MTH 20: Division
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So I admitted that most of us pull
our calculators out long before we would ever do a division by hand. And for that reason, you’re not
going to be asked to do a division by hand anywhere except for right
here on this take home thing. An advantage to that is, you can use
your calculator, you can get help on similar problems
until you get this. But it turns out that knowing how to
divide by hand helps you a lot just with your intuition for
factoring and things coming up in 1665. I don’t want to assess you
over it, other than in the take home, though. So first we need to know that the
divisor goes outside of the division symbol. And that’s even separate from the
fact that it has a decimal in it. So in this particular problem,
because the divisor didn’t have a decimal in it, we move the
decimal straight up. After the break, I’ll show you an
example where the divisor has a decimal in it. So what moving the decimal straight
up means is moving it right here. OK, here’s the problem. I could say divide like normal
because that’s what it is. But not everybody learned
how to divide. And it’s not your fault because
there was a whole period of 10 years where they didn’t
teach division. And they stopped doing that, because
it’s not a good idea, because it doesn’t help you later
in your algebra classes. So it’s not like you’re actually
going to divide by hand very often, but the skill set to do it
helps a lot with algebra classes. So that’s where it’s easiest to
teach you one on one, or go to Khan Academy. But I’ll walk you through it. I start by asking if
five goes into one. I move my finger. And here I’ve got to know my
multiplication tables pretty well. But five does go into
19 three times. The other advantages is, it helps
practice the multiplication table. One of the reasons a lot people
don’t know their multiplication tables very well is because they
weren’t taught to divide by hand– not that any of us actually
do divide by hand anymore. So what did we do with
those two numbers? Well, 19 divided by 15 is 4. Do what with the 2? [INAUDIBLE]. [INAUDIBLE]. Put the 8 up there? Hmm? The 8. 8’s next, yeah. What? Just a sec. So good so far. Brought the two down so far. They’re telling me that 8
goes into this how many times 5 goes into 40. That 8 goes above the two because
the 8 is involved with the 2. And 8 times 5 is– 40. Then here’s the other thing not
just divide by normal– add 0’s as necessary. Cancel it out. [INAUDIBLE]. Yeah, Brian? [INAUDIBLE]. Because we’re in the
decimals chapter. [INAUDIBLE]. They’ll give you some
kind of hint, Brian. They’ll say go out to the
hundreds and round. Or in this case, we won’t need
to round if we keep going. We’d rather that the decimals
not have a remainder. So 5 goes into 20– Sweet. By doing that, we did end up
with our remainder problem. So we ended up with 3.84. And what I want you to do on that
take home is, you should get all 10 points on that take home. Because after you’ve done it, and
shown me your work, I want you to pull out your calculator and say,
hey, is 19.2 divided by 5, hey, sweet, it’s 3.84. I got that one. Check. So you should get 100%
on that take home. So I want you to take
19.56 divided by 6. I’ll be able to help you a little
bit on that over the break here after I pass some [INAUDIBLE]. So we’re just going to start it all
again on that one, first of all because I wrote it down wrong. So this is example 5, which
has 9.35 divided by 0.7 round to the 100. And to get you started, it’s
written like this. And it actually, I kind
of changed my mind. I want you to try that so I can walk
around and help little bit. So remember, you’re going to
move the decimal over. So I want everybody to get a start
on that one, at least. Do you just move it for the 1’s? Stop. Over the next two weeks, we will
do 5.3 and 5.4 for sure. And those are about conversion. And I will honestly do them pretty
darn quick next week. Said this week, I would like for you
to look at them quite a bit. And then next week’s going to be the
fastest week because next week we’re going to do 6.1,
6.2, and 6.3. I can’t find the syllabus. And that’s a pretty fast way
to see percent problems. So the more you can do
up front this week. And don’t do anything before,
Wednesday but the more you can do up front this weekend, the better. And then once we do that
during week 9– oh no, that was week 9. During week 10 I’ve got
to give you the graphs chapter, which is 7.1. If I get those done, we
can skip the rest. I’d recommend doing the rest
at home over Spring Break. But you’ll be fine. But we’ve got to hit the Percents
chapter to get you ready for Math 60. And you really should look
at the Graphs chapter, which isn’t as bad. But next week’s going to
seem a bit hectic. And we’re best to get
through it quickly. So any questions on that? What does that [INAUDIBLE]? I would like you to look quite
a bit at them this weekend. So are we doing them, maybe,
next week, then? I’m going to give you the short
and dirty lecture on 5.3 and 5.4 right now. I’ve still got 15 minutes. I’m doing it as a [? PenCast ?] on purpose, so you can
look back at it. To be clear, is this on
Wednesday’s test? No. Not on this Wednesday’s test. So to begin– but all throughout 5.3, they give
these things called unit factors. So on that sheet I just gave you, it
says 12 inches equals 1 foot on the US distance piece. And in 5.1, they say this thing
called a unit fracture. So 12 inches over a foot, they
make it into a fraction. And they make it into an equivalent
fraction of one foot over 12 inches. I’m going to show you
why they do that. It came up in today’s homework that
example that somebody wanted, I don’t know. I don’t remember what it was. But in those problems that I said
hold off on, 88, 93, and 85, on one of the problems was that they
wanted you to think about conversions. So here, I’ll do an example
where I want to convert three feet to inches. And some of you can do these one
step, right in your head, no problem, and say that
that’s 36 inches. I would like you to get
