910
1 plus 1 is 2.

00:04:54.910 --> 00:04:56.990
So the exact number
of marbles he had

00:04:56.990 --> 00:04:59.640
was 242, which is
pretty close to 240.

00:04:59.640 --> 00:05:02.620
So 240 was a good approximation.

00:05:02.620 --> 00:05:05.020
And then when you divide
that by-- dividing it by 31

00:05:05.020 --> 00:05:07.405
is a bit of a pain, and
luckily we can just estimate.

00:05:07.405 --> 00:05:11.440
So we divided by
30, and we got 8.

00:05:11.440 --> 00:05:15.530
And just as another kind
of aside here, notice,

00:05:15.530 --> 00:05:21.860
24 divided by 3 is equal to 8.

00:05:21.860 --> 00:05:32.230
And if you divide 240 divided
by 30, this is also equal to 8.

00:05:32.230 --> 00:05:34.440
So if you divide something
10 times as large

00:05:34.440 --> 00:05:36.334
by something 10 times
as large, you're

00:05:36.334 --> 00:05:37.750
still going to get
the same value.

00:05:37.750 --> 00:05:40.110
But either way, each
of his classmates

00:05:40.110 --> 00:05:42.630
are going to get
roughly 8 marbles.


Total seats in a theater

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:04.520
A theater has a total of 63
seats in a rectangular grid.

00:00:04.520 --> 00:00:06.370
Here they are, right over here.

00:00:06.370 --> 00:00:10.210
It currently has 9 rows, each
with an equal number of seats.

00:00:10.210 --> 00:00:15.230
We see that-- 1, 2, 3,
4, 5, 6, 7, 8, 9 rows.

00:00:15.230 --> 00:00:17.950
How many total
seats will it have

00:00:17.950 --> 00:00:20.400
if it adds 2 seats per row?

00:00:26.140 --> 00:00:29.140
So what we want to figure out
is the total number of seats.

00:00:29.140 --> 00:00:33.520
So let's say that
the total is going

00:00:33.520 --> 00:00:35.370
to be equal to the
number of seats

00:00:35.370 --> 00:00:36.780
that the theater already has.

00:00:36.780 --> 00:00:40.760
And they tell us that they have
63 seats in a rectangular grid.

00:00:40.760 --> 00:00:44.450
So it's going to be 63
seats plus the new seats,

00:00:44.450 --> 00:00:46.350
plus however many it adds.

00:00:46.350 --> 00:00:50.490
So plus the new seats.

00:00:50.490 --> 00:00:52.820
Well, what are the
new seats going to be?

00:00:52.820 --> 00:00:56.730
Well, the new seats are
going to be-- I have 9 rows,

00:00:56.730 --> 00:00:59.250
and I'm adding 2 seats per row.

00:00:59.250 --> 00:01:05.470
So the new seats are going to
be 9 rows times 2 seats per row.

00:01:05.470 --> 00:01:09.500
So we could say
that the total is

00:01:09.500 --> 00:01:17.332
going to be equal to
63 plus 9 times 2.

00:01:17.332 --> 00:01:19.290
And we 'll talk more
about order of operations.

00:01:19.290 --> 00:01:21.470
But clearly, in
this situation, we

00:01:21.470 --> 00:01:23.900
want to multiply 9
times 2 to figure out

00:01:23.900 --> 00:01:25.760
the total new number of seats.

00:01:25.760 --> 00:01:28.050
And then we want
to add that to 63.

00:01:28.050 --> 00:01:30.210
And if we just
write it like this,

00:01:30.210 --> 00:01:34.187
multiplication takes-- you
will always do multiplication.

00:01:34.187 --> 00:01:36.020
And when you just see
it in a row like this,

00:01:36.020 --> 00:01:38.580
you'll do the multiplication
before you do the addition.

00:01:38.580 --> 00:01:39.954
So this is literally
saying, hey,

00:01:39.954 --> 00:01:42.040
multiply 9 times
2 first, then add

00:01:42.040 --> 00:01:45.460
to 63, which is exactly
what we care about.

00:01:45.460 --> 00:01:47.300
And what is 9 times 2?

00:01:47.300 --> 00:01:49.410
Well, let's add those
2 seats per row.

00:01:49.410 --> 00:02:10.330
So that's 2, 4, 6, 8,
10, 12, 14, 16, and 18.

