Unit Conversions With American (Standard) Units – Length, Weight, Capacity
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Welcome to a lesson on unit conversions using American units. The United States customary units system also referred to as a
American units system or Standard units system is
the most commonly used system of measurement in the United States. The United States is the
only industrialized nation that does not mainly use the metric system in its commercial and
standards activities, although the metric system is
universally used in science, and increasingly in medical, government, and other sectors of industry, even within the United States. So here are the conversions
that we’ll be using. We’ll be doing conversions
of length, weight, as well as capacity in this lesson. And there are two main ways of
converting measurement units. Method one is by multiplying and dividing, where we multiply when converting from larger units to smaller units and we divide when converting from smaller units to larger units. We’re not going to be using
this method in this lesson, we’ll be using method two, the method of using unit fractions. So we’re going to
multiply by unit fractions to do our conversions,
where a unit fraction is a fraction equal to one. Each unit fraction will
have different units in the numerator and denominator formed by using a known conversion. So let’s take a look at our first example. Here we have to perform the
following length conversions, we want to convert to 45 inches
into feet for number one. So because we’re using unit fractions, we’ll begin by writing
45 inches as a fraction with a denominator of one and now we’re going to
multiply by a unit fraction, or fraction equal to one to
convert from inches to feet as long as there is a direct
conversion from inches to feet. So looking at our table below, notice how we’re told here that one foot is equal to 12 inches. So using this conversion, we
can form two unit fractions, either one foot over 12 inches,
or 12 inches over one foot. Both of those fractions
would be equal to one. But because we’re trying
to convert inches to feet, we don’t want inches in our answer so we want inches to simplify out and because we have
inches in the numerator we’ll put inches in the denominator and feet in the numerator. And again the conversion is
one foot equals 12 inches. Notice in this form, the
units of inches simplifies out because inches divided by
inches would simplify to one. And now we multiply 45 times one is 45. Of course one times 12 is 12, and now we have our
conversion, this quotient here will give us the number
of feet in 45 inches. So remember fraction bar means division, so using the calculator, 45
divided by 12 is equal to 3.75. So now we know that 45
inches is equal to 3.75 feet. Of course we could also
express it as a fraction going back to the calculator, if we press Math, Enter, Enter, notice how it tells us
that 3.75 is equal to 15/4. So we could also express
this as 15/4 feet, or if we want 15/4 would be
equal to three and 3/4 feet. We’ll go and express it as 3.75 feet. Next we’re asked to
convert six miles to yards. So we begin by writing
six miles as a fraction. So we have six miles over one. And now we’ll look at
our conversions to see if there’s a conversion
from miles to yards. Notice how there’s not a
direct conversion given that goes from miles to yards, notice how we have one
mile equals 5,280 feet, so we can convert miles to
feet using this conversion and then also here we have
one yard equals three feet. So in this case we’ll have to multiply it by two unit fractions to
convert miles to yards from the given information. So we’ll have two unit fractions,
to convert miles to yards. So let’s first convert miles to feet. We don’t want miles in our answer, so we’ll put miles in the denominator and feet in the numerator, and the conversion is 5,280
feet is equal to one mile. Notice how the units of
miles would simplify out, and now we have feet, we want
to convert feet to yards, and again because one
yard equals three feet and we don’t want feet in our answer, we’ll put feet in the denominator and yards in the numerator. And the conversion is one
yard equals three feet. Notice how the units
of feet simplifies out. So now we multiply, we
have six times 5,280 in the numerator, and we have one times one
times three in the denominator, So the denominator is three
and the numerator is 31,680. Now we’ll find this quotient to determine how many yards
there are in six miles. So we have 31,680 divided by three, which gives us 10,560. And again this would be the
number of yards in six miles. Our last conversion of length, we want to convert 9.6 yards to feet. So we’ll write 9.6 yards as a fraction. We want to convert yards to feet. And remember we have one
yard equals three feet, so because we want yards to simplify out, we’ll write yards in the denominator and feet in the numerator, and the conversion is
three feet equals one yard. The units of yards simplifies out. So notice here, our denominator is one, so we just need to find the
product of 9.6 and three. 9.6 times three is equal to 28.8. So 9.6 yard equals 28.8 feet. Now let’s take a look at
some conversions of weight. We have 6.3 tons equals how many pounds. So we write 6.3 tons as a fraction, with a denominator of one, and then we take a look at our conversions to see if there’s a conversion
from tons to pounds. And notice how we have a conversion here, one ton equals 2,000 pounds, because we don’t want tons in our answer, we’ll write tons in the denominator and pounds in the numerator. And the conversion is one
