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5.1c: Convert units - dual unit conversions
Dual unit simply means that there are two units.
Examples of this could be something like miles per hour.
The word per is the fraction bar or, remember, it is divide.
With dual units, we convert one unit at a time.
We will see how this is done with example 1.
In example 1, you can see that we have 35 miles per hour
and we would like to change this to feet per second.
Sometimes it is helpful to immediately change these units into their fractional form,
in which miles per hour would be miles over hours and feet per second
would be feet over seconds.
Next, we need to set up the beginning of our conversion.
We have 35 miles,
remember per is a fraction bar, so over hour.
We now need to multiply to convert these.
We would need to look at a table
and see if there is a conversion to get from miles to feet
and other conversions to get from hours to seconds.
You can find that there are 5,280 feet
equals 1 mile.
Another conversion factor also shows you
that there are 3,600 seconds equals 1 hour.
We will use these conversions to solve this problem.
We start with 35 miles per hour.
We can multiply this only by the first conversion,
which gives us miles and feet.
Once again, we put the miles diagonally
so that they will reduce.
We have 5,280 feet
so that number goes with feet and 1 mile.
We can now reduce the miles.
We are left