00:02:10.330 --> 00:02:11.690
So 2 times 9.

00:02:11.690 --> 00:02:19.120
2, 4, 6, 8, 10, 12,
14, 16, 18 is 18.

00:02:19.120 --> 00:02:21.387
So we're adding 18 new seats.

00:02:21.387 --> 00:02:22.470
So let me write this down.

00:02:22.470 --> 00:02:23.560
I covered up my old total.

00:02:23.560 --> 00:02:30.980
So total is equal to 63 plus 18.

00:02:30.980 --> 00:02:32.510
I had 63 seats.

00:02:32.510 --> 00:02:34.720
I'm now adding 18 seats.

00:02:34.720 --> 00:02:37.240
So total-- my total
number of seats--

00:02:37.240 --> 00:02:41.440
is now going to be 63 plus 18.

00:02:41.440 --> 00:02:44.170
Let's see, 8 plus 3 is 11.

00:02:44.170 --> 00:02:47.020
60 plus 10 is 70.

00:02:47.020 --> 00:02:53.720
70 plus 11 is going to be--
I have 80-- I have 81 seats.

00:02:53.720 --> 00:02:59.871
I now have 9 rows with 9 seats
each, which gets me 81 total.


How many truffle eating guests attended a party

WEBVTT
Kind: captions
Language: en

00:00:00.930 --> 00:00:04.770
Akshay brought four boxes of
chocolate truffles to a party.

00:00:04.770 --> 00:00:08.180
Each box contains 6 truffles.

00:00:08.180 --> 00:00:11.500
Every guest at the party
ate exactly 3 truffles,

00:00:11.500 --> 00:00:13.660
and there were none left over.

00:00:13.660 --> 00:00:15.770
How many guests
must there have been

00:00:15.770 --> 00:00:18.590
at the party, must have
attended the party?

00:00:18.590 --> 00:00:22.250
So we're trying to figure
out how many guests

00:00:22.250 --> 00:00:24.120
must have attended the party.

00:00:24.120 --> 00:00:28.750
So let's actually define a
letter to represent that.

00:00:28.750 --> 00:00:34.780
So let's say that p, or
let's say g, g for guests,

00:00:34.780 --> 00:00:41.590
let's say that g is equal to the
number of guests at the party.

00:00:41.590 --> 00:00:44.050
Then we could actually
set up a relation

00:00:44.050 --> 00:00:46.990
between the number of guests,
the number of truffles

00:00:46.990 --> 00:00:50.130
each guest ate, and then the
total number of chocolates.

00:00:50.130 --> 00:00:52.310
So what was the total
number of chocolates

00:00:52.310 --> 00:00:54.300
that we have at this party?

00:00:54.300 --> 00:00:56.770
Well, he bought 4 boxes.

00:00:56.770 --> 00:00:59.410
And each box
contains 6 truffles.

00:00:59.410 --> 00:01:02.080
So the total number of
chocolates at the party

00:01:02.080 --> 00:01:05.540
must have been 4 times 6.

00:01:05.540 --> 00:01:08.990
4 times 6 truffles
must have been

00:01:08.990 --> 00:01:12.600
the total number of
truffles at the party.

00:01:12.600 --> 00:01:13.730
So let me write this down.

00:01:13.730 --> 00:01:17.835
This is the number
of truffles total.

00:01:21.532 --> 00:01:22.990
Now, what's another
way of thinking

00:01:22.990 --> 00:01:25.970
about the total number
of truffles at the party?

00:01:25.970 --> 00:01:28.430
Well, you have g guests.

00:01:28.430 --> 00:01:30.630
So you have g guests.

00:01:30.630 --> 00:01:32.212
And each guest ate 3 truffles.

00:01:36.060 --> 00:01:40.640
So g times 3 is also going
to be the number of truffles

00:01:40.640 --> 00:01:44.775
at the party-- number
of truffles total.

00:01:47.390 --> 00:01:51.160
So these two things need
to be equal to each other.

00:01:51.160 --> 00:01:53.880
So we could figure
out what 4 times 6 is.

00:01:53.880 --> 00:01:57.510
And then we say, well, 4 times
6 is going to be some number.

00:01:57.510 --> 00:02:00.430
And g times 3 has to
equal that same number.

00:02:00.430 --> 00:02:01.780
What must g be?

00:02:01.780 --> 00:02:04.170
So let's think about
that step by step.

