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.