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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.