in the habit of using these unit fractions. 12 inches over 1 foot, the unit
factor has a huge advantage. It tells me to three
times 12 is 36. And it tells me that I did 3 times
12 equals 36 correctly because my feet cancel. My sister’s a nurse, and she’ll do
these big long drug translations. The doctor will give a certain
amount, in a certain grams, and she’ll have to translate it over
to a totally different amount. Or she’ll do drops per minute
in an IV, and she’ll have to translate it to CCS per second. And she uses the skill of these unit
fractions and being able to proofread herself that this
is correctly 36 inches. You really, actually, won’t need
this skill in this chapter because they are all one step conversions. For example, it might say convert
40 ounces to pounds. Then it might say, because
I think we’ll need to, round to the hundreds. On your [? table of ?] conversions
here, where am I looking? At 16 ounces is a pound. 16 ounces equals a pound? I picked this particular conversion
sheet because it’s a little bit simpler than
some of them. They just got some of the main
highlighted ones, and not some of the most random ones. On your book, they give you a unit
conversion factor for ounces to pounds, making it look like a
fraction, 16 ounces over 1 pound, or 1 pound over 16 ounces. And the reason is– now remember, my sister
can’t screw these up. She’d kill somebody if she did
because she’s doing drug dosage. So she wants to get every
single one of these 100% right all the time. She knows that she’s either
multiplying or dividing by 16. Because of the canceling, she’s
guaranteed on this one that it’s 40 divided by 16. It’s a division problem. And then, the denominator,
I’m going to type it in like a division. And if you want you could think of
that as a fraction multiplying straight across. I don’t actually think about it– Does it matter? Can I just take 40 and 16 and know
that that’s going to be my addition column and just
leave it at that? Yes. And then this one because it
was in the numerator, was a multiplication problem. So if it ends up in the numerator,
it’s multiplication. If it ends up in the denominator,
it’s division. That’s really all that conversion
is, either dividing or multiplying. Why it’s so hard for people is
because you get mixed up about whether to divide or multiply. So the book and I both recommend
that you write it down and make there be a cancellation so that
you don’t screw the two up. And my sister has to because
she can’t give bad dosages. Yeah, Nina? Just looking at the remainder,
do you put a decimal? Yeah, so on this one, I would, for
a conversion, never really, personally, want a fraction. I would just go with the decimal. So I would take 40 divided by 16. I can see there being reasons to
have fractions occasionally. But 2.5 pounds is way better. So that was the quick fast
English conversions. The quicker and faster metric
conversions, there’s this little cheat sheet down at the bottom. And it goes from largest
to smallest. It does so on purpose. Here’s what is good for you. You don’t need to memorize
any of the stuff on this thing at all, period. You can have the conversion
sheets. So you’ll get this exact version
conversion sheet, and it will have this exact little thing
on the bottom. So you don’t need to memorize. If you’re going into a science
class, you should work on thinking about memorizing a lot
of these soon. But I don’t make you
memorize anything. Does anybody know I say that one? Kilo-meters. Kilometers. Skipping a few, how
about that one? [INAUDIBLE] OK, there’s a few between
they may not know. Hecameter, decameter– yeah. What’s [? ones ?], then decimeter. Decimeter? Yeah. What do you use that for? And you don’t because, typically,
we use the ones that I just had you say that you know. You need them for conversions,
though. Decameter. You do need them for conversions. [INAUDIBLE] 6 kilometers can give them. Yeah, you get in trouble. See up here that 1 kilometer
is 1,000 meters. And you might know that. Everybody agree 1 kilometer
is 1,000 meters? The fast way, and I’ll show you
how this works, is that 1 kilometer is three spaces, 1,000,
three 0’s, three spaces, away. So if I wanted to, and I’ll
do that on here– Can you put it up higher? Yeah. In section 5.4, if I want to convert
5.3 kilometers to meters, one way to convert 5.3 kilometers to
meters is use this 1 kilometer equals 1,000 meters. And the way that would look like,
the way we were just doing it, is multiplying by 1,000– take out my calculator,
multiply it by 1,000. What does multiplying by 1,000
do with the decimal? [INAUDIBLE]. Be careful. It moves the decimal rather
than just adding 0. We’re going to have
to add some 0’s. [INAUDIBLE]. Three places over because
of the three 0’s. So it goes one, two, three
making it 5,300 meters. Does that make sense? Here’s the quick easy way. We had 5.3 kilometers. We wanted to go to meters. And so we move the decimal
place one, two, three, places to the right. It goes from where we are to where
we want with this quick, nice, easy conversion– god, I wish we had the
metric system– example. Right? [INAUDIBLE]. Do you see it, though? We started there? We had three places to go. And so even though we don’t
use the ones I can’t ever remember, hecto– duh, there’s a secret right up
there, deka, and deci, we need them to know how many
places to move. So it’s not that we need
them or their names. We just need their moves. Oh, by the way, meters were
what kind of unit? What do they measure? Length. Yeah, they are a measurement
of length. And in metric, if you want to go
to a measurement of weight, nothing changes at all. What does G stand for? Grams. What do you do when you convert
800 milligrams to grams? And I’m going to put it over
here in the corner. Where is my decimal to begin with? The last 0? Yeah, so you do need
to find your 0. And then I’m trying to go from
milligrams to grams. So I move the decimal one, two,
three places in which direction? To the left. To the left this time. I can see it right there
as I move it. So one, two, three, places
is 0.8 grams. OK, thanks.

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