Common Customary Weight Conversions Using Unit Fractions
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In this video we will perform weight conversions using unit fractions. To begin, we want to
convert 25 pounds to ounces. The first thing we need to do is write 25 pounds as a fraction with a denominator of one. And now we will multiply
by a unit fraction to perform the conversion. Looking at the conversions below, notice that one pound
is equal to 16 ounces. We use this conversion to
form the unit fraction. Because we have pounds in the numerator, and we want pounds to simplify out, in the unit fraction pounds
must be in the denominator and ounces in the numerator. And since one pound equals 16 ounces, the unit fraction is 16
ounces over one pound. Because we have pounds divided by pounds, the units of pounds simplify
out, leaving us with ounces. And now we multiply, notice in this case the denominator is just
one, and therefore, the product is 25 times 16, which is 400, and now the units are ounces. So now we know 25 pounds
equals 400 ounces. Next, we want to convert
8,500 pounds to tons. We begin by writing 8,500
pounds as a fraction with a denominator of one. And now we’re going to
multiply it by a unit fraction. We form the unit fraction
using the conversion one ton equals 2,000 pounds. Because we want pounds to simplify out, and right now we now have
pounds in the numerator, for the unit fraction, pounds
must be in the denominator and tons in the numerator. Because the conversion is
one ton equals 2,000 pounds, the unit fraction is one
ton over 2,000 pounds. Because we have pounds divided by pounds, the units of pounds simplify
out, leaving us with tons. Now we multiply. Notice how we have 8,500 divided by 2,000 and the units are now tons. And now we need to find the quotient. 8,500 divided by 2,000 is 4.25, giving us 4.25 tons. 8,500 pounds equals 4.25 tons. Next, we want to convert
1.5 tons to ounces. We first write 1.5 tons as a fraction with a denominator of one. Notice in this case,
there’s no direct conversion from tons to ounces. Since one ton equals 2,000 pounds, we can use this conversion
to convert tons to pounds, and then we can convert
the pounds to ounces using the conversion one
pound equals 16 ounces. Because we have to use two conversions, we need two unit fractions. Let’s first convert tons to pounds. Because we want tons to simplify out and we have tons in the numerator here, we must have tons in the
denominator of the unit fraction and pounds in the numerator. Since one ton equals 2,000 pounds, the first unit fraction is
2,000 pounds over one ton, then the units of tons simplify out. And now we need to
convert pounds to ounces using the conversion one
pound equals 16 ounces. We want pounds to simplify
out, and therefore, pounds must be in the denominator and ounces in the numerator. One pound equals 16 ounces, and therefore, the second unit fraction is
16 ounces over one pound. And again, pounds simplify
out, leaving us with ounces. Now we multiply and the units are ounces. Notice how the denominator
is one, and therefore, the product is just 1.5
times 2,000 times 16, which is 48,000. 1.5 tons is equal to 48,000 ounces. For the last example, we want to convert 96,000 ounces to tons. We first write 96,000 ounces as a fraction with a denominator of one. And there’s no direct
conversion from ounces to tons, so we have to use both
of these conversions, and therefore, we need two unit fractions. Let’s first convert ounces to pounds. Because we want ounces to simplify out, we need to have ounces in the denominator. Because we have ounces
in the numerator here, and we have pounds in the numerator. Because one pound equals 16 ounces, this first fraction is
one pound over 16 ounces. Notice the units have ounces, simplify it out, leaving us with pounds, and now we convert pounds to tons. Because we want pounds to simplify out, we have pounds in the denominator and tons in the numerator. One ton equals 2,000
pounds, and therefore, the unit fraction is one
ton over 2,000 pounds. And the units of pounds simplify
out leaving us with tons. Now we multiply and we
know the units are tons. In the numerator, we
have 96,000 divided by, in the denominator we have 16 times 2,000, which is 32,000. And 96,000 divided by 32,000 is three, giving us three tons. 96,000 ounces equals three tons. I hope you found this helpful.

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