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Solving word problems involving factors and multiples

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    - [Instructor] We are
    told glue sticks are sold
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    in packs of 6 and packs of 4.
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    Mr. Ramiro wants to buy
    glue sticks for 28 students.
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    It's okay with him to purchase extras.
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    So the first question is,
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    if Mr. Ramiro chooses the
    packs of 6 glue sticks,
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    how many packs should he buy?
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    And the second question,
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    if Mr. Ramiro chooses the
    packs of 4 glue sticks,
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    how many packs should he buy?
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    So pause this video and have a
    go at both of these questions
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    before we do this together.
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    All right, now let's tackle
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    this first question right over here,
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    if we have packs of 6 glue sticks.
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    Well, one way to think about
    it is we could just say,
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    all right, if I have one pack that's 6.
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    If I get another pack, that's another 6.
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    How many do I have right now?
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    Well, that's a total, actually,
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    let me just write it this way.
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    Maybe I'll say packs.
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    We have 1, 2, 3, 4, 5, 6.
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    That should be enough.
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    And then let's say the total sticks,
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    the total number of glue sticks.
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    So if he buys 1 pack,
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    he's going to have 6 glue sticks.
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    That's not enough.
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    So 2 packs, he's gonna add 6 to that.
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    So that's 12 glue sticks.
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    You might recognize that as 2 times 6.
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    That's still not enough.
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    We still don't have 28.
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    So let's add another 6.
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    That's 3 packs, we get to 18.
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    I'm just adding 6 each time.
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    Let's add another 6,
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    because we're still not at 28 yet.
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    We get to 24 and 4 times 6 is 24.
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    We're still not at 28 yet.
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    So now let's add another 6.
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    And we get to 30 because 5 times 6 is 30.
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    So what I've just listed
    over here are multiples of 6.
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    And that makes sense
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    because for every pack
    I have exactly 6 in it.
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    Now we see that 30 is more than
    enough for the 28 students.
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    So 5 packs is how many Mr.
    Romero would have to buy.
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    4 would not be enough.
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    because that only gets us to 24 packs.
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    Now there's something
    interesting about 30.
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    It doesn't get us exactly to 28.
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    So we have a remainder here.
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    We have a remainder.
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    We have 2 extra glue sticks.
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    And that's because 28
    is not a multiple of 6.
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    Or another way to think about it is
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    6 is not a factor of 28.
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    So we're gonna have to overshoot,
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    we're gonna have to
    buy a little bit extra.
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    Now let's think about the
    situation when we have packs of 4.
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    So I'll do the same thing.
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    Packs 1, 2, 3, 4, 5, 6, 7, 8.
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    And now let's see the
    total number of sticks.
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    So 1 pack, we're talking
    about the packs of 4 now,
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    that's gonna be 4.
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    2 packs is 8.
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    I'm just counting up by 4.
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    3 packs is 12.
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    I'm just adding 4 each time.
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    4 packs is 16.
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    You could also think about 4
    packs of 4 is 4 times 4 is 16.
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    If I have 5 packs, I'm
    gonna add 4 to that.
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    So what I'm really doing is
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    listing all the multiples of 4.
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    I'm increasing multiples
    of 4, still not at 28.
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    Well, I'm gonna add 4 more, I get to 24.
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    Still not there.
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    Add 4 more, I get to 28.
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    That is looking good.
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    That is exactly 7 packs.
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    And we know that if we
    think about it this way too,
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    7 times 4 is equal to 28.
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    Another way to think about
    it is because if I take 4
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    and I multiply it times
    a whole number like this,
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    I get a multiple of 4.
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    So 28 is a multiple of 4,
    or 4 is a factor of 28.
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    And then I would buy exactly
    how many I need with no extra.
Title:
Solving word problems involving factors and multiples
Description:

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Video Language:
English
Team:
Khan Academy
Duration:
03:32

English subtitles

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