00:02:04.170 --> 00:02:06.770
So let's just
visualize 4 times 6.

00:02:06.770 --> 00:02:09.570
So here is one box of truffles.

00:02:09.570 --> 00:02:10.509
We get 6 truffles.

00:02:10.509 --> 00:02:18.550
So it's 1 times 6, 2 times
6, 3 times 6, and 4 times 6.

00:02:18.550 --> 00:02:21.700
Or another way of
thinking about 4 times 6,

00:02:21.700 --> 00:02:26.670
that's the same thing
as 6 plus 6 plus 6

00:02:26.670 --> 00:02:32.270
plus 6, which is 6, 12, 18, 24.

00:02:32.270 --> 00:02:35.500
So what we have here on
the left hand side is 24.

00:02:35.500 --> 00:02:37.894
So we get 24.

00:02:37.894 --> 00:02:39.310
And now we know
that this is going

00:02:39.310 --> 00:02:42.260
to be equal to the number
of guests at the party.

00:02:42.260 --> 00:02:45.060
This is going to be equal to the
number of guests at the party

00:02:45.060 --> 00:02:48.390
times 3.

00:02:48.390 --> 00:02:51.620
So what times 3 is equal to 24?

00:02:51.620 --> 00:02:59.540
And another way of viewing this
is if g times 3 is equal to 24,

00:02:59.540 --> 00:03:08.800
that means that 24 divided
by 3 must be equal to g.

00:03:12.830 --> 00:03:14.440
So one way of thinking
about it, if I

00:03:14.440 --> 00:03:18.520
were to divide these
truffles, these 24 truffles,

00:03:18.520 --> 00:03:21.197
into groups of 3,
3 for each guest,

00:03:21.197 --> 00:03:23.030
well, the number of
groups I'm going to have

00:03:23.030 --> 00:03:24.750
will tell me the number
of guests I have.

00:03:24.750 --> 00:03:26.130
So let's do that.

00:03:26.130 --> 00:03:29.010
So let's divide it
into groups of 3.

00:03:29.010 --> 00:03:29.730
So let's see.

00:03:29.730 --> 00:03:33.330
Here is one group of
3, right over here.

00:03:33.330 --> 00:03:34.990
One group of 3.

00:03:34.990 --> 00:03:38.680
And now I have another group
of 3, so two groups of 3.

00:03:38.680 --> 00:03:42.045
And now I have
three groups of 3.

00:03:44.730 --> 00:03:47.620
Here's four groups of 3.

00:03:47.620 --> 00:03:55.630
Here is five groups of 3, six
groups of 3, seven groups of 3,

00:03:55.630 --> 00:03:58.060
and eight groups of 3.

00:03:58.060 --> 00:04:01.170
So if I were to take 24 things
and divide it into groups of 3,

00:04:01.170 --> 00:04:02.810
I get 8 groups.

00:04:02.810 --> 00:04:07.790
So we see that g-- let
me get my pen tool.

00:04:07.790 --> 00:04:11.910
We see that g, or I
could say 24 divided by 3

00:04:11.910 --> 00:04:16.782
is 8, which must be equal to the
number of guests at the party.

00:04:16.782 --> 00:04:18.740
The other way of thinking
about it is I'm like,

00:04:18.740 --> 00:04:20.962
hey, some mystery
number here, g,

00:04:20.962 --> 00:04:22.670
that I'm trying to
figure out, the number

00:04:22.670 --> 00:04:25.910
of guests at the party
times 3 is equal to 24.

00:04:25.910 --> 00:04:28.330
So what times 3 is 24?

00:04:28.330 --> 00:04:31.615
Well, you could just think about
all the multiples of three.

00:04:31.615 --> 00:04:33.110
3 times 1 is 3.

00:04:33.110 --> 00:04:34.350
3 times 2 is 6.

00:04:34.350 --> 00:04:41.620
3 times 3 is 9,
12, 15, 18, 21, 24.

00:04:41.620 --> 00:04:45.916
That's three times 1,
2, 3, 4, 5, 6, 7, 8.

00:04:45.916 --> 00:04:52.080
3 times 8 is 24, so
g must be equal to 8,

00:04:52.080 --> 00:04:54.750
or 8 must be equal to g.

00:04:54.750 --> 00:04:59.390
Or we had exactly 8
guests at our party.


