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Multiplying 3 digit by 2 digit with area models

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    - What we're gonna do in this video is try
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    to figure out what 259 times 35 is.
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    And there's a lot of
    ways to approach this,
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    but one way to think about it is,
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    imagine we had a rectangle.
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    I'll make it a really wide rectangle.
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    So that's the width of our rectangle,
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    and then that's the
    height of our rectangle.
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    And let me just draw the entire rectangle.
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    And let's imagine that this width
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    of this rectangle over here is 259 units,
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    whatever those units might
    be, that's its width.
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    And then this height
    over here is 35 units.
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    Well then the area of this
    rectangle would be 259 times 35,
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    whatever that product is.
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    Now, why am I even talking
    about this? Why is this useful?
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    Well, we can actually break
    up 259 into 200 plus 50
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    plus nine and think about
    those chunks of the area
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    and do the same thing for 35.
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    What do I mean by that? Well,
    let's first imagine 200.
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    So if this whole thing
    is 259, then maybe 200.
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    And I'm not going to get it exactly right,
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    but maybe 200 is going to be about,
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    about, let's see, am eyeballing it.
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    It's about that much
    of it right over there.
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    And then the 50,
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    50 would be about that much of it.
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    And then the nine, I'll
    do this in a new color,
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    might be that much of it.
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    That much of it.
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    So 259 is the same thing
    as 200 plus 50 plus nine.
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    And I can divide this
    rectangle into these areas.
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    So one way to think about it is
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    that this area over here is
    going to be 200 times 35.
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    This area is gonna be 50 times 35,
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    and this area is nine times 35.
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    Well, as I said, I could
    do the same thing with 35.
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    Let's say that, let's say that this is 30.
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    That is 30 right over there,
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    and then the rest of it is five.
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    So this right over here is five.
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    Well, I can further,
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    I can split up this bigger rectangle
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    into even more rectangles.
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    Now, why is this interesting?
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    Well, this top left area
    is going to be what?
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    It's going to be 30 times 200.
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    And we might be able to
    do that in our heads.
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    If I did three times two
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    it would be six, 30 times two is 60,
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    30 times 20 is 630 times 200 is 6,000.
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    Or some of you might say,
    okay, three times two is six.
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    And then I have these three
    zeros, which is the equivalent
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    to multiplying by ten three times
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    or multiplying by a thousand.
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    So it's 6,000.
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    And now what is the area of
    this section right over here?
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    Well, that's going to be 30 times 50.
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    So 30 times 50 is going to be equal
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    to three times five is 15.
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    And then I have two more
    zeros. So it's 1500.
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    And then this over here is
    going to be 30 times nine,
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    which, three times nine is 27.
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    So 30 times nine is 270.
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    And now if I go down here,
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    this a little area is going to be,
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    I probably should have drawn
    it a little bit bigger,
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    but it's going to be five times
    200, which is equal to 1000.
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    This one over here is
    gonna be five times 50,
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    five times 50, which is equal to 250.
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    And then last but not least
    five times nine is 45.
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    Now why is this interesting?
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    Because each of these
    little smaller areas,
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    if I add them all up,
    I get the bigger area.
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    So the bigger area is going to be 6,000
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    plus 1500
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    plus 270.
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    And one way to think about it is each
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    of these are partial products.
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    They're partial products of
    just 30 times 200 or 30 times 50
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    or 30 times nine.
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    But I'm gonna keep going.
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    And then I have this a thousand here,
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    which was the five times 200.
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    Then I have the 250 here,
    and then I have the 45.
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    If I add up all of these partial products
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    or partial areas, I could say,
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    then I'm gonna get the total product
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    or the total area of this rectangle.
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    So let's see, in the
    one's place, I just end up
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    with a five, in the tens
    place, seven tens plus five,
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    that's 12 plus four is 16 10s.
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    So six tens and a hundred.
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    One plus five is six, plus two is eight,
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    plus two more is 10.
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    So that gets regrouped that one,
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    and we get one plus six is
    seven, plus one is eight,
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    plus one more is nine.
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    So we get to 9,065 in total.
Title:
Multiplying 3 digit by 2 digit with area models
Description:

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Video Language:
English
Team:
Khan Academy
Duration:
04:50

English subtitles

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