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- Welcome to the presentation on units.
- Let's get started.
- So if I were to tell you -- let me make sure my pen is set up
- right -- if I were to tell you that someone is, let's say
- they're driving at a speed of -- let's say it's Zack.
- (Wait, where did my pen go? Oh, I was using the wrong tool.)
- So let's say I have Zack.
- And they're driving at a speed of, let me say,
- twenty-eight feet per minute.
- So what I'm going to ask you is if he's going twenty-eight feet in every
- minute, how many inches will Zack travel in one second?
- So how many inches per second is he going to be going?
- Let's try to figure this one out.
- So let's say if I had twenty-eight, and I'll write "ft" short for feet,
- feet per minute, and I'll write "min" short for a minute.
- So twenty-eight feet per minute, let's first figure out how many
- inches per minute that is.
- Well, we know that there are twelve inches per foot, right?
- (And if you didn't know that you do now.)
- So we know that there are twelve inches per foot.
- So if he's going twenty-eight feet per minute, he's going to be going
- twelve times that many inches per minute.
- So, twelve times twenty-eight -- let's see. Let me do the little work down here --
- twenty-eight times twelve is sixteen, fifty-six into two hundred and eighty.
- (I probably shouldn't be doing it this messy.)
- And this kind of stuff it would be OK to use a calculator,
- although it's always good to do the math yourself.
- It's good practice.
- So that's six, five plus eight is thirteen.
- three hundred and thirty-six.
- So that equals three hundred and thirty-six inches per minute.
- And something interesting happened here is that
- you notice that I had a foot in the numerator here, and I had a
- foot in the denominator here.
- So you can actually treat units just the same way
- that you would treat actual numbers or variables.
- You have the same number in the numerator and you have the same
- number in the denominator, and your multiplying not adding,
- you can cancel them out.
- So the feet and the feet canceled out and that's
- why we were left with inches per minute.
- I could have also written this as three hundred and thirty-six foot per minute
- times inches -- that's "inches" -- inches per foot.
- And -- and -- because the foot per minute came from here,
- and the inches per foot came from here.
- Then I'll just cancel this out and now I've got inches per minute.
- So anyway, I don't want to confuse you too much
- with all of that unit cancellation stuff.
- The bottom line is you just remember, well if I'm going twenty-eight
- feet per minute, I'm going to go twelve times that many inches
- per minute, right, because there are twelve inches per foot.
- So I'm going three hundred and thirty-six inches per minute.
- So now I have the question, but we're not done, because the
- question is how many inches am I going to be traveling
- in one second.
- So let me erase some of the stuff here at the bottom.
- (Let me erase this...this is probably just going to confuse everybody.)
- (Actually I'll erase this too.)
- Ok.
- So I'm going to be going...
- So three hundred and thirty-six inches -- let's write it like that -- inches per minute,
- and I want to know how many inches per second.
- Well what do we know?
- We know that one minute -- and notice, I write it in the
- numerator here because I want to cancel it out with
- this minute here.
- one minute is equal to how many seconds?
- It equals sixty seconds. Right?
- And this part can be confusing, but it's always good to just
- take a step back and think about what I'm doing.
- If I'm going to be going three hundred and thirty-six inches per minute, how many
- inches am I going to travel in one second?
- Am I going to travel more than three hundred and thirty-six or am I going
- to travel less than three hundred and thirty-six inches per second.
- Well obviously less, because a second is a much
- shorter period of time.
- So if I'm in a much shorter period of time, I'm going
- to be traveling a much shorter distance,
- if I'm going the same speed.
- So I should be dividing by a number, which makes sense.
- I'm going to be dividing by sixty.
- I know this can be very confusing at the beginning, but
- that's why I always want you to think about should I be getting
- a larger number or should I be getting a smaller number and
- that will always give you a good reality check.
- And if you just want to look at how it turns out in terms of
- units, we know from the problem that we want this minutes to
- cancel out with something and get into seconds.
- So if we have minutes in the denominator in the units here,
- we want the minutes in the numerator here, and the seconds
- in the denominator here.
- And one minute is equal to sixty seconds.
- So here, once again, the minutes and the
- minutes cancel out.
- And we get three hundred and thirty-six over sixty inches per second.
- [coughs] (Excuse me.)
- Now if I were to actually divide this out, we could see --
- actually we could just divide the numerator and the denominator by six.
- six goes into three hundred and thirty-six, what, fifty-six times?
- fifty-six over ten, and then we can divide that again by two.
- So then that gets us twenty-eight over five.
- And twenty-eight over five -- let's see, five goes into twenty-eight five times, twenty-five.
- Three, five point six.
- So this equals 5.6.
- So I think we now just solved the problem.
- If Zack is going twenty-eight feet in every minute, that's his
- speed, he's actually going 5.6 inches per second.
- Hopefully that kind of made sense.
- Let's try to see if we could do another one.
- If I'm going ninety-one feet per second, how many miles
- per hour is that?
- Well, ninety-one feet per second.
- So how many -- If we want to say how many miles that is, should we be
- dividing or should we be multiplying?
- We should be dividing because it's going to be a
- smaller number of miles.
- And we know that one mile is equal to -- and you might want to just
- memorize this -- five thousand, two hundred and eighty feet.
- It's actually a pretty useful number to know.
- And then that will actually cancel out the feet.
- Then we want to go from seconds to hours, right?
- So, if we go from seconds to hours, if I can travel ninety-one feet
- per second, how many will I travel in an hour, I'm going to
- be getting a larger number because an hour's a much larger
- period of time than a second.
- And how many seconds are there in an hour?
- Well, there are three thousand, six hundred seconds in an hour.
- sixty seconds per minute and sixty minutes per hour.
- So three thousand, six hundred over one seconds per hour.
- And these seconds will cancel out.
- Then we're just left with, we just multiply everything out.
- We get in the numerator, ninety-one times thirty-six hundred, right?
- ninety-one times one times thirty-six hundred.
- In the denominator we just have five thousand, two hundred and eighty.
- This time around I'm actually going to use a calculator --
- let me bring up the calculator just to show you that I'm
- using the calculator.
- Let's see, so if I say ninety-one times thirty-six hundred, Woops! I messed up.
- (carefully) Ninety-one times thirty-six hundred. that equals a huge
- number divided by five thousand, two hundred and eighty.
- (Oh, man. I keep messing up.) [More errors.] This calculator -- I think my mouse is messed up. Let me see if I can type it.
- 91 times 3,600 divided by 5,280 -- 62.05!
- So that equals 62.05 miles per hour.