Examples relating multiplication to division

WEBVTT
Kind: captions
Language: en

00:00:00.658 --> 00:00:02.508
- [Voiceover] Let's say
someone walks up to you

00:00:02.508 --> 00:00:05.067
on the street and says to you,

00:00:05.067 --> 00:00:09.798
50 divided by five,

00:00:10.720 --> 00:00:13.840
50 divided by five is equal to blank,

00:00:14.470 --> 00:00:16.407
is equal to blank.

00:00:16.407 --> 00:00:18.035
How can you think about this

00:00:18.035 --> 00:00:20.203
as a multiplication problem?

00:00:21.227 --> 00:00:24.768
Well, whatever blank
is, whatever blank is,

00:00:24.768 --> 00:00:27.403
if you multiply it by five,

00:00:27.403 --> 00:00:30.085
if you multiply by five,

00:00:30.085 --> 00:00:31.641
you should get 50.

00:00:31.641 --> 00:00:35.924
You should get 50. You should get 50.

00:00:35.924 --> 00:00:37.666
So one way of thinking
about it, you could say

00:00:37.666 --> 00:00:40.304
"what times five is 50?"

00:00:41.044 --> 00:00:43.201
Well, 10 times five is 50.

00:00:43.201 --> 00:00:47.401
10 times five is 50, so 50 divided by five

00:00:47.401 --> 00:00:49.917
is going to be 10.

00:00:49.917 --> 00:00:51.543
Hopefully you see the relationship here.

00:00:51.543 --> 00:00:55.594
If 50 divided by five is 10,
then 10 times five is 50.

00:00:55.594 --> 00:00:59.055
10 times five is 50.

00:00:59.055 --> 00:01:01.510
And you could do it the other way around.

00:01:01.510 --> 00:01:04.795
What is 50 divided by 10 going to be?

00:01:05.594 --> 00:01:09.722
50 divided by 10, well that's
going to be equal to five.

00:01:10.537 --> 00:01:12.931
50 divided by 10 is going
to be equal to five.

00:01:12.931 --> 00:01:14.238
How do I know that?

00:01:14.238 --> 00:01:18.499
Well, five times 10, five times 10,

00:01:18.499 --> 00:01:21.605
five times 10, is equal to 50.

00:01:21.630 --> 00:01:24.487
Is equal to 50.

00:01:24.512 --> 00:01:26.335
So let's keep thinking about this.

00:01:26.335 --> 00:01:28.540
If someone walked up to
you in the street again,

00:01:28.565 --> 00:01:33.354
and said blank, blank, divided by,

00:01:34.537 --> 00:01:36.713
divided by two,

00:01:37.389 --> 00:01:41.531
blank divided by two is equal to,

00:01:41.531 --> 00:01:44.073
is equal to nine.

00:01:44.073 --> 00:01:46.198
How would you figure out what blank is?

00:01:46.198 --> 00:01:48.798
Something divided by two is equal to nine.

00:01:49.659 --> 00:01:51.536
Well, one way to think about
it, and if we just follow here,

00:01:51.536 --> 00:01:52.993
if you said 50 divided by five is 10,

00:01:52.993 --> 00:01:55.205
you could say 10 times five is 50,

00:01:55.205 --> 00:01:56.731
so right over here we could say

00:01:56.731 --> 00:01:59.891
well, nine times two,

00:02:00.493 --> 00:02:02.504
nine times two,

00:02:02.529 --> 00:02:05.227
must be equal to blank.

00:02:05.252 --> 00:02:07.795
Must be equal to our blank.

00:02:07.795 --> 00:02:09.478
Well we know what nine times two is,

00:02:09.478 --> 00:02:12.856
that is 18, so this must be 18.

00:02:12.856 --> 00:02:15.288
18 divided by two is nine.

00:02:15.288 --> 00:02:17.626
And that's really describing how

00:02:17.626 --> 00:02:19.914
18, two, and nine relate to each other.

00:02:19.914 --> 00:02:23.254
Two nines is 18, or nine twos is 18,

00:02:23.962 --> 00:02:26.473
or if I were to divide 18 into two groups,

00:02:26.473 --> 00:02:27.971
each group would have nine.

00:02:27.971 --> 00:02:29.840
Or if I were to divide into groups of two,

00:02:29.840 --> 00:02:31.233
you would have nine groups.

00:02:31.233 --> 00:02:32.417
Any way you look at it,

00:02:32.417 --> 00:02:36.956
18 divided by two is nine,
nine times two is 18.