ton equals 2,000 pounds. Notice how the units
of tons simplifies out. So now we multiply, so we
just have 6.3 times 2,000, which is equal to 12,600. So 6.3 tons is equal to 12,600 pounds. Next we’re asked to convert
86 ounces to pounds. So notice how, looking at our conversions, we know that one pound
is equal to 16 ounces, so because we’re converting
ounces to pounds, we don’t want ounces in our answer, so we’ll write ounces in the denominator and pounds in the numerator. And again the conversion is
one pound equals 16 ounces. Notice how ounces divided
by ounces simplifies to one. So multiplying we have
86 divided by 16 pounds, and now we’ll find this quotient, to know how many pounds
there are in 86 ounces. So 86 divided by 16 is equal to 5.375. So 86 ounces is equal to 5.375 pounds. Next we’re asked to convert
6,400 ounces to tons. So we write 6,400 ounces as a fraction, with a denominator of one, looking at our conversions though, there’s not a direct
conversion from ounces to tons, which means we’ll have to
multiply by two unit fractions, one where we convert ounces to pounds and then we’ll convert pounds to tons. So we want our answer to be in tons. Because we don’t want ounces, we’ll put ounces in the denominator here, and we’re converting ounces to pounds, the conversion is one
pound equals 16 ounces. Notice how the units of
ounces would simplify out. Next we know that one ton
is equal to 2,000 pounds. Because we don’t want pounds in our answer we’ll put pounds in the denominator and tons in the numerator, so that the units of
pounds will simplify out. The conversion is 2,000
pounds equals one ton. So now we multiply. The units of pounds simplifies out. Now multiplying, notice how we
have 6,400 in the numerator, our denominator is 16 times
2,000, which should be 32,000. Now we find this quotient to know how many tons there are in 6,400 ounces. So 6,400 divided by 32,000, is equal to .2 or 0.2. And, of course, this is tons. So 6,400 ounces is equal to 0.2 tons. Now let’s take a look at three examples of converting capacity. Here we’re asked to convert
three quarts to cups, so we have three quarts as a fraction with a denominator of one, we’re going to convert to cups, so looking at our conversions, we’re looking for a conversion that involves quarts and cups. And notice how there isn’t one, but we can convert quarts to pints and then pints to cups. Which means that we have to multiply by two unit fractions to
perform this conversion, at least from the given conversions. So we’ll first convert
again, quarts to pints, we don’t want quarts in our answer so we’ll write quarts in the denominator, so we’ll simplify with these
quarts in the numerator, we’ll have pints in the numerator, and the conversion, again, is
one quart equals two pints. Now quarts simplifies out. And we have pints, but now we
need to convert pints to cups. So we’ll have pints in the denominator, cups in the numerator. The conversion is two cups equals one pint and the units of pints simplifies out. So here we have three times two times two, all over one, which would just be 12. Which means three quarts equals 12 cups. Next we’re asked to convert
72 fluid ounces to pints. So 72 fluid ounces over one. We’re converting to pints. And again there’s not
one direct conversion from fluid ounces to pints,
at least from what’s given, we have eight fluid ounces equals one cup and then we have one pint equals two cups. So again we have to multiply
by two unit fractions to perform this conversion. So we’ll first convert
fluid ounces to cups. So fluid ounces to cups. The conversion is eight fluid
ounces is equal to one cup. So now the ounces simplifies out, and we have cups but we want pints. And we know that one pint
is equal to two cups, so we’ll right cups in the denominator, pints in the numerator,
and again the conversion is two cups equals one pint. So multiplying we have 72
over, eight times two is 16. This quotient will tell us how many pints there are in 72 fluid ounces. So we’ll go back to the
calculator, and this gives us 4.5. Which means, 72 fluid ounces
is equal to 4.5 pints. For our last conversion, we
want to convert 3.5 gallons to fluid ounces. Notice how we’ll have to have
several conversions here. We’ll first convert gallons to quarts. So gallons in the denominator,
quarts in the numerator. Four quarts equals one gallon. So now we have converted
gallons to quarts, and now we’ll convert quarts to pints, then pints to cups, and
cups to fluid ounces. Actually, let’s add our
own conversion here. If one quart equals two pints
and one pint equals two cups, maybe we can recognize that one
quart is equal to four cups. So let’s use our own conversion, one quart equals four cups,
to speed up the process. So we’re going to
multiply by unit fraction, where we’ll have quarts
in the denominator, cups in the numerator, and, again, the conversion we recognized is that one quart is equal to four cups. Quarts simplifies out,
leaving us with cups, but again our goal is to have ounces, so we’ll need one more unit fraction, using the conversion, one cup
equals eight fluid ounces. So I’m multiplying by
cups in the denominator, fluid ounces in the numerator, and again, eight fluid
ounces is equal to one cup, so cups simplifies out
and now we can determine how many fluid ounces
there are in 3.5 gallons. Notice how the denominator is one, so we can just multiply the numerators. So we have 3.5 times four
times four times eight, which equals 448. Which means there are 448
fluid ounces in 3.5 gallons. Okay I hope you found this lesson helpful.

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