Math 20

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Good morning!
Here is today's warm-up problem How many minutes
are in 0.6 hours?
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Lecture Canceling Words
Today we start Chapter Eight, about measurement
units. The key to almost all of this chapter is a
method of doing unit conversions called
"canceling words".
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Lecture Canceling Words
What is "canceling words"? Here is an
example How many inches are in 3.7 feet?


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Lecture Canceling Words
How many inches are in 3.7 feet? Notice that
the words "feet" and "foot" cancel during the
fraction multiplication, just like factors do.


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Lecture Canceling Words
The importance of this process is that it works
even if we need to do more than one
transition. The process keeps track of when to
multiply and when to divide, so we do not have to
keep track in our heads. All we need to do is
look up (or memorize) the unit conversion rates
and line them up.
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Lecture Canceling Words
How many miles per hour is 200 inches per
minute? Notice we want miles on top and hours
on the bottom. So we are changing inches to
miles, and minutes to hours.
?
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Lecture Canceling Words
How many miles per hour is 200 inches per
minute? First we set up the multiplication
of rates.
minutesto hours
inches to miles



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Lecture Canceling Words
Then we do the fraction multiplication. Instead
of simplifying the answer, we'll be lazy and
change it into a decimal.



12,000 63,360


0.2
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Lecture Canceling Words
There is another way to do unit conversion that
uses proportions, if you only need to do one
transition. This lecture does not teach that
method, since it is not always applicable. In
real life (and higher level math classes) the
problems often involve more than one transition.
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Lecture Canceling Words
We will do some more examples, but first we need
to look at the textbook more closely.
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Textbook Use Unit Conversion Tables
Turn to page 466, the beginning of 8.1. Notice
there is a blue box that has all of the section's
conversion rates.
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Textbook Use Unit Conversion Tables
This is the basic "plot"for all of chapter
8. Each chapter has a bluebox of unit
conversionrates Simply look up the rates you
need and then do the "canceling words" process.
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Textbook Use Unit Conversion Tables
This is the basic "plot"for all of chapter
8. Each chapter has a bluebox of unit
conversionrates (except for 8.3with its
table, picturedhere don't worry aboutit
yet). Simply look up the rates you need and then
do the "canceling words" process.
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Textbook Use Unit Conversion Tables
The only different taskis when we finally get
tochanging temperaturesbetween Celsius
andFahrenheit. We will learn a differentprocess
for this task. The "canceling words" method no
longer works, due to an accident of
history. Remember, the rest of chapter 8 is all
similar!
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Lecture Canceling Words
Now for more example problems from the textbook.
These are all easy "one step" problems. 8.1
18 9.6 yards _____________ feet
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Lecture Canceling Words
8.1 7 3 yards _____________ inches
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Lecture Canceling Words
8.1 3 1 inch _____________ feet
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Lecture Canceling Words
8.1 24 6 yard _____________
inches
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Lecture Mass and Volume
So far we have only done measurement conversions
with length and time. The same process of
"canceling words" also works with mass (8.4) and
volume (8.5). Unlike sections 8.1 through 8.3,
these two sections include both the "standard"
and the metric units. Today we'll only discuss
the "standard" units.
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Lecture Mass and Volume
As a cultural tangent, note that the "standard"
lengths are also called "American", "British", or
"Imperial" in different countries.
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Lecture Mass and Volume
For mass 1 pound (lb) 16 ounces (oz) 1
standard ton 2,000 pounds
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Lecture Mass and Volume
As an aside, scientists use the word mass to
denote how much physical stuff an object is made
up of. This is different than weight because it
is independent of an object's location. The
weight of an object changes proportional to the
local gravity. The moon's gravity is one-sixth as
strong as the Earth's gravity. If I weigh 144
pounds on Earth, how much do I weigh on the moon?
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Lecture Mass and Volume
(My mother used to have a t-shirt that said I'm
not overweight,I'm just on the wrong
planet. because she had a thyroid condition that
meant she would always be overweight.)
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Lecture Mass and Volume
For volume 8 ounces 1 cup 2 cups 1
pint 2 pints 1 quart 4 quarts 1 gallon
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Lecture Mass and Volume
Why do people say "Mind your p's and q's"? Pubs
in England used to give credit to regular
customers. People would only get paid once per
month, and in the meanwhile the bartender would
mark p's and q's (for pints and quarts) below
their name on the wall behind the bar. At the
end of the month this record would show what they
owed to bar. So "Mind your p's and q's" meant
"Don't drink too much before payday!"
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Lecture Mass and Volume
As a tangent, be aware that there is a different
unit of volume called a "dry quart" which is not
quite the same amount as the liquid quarts we use
in Math 20. Unless you shop for bushels of grain
the dry quart is not very important. (It is
almost the same amount as a liquid quart, so for
grocery shopping no one notices the difference.)
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Lecture Mass and Volume
Let's do a problem from the book. 8.5 21 11
gallons __________ pints
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