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Studying for a test? Prepare with these 10 lessons on Ratios, rates, proportions.

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Video transcript

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. So let's say I have Zack. And they're driving at a
speed of, let me say, 28 feet per minute. So what I'm going to ask you is
if he's going 28 feet in every minute, how many inches will
Zack travel in 1 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 28, and
I'll write ft short for feet, feet per minute, and I'll
write min short for a minute. So 28 feet per minute, let's
first figure out how many inches per minute that is. Well, we know that there are
12 inches per foot, right? If you didn't know
that you do now. So we know that there
are 12 inches per foot. So if you're going 28 feet per
minute, he's going to be going 12 times that many
inches per minute. So, 12 times 28 -- let me do
the little work down here -- 28 times 12 is 16, 56 into 280. 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 6, 5 plus 8 is 13. 336. So that equals 336
inches per minute. And something interesting
happened here is that you noticed 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 336 foot per minute times inches per foot. Because the foot per minute
came from here, and the inches per foot came from here. Then I'll just cancel this
out and I would have gotten 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 28 feet per minute, I'm going to
go 12 times that many inches per minute, right, because
there are 12 inches per foot. So I'm going 336
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 1 second. So let me erase some of the
stuff here at the bottom. So 336 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 1 minute -- and
notice, I write it in the numerator here because I want
to cancel it out with this minute here. 1 minute is equal to
how many seconds? It equals 60 seconds. 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 336
inches per minute, how many inches am I going to
travel in 1 second? Am I going to travel more
than 336 or am I going to travel less than
336 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 60. 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 1 minute is equal
to 60 seconds. So here, once again,
the minutes and the minutes cancel out. And we get 336 over 60
inches per second. Now if I were to actually
divide this out, actually we could just divide the numerator
and the denominator by 6. 6 goes into 336,
what, 56 times? 56 over 10, and then we can
divide that again by 2. So then that gets us 28 over 5. And 28 over 5 -- let's see, 5
goes into 28 five times, 25. 3, 5.6. So this equals 5.6. So I think we now just
solved the problem. If Zack is going 28 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 91 feet per
second, how many miles per hour is that? Well, 91 feet per second. 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. We know that 1 mile is equal to
-- and you might want to just memorize this -- 5,280 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 91 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 3,600
seconds in an hour. 60 seconds per minute and
60 minutes per hour. So 3,600 over 1
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,
91 times 3,600, right? 91 times 1 times 3,600. In the denominator
we just have 5,280. 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 91 times
3,600, that equals a huge number divided by 5,280. 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.