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.