00:02:36.956 --> 00:02:38.651
Let's do one more of these.

00:02:38.651 --> 00:02:40.474
So, someone walks up to you on the street,

00:02:40.474 --> 00:02:43.214
and tells you, and tells you that

00:02:43.214 --> 00:02:46.112
12 divided by,

00:02:46.679 --> 00:02:48.376
divided by blank,

00:02:49.283 --> 00:02:53.313
12 divided by blank is equal to three.

00:02:53.313 --> 00:02:55.577
Is equal to three.

00:02:55.577 --> 00:02:57.992
What is blank going to be?

00:02:57.992 --> 00:03:00.012
Well one way to think about this

00:03:00.012 --> 00:03:03.529
is three times blank is
going to be equal to 12.

00:03:03.529 --> 00:03:05.962
Three times blank,

00:03:06.530 --> 00:03:09.627
three times this unknown number,

00:03:09.627 --> 00:03:11.337
is going to be equal to 12.

00:03:12.677 --> 00:03:15.163
And three times what is equal to 12?

00:03:15.824 --> 00:03:19.390
Well three times four is equal to 12,

00:03:19.390 --> 00:03:23.783
so 12 divided by four is equal to three.


Patterns in multiplication tables practice

WEBVTT
Kind: captions
Language: en

00:00:00.511 --> 00:00:02.809
- [Voiceover] We are asked,
"What numbers should replace

00:00:02.809 --> 00:00:05.836
"the A and B in the multiplication table?"

00:00:05.836 --> 00:00:06.894
So let's just make sure we can read

00:00:06.894 --> 00:00:08.777
this multiplication table.

00:00:08.777 --> 00:00:11.346
The way you think about it is,
if you wanted to figure out--

00:00:11.348 --> 00:00:12.700
It goes up to six.

00:00:12.700 --> 00:00:14.572
So if you want to figure
out what any number

00:00:14.572 --> 00:00:17.308
up to six times another
number up to six is,

00:00:17.308 --> 00:00:18.943
this table will tell you.

00:00:18.943 --> 00:00:20.241
So for example, if you
wanted to figure out

00:00:20.241 --> 00:00:22.536
what three times two is, you say,

00:00:22.536 --> 00:00:26.040
"Ok, three. Let me take the
row that has this three in it.

00:00:26.040 --> 00:00:28.846
"And then the column for the two.

00:00:28.846 --> 00:00:31.747
"So three times two."

00:00:31.747 --> 00:00:34.604
So if you're in this row, the three row,

00:00:34.604 --> 00:00:36.603
and you're in the two column,

00:00:36.603 --> 00:00:39.501
three times two is going to be six here.

00:00:39.501 --> 00:00:41.043
Or you could go the other way around.

00:00:41.043 --> 00:00:42.775
This 12, this means

00:00:42.775 --> 00:00:47.377
that 3 times 4 is 12.

00:00:47.377 --> 00:00:50.001
Or right over here, this 25.

00:00:50.001 --> 00:00:52.308
Notice, this is the same row as this five

00:00:52.308 --> 00:00:54.646
and the same column as that 5.

00:00:54.646 --> 00:00:59.403
So it's saying that five times five is 25.

00:00:59.403 --> 00:01:01.909
And so you notice that
if you go in any row,

00:01:01.909 --> 00:01:05.946
you're counting by that number
and if you go in column,

00:01:05.946 --> 00:01:07.738
you're also counting by that number.

00:01:07.738 --> 00:01:10.339
So for example, in this
two's column right over here

00:01:10.339 --> 00:01:11.606
you're counting by twos.

00:01:11.606 --> 00:01:13.814
Two, four, six, eight.

00:01:13.814 --> 00:01:16.110
In this five column,
you're counting by fives.

00:01:16.110 --> 00:01:18.311
Five, 10, 15, 20.

00:01:18.311 --> 00:01:21.007
And that makes sense because
five times one is five.

00:01:21.007 --> 00:01:25.000
Five times two is 10.
Five times three is 15.

00:01:25.000 --> 00:01:27.043
Five times four is 20.

00:01:27.043 --> 00:01:29.208
And the same thing is
happening as you go up a row.

00:01:29.208 --> 00:01:31.509
Two, four, six, eight.

00:01:31.509 --> 00:01:35.276
Because two times one is
two. Two times four is four.

00:01:35.276 --> 00:01:37.009
On and on and on, you're counting by twos.

00:01:37.009 --> 00:01:38.641
Here you're counting by sixes.

00:01:38.641 --> 00:01:40.668
Six times one is six. Six times two is 12.

00:01:40.668 --> 00:01:44.568
Six times three is 18.
Six times four is 24.

00:01:44.568 --> 00:01:46.743
So hopefully now we understand
the multiplication table.

00:01:46.743 --> 00:01:49.576
And it is actually pretty cool
to just keep looking at it

00:01:49.576 --> 00:01:51.074
and thinking about how it works.

00:01:51.074 --> 00:01:53.339
But let's answer their
question, what would A and B be?

00:01:53.978 --> 00:01:56.202
Well we have this A right over here.

00:01:56.202 --> 00:01:57.233
So one way to think about it,

00:01:57.233 --> 00:02:01.339
it needs to be whatever
four times four is.

00:02:01.339 --> 00:02:05.535
And you might know that
four times four is 16.

00:02:05.535 --> 00:02:06.735
Four times four is 16.

00:02:06.735 --> 00:02:08.041
Or another way is, you could just go down

00:02:08.041 --> 00:02:09.841
this column and count by fours.

00:02:09.841 --> 00:02:13.569
Four, eight, 12 and
then you add four again.

00:02:13.569 --> 00:02:15.272
12 plus four is 16.

00:02:15.840 --> 00:02:16.834
Now let's figure out what B is.

00:02:16.834 --> 00:02:18.670
And actually, let's do it that way.

00:02:18.670 --> 00:02:21.513
B is in this column so
we can count by threes.

00:02:21.513 --> 00:02:25.805
Three, six, nine. Add three
to that and you get to 12.

00:02:25.805 --> 00:02:27.569
So b could be 12.

00:02:27.569 --> 00:02:29.345
Or you could go from the row.

00:02:29.345 --> 00:02:32.735
You could go four, eight, add
four to that and you get 12.

00:02:32.735 --> 00:02:35.437
And that makes sense
because this, where B is,

00:02:35.437 --> 00:02:38.968
that should be whatever
four times three is.

00:02:38.968 --> 00:02:41.109
Cause four times three is 12.

00:02:41.109 --> 00:02:43.965
Then they say, "Complete the inequalities

00:02:43.965 --> 00:02:47.871
"with the greater-than,
less-than or equal symbol."

00:02:48.543 --> 00:02:52.945
So A is greater than B. Greater than.

00:02:52.945 --> 00:02:54.646
And I always remember
the greater than symbol

00:02:54.646 --> 00:02:58.412
because it is opened
to the number on left.

00:02:58.412 --> 00:02:59.778
The number on the left is greater than,

00:02:59.778 --> 00:03:01.744
it's opened to larger number.

00:03:01.744 --> 00:03:04.808
A is greater than B
because four times four

00:03:04.808 --> 00:03:07.639
is going to be greater
than four times three.

00:03:07.639 --> 00:03:10.402
Is greater than four times three.

00:03:10.402 --> 00:03:13.011
All right, four times four is
greater than four times three.

00:03:13.011 --> 00:03:14.209
It makes sense.

00:03:14.209 --> 00:03:17.601
If four times four is four fours

00:03:17.601 --> 00:03:20.067
and if four times three is three fours,

00:03:20.067 --> 00:03:21.977
you have more fours here.

00:03:21.977 --> 00:03:23.375
So hopefully that makes sense.

00:03:23.375 --> 00:03:26.336
Let's do a couple more of these.

00:03:26.336 --> 00:03:27.976
So now what number should replace A and B

00:03:27.976 --> 00:03:29.629
in the multiplication table?

00:03:29.629 --> 00:03:31.079
So same idea.

00:03:31.079 --> 00:03:35.480
So A should be whatever
four times five is.

00:03:35.480 --> 00:03:37.178
So it should be 20.

00:03:37.178 --> 00:03:39.504
Or you could look at whatever
row or column it's in.

00:03:39.504 --> 00:03:43.577
If you look at its
column, five, 10, 15, 20.

00:03:44.343 --> 00:03:45.976
Now let's do the same thing for B.

00:03:45.976 --> 00:03:50.976
B should be whatever five times four is.

00:03:51.112 --> 00:03:52.644
Well that's going to be 20 as well.

00:03:53.601 --> 00:03:54.940
That's going to be 20.

00:03:54.940 --> 00:03:56.413
And you could say, "Well
look, A is gonna be

00:03:56.413 --> 00:03:58.778
"four times five which is 20.

00:03:58.778 --> 00:04:02.803
"And B is gonna be five
times four which is 20."

00:04:02.803 --> 00:04:04.973
So either way you look
at it, they are the same.

00:04:04.973 --> 00:04:06.300
So, complete the inequalities?

00:04:06.300 --> 00:04:09.333
Well, A is equal to B
because four times five

00:04:09.333 --> 00:04:11.143
is the same thing as five times four.

00:04:11.143 --> 00:04:13.409
It doesn't matter what
order you multiply them in.

00:04:14.172 --> 00:04:15.381
Let's do one more of these.

00:04:15.937 --> 00:04:17.104
I think you're getting the sense of it.

00:04:17.104 --> 00:04:18.446
So what is A?

00:04:18.446 --> 00:04:21.837
So we see where it's located,

00:04:21.837 --> 00:04:25.409
it's in this row for this two
and the column for the six.

00:04:25.409 --> 00:04:28.433
So it needs to be
whatever two times six is.

00:04:28.433 --> 00:04:29.670
Which is 12.

00:04:30.543 --> 00:04:33.941
And you could count by sixes. Six, 12.

00:04:33.941 --> 00:04:34.571
Or you could count by twos.

00:04:34.571 --> 00:04:37.934
Two, four, six, eight, 10, 12 to get to A.

00:04:38.473 --> 00:04:42.738
Now B, this is going to be
whatever six times 2 is.

00:04:42.738 --> 00:04:46.171
Well, that's gonna be 12 again.

00:04:46.171 --> 00:04:47.770
And so it's just like the last one we saw.

00:04:47.770 --> 00:04:49.644
A is gonna be equal to B

00:04:49.644 --> 00:04:53.169
because two times six is
equal to six times two.

00:04:53.169 --> 00:04:56.011
Let's do one more, this
is actually a lot of fun.

00:04:56.911 --> 00:05:01.433
All right, so A is
whatever four times one is

00:05:01.433 --> 00:05:03.504
which we know is gonna be four.

00:05:03.504 --> 00:05:05.770
B is gonna be whatever one times four is

00:05:05.770 --> 00:05:07.434
which is also gonna be four.

00:05:07.434 --> 00:05:09.010
And I think you see a pattern here.

00:05:09.010 --> 00:05:10.945
A equals B because four times one

00:05:10.945 --> 00:05:13.741
is the same thing as one times four.


Missing number for addition and subtraction within 1000

WEBVTT
Kind: captions
Language: en

00:00:00.480 --> 00:00:03.905
- [Voiceover] So we have blank plus 261 is equal to 630.

00:00:03.905 --> 00:00:05.141
And I encourage you to pause the video and see

00:00:05.141 --> 00:00:07.293
if you can figure out what blank is.

00:00:07.293 --> 00:00:09.788
So there's a couple of ways to tackle this.

00:00:09.788 --> 00:00:12.234
Let's visualize it on a number line.

00:00:12.234 --> 00:00:15.213
So that's my number line right over there.

00:00:15.213 --> 00:00:17.778
And we could start at blank,

00:00:17.778 --> 00:00:19.547
or I'll call that question mark.

00:00:19.547 --> 00:00:24.512
So we could start at question mark and if we add 261 to it,

00:00:24.512 --> 00:00:29.138
so if we add 261, plus 261,

00:00:29.138 --> 00:00:31.496
we can get to 630.

00:00:31.496 --> 00:00:35.195
We can get to 630.

00:00:35.195 --> 00:00:37.235
That's the 630 right over there.

00:00:37.235 --> 00:00:40.025
Which means if we started at 630,

00:00:40.025 --> 00:00:44.770
if we start at 630, and we were to subtract 261,

00:00:44.770 --> 00:00:46.369
if we were to go the other way.

00:00:46.369 --> 00:00:50.843
If we were to subtract 261, so let's do that.

00:00:50.843 --> 00:00:53.624
So minus 261.

00:00:53.624 --> 00:00:57.761
Minus 261, we're gonna get back to blank.

00:00:57.761 --> 00:01:01.483
We're gonna get back to our question mark.

00:01:01.483 --> 00:01:04.318
Now there's a bunch of ways that you could compute this.

00:01:04.318 --> 00:01:05.989
But I'm gonna try to tackle it in a way

00:01:05.989 --> 00:01:08.196
that I would actually try to do it in my head,

00:01:08.196 --> 00:01:09.694
or it'll simplify my computation,

00:01:09.694 --> 00:01:12.626
it's just one of many ways to figure this out.

00:01:12.626 --> 00:01:16.702
So the way I would do it is I would first subtract 200.

00:01:16.702 --> 00:01:20.168
So I'd first subtract 200, so that's about,

00:01:21.221 --> 00:01:23.370
I'm not drawing it perfectly to scale.

00:01:23.370 --> 00:01:25.161
So I would subtract 200,

00:01:25.161 --> 00:01:27.700
so that's minus 200 right over there.

00:01:27.700 --> 00:01:30.939
Which would get me to 430, I can do that in my head,

00:01:30.939 --> 00:01:33.743
I just subtracted two hundreds from that.

00:01:33.743 --> 00:01:36.916
And let's see, now I wanna subtract 60.

00:01:36.916 --> 00:01:39.703
So then I would subtract 60.

00:01:40.388 --> 00:01:42.135
So minus 60.

00:01:42.135 --> 00:01:44.748
So let's see 430 minus 60.

00:01:44.748 --> 00:01:48.685
That's 43 tens minus six tens.

00:01:48.685 --> 00:01:52.516
Well that's gonna be 37 tens, or 370.

00:01:52.516 --> 00:01:56.786
This gets us to 370, and then we gotta subtract one more.

00:01:56.786 --> 00:02:01.516
We have to subtract 260 and then we subtract one.

00:02:01.516 --> 00:02:06.716
So 370 minus one is 369.

00:02:06.716 --> 00:02:13.109
So this right over here is 369.

00:02:13.692 --> 00:02:15.275
Now another way we could've done it

00:02:15.275 --> 00:02:16.598
is we could have swapped the order.

00:02:16.598 --> 00:02:19.544
We could have said if blank plus 261 is 630.

00:02:20.216 --> 00:02:22.302
We could have said, we could have said,

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261 plus blank

00:02:27.701 --> 00:02:30.516
is equal to 630.

00:02:31.437 --> 00:02:33.637
All I did is I swapped the order here.

00:02:33.637 --> 00:02:36.005
But we could visualize that as a different,

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as a different thing on the number line.

00:02:38.023 --> 00:02:41.138
So I'm going to, let me draw my number line again.

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So there's my number line.

00:02:46.023 --> 00:02:48.801
And I could start at 261.

00:02:49.673 --> 00:02:53.611
So this time I'm starting at 261, 261.

00:02:53.611 --> 00:02:55.784
And I wanna get to 630.

00:02:55.784 --> 00:02:58.511
And I'm gonna get to 630.

00:02:59.478 --> 00:03:02.541
And the amount that I add is going to be the blank.

00:03:02.541 --> 00:03:05.308
So let's see what I have to add to get to 630.

00:03:05.308 --> 00:03:07.902
And I'm gonna add numbers that are easy for me to compute.

00:03:07.902 --> 00:03:11.206
So I could add nine, I could add nine.

00:03:11.206 --> 00:03:12.775
Now why did I add nine?

00:03:12.775 --> 00:03:16.839
Because that gets me to 270 which is a nice round number.

00:03:16.839 --> 00:03:17.703
And then I could add,

00:03:17.703 --> 00:03:19.552
let's see I could add 30 here to get to 300,

00:03:19.552 --> 00:03:21.062
So let me do that.

00:03:21.062 --> 00:03:23.831
So plus 30, I'm not doing this quite to scale,

00:03:23.831 --> 00:03:26.341
but this is gonna get me to 300.

00:03:26.341 --> 00:03:31.275
And then from 300 to 630 well I could just add 330.

00:03:31.275 --> 00:03:36.523
So I could just add, I could just add 330 there.

00:03:36.523 --> 00:03:38.104
So how much did I add in total?

00:03:38.104 --> 00:03:42.193
This is 39 plus 330, that's 369.

00:03:42.193 --> 00:03:45.218
I added 369.

00:03:45.218 --> 00:03:48.353
So these are all ways of getting to the same value.

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All ways of viewing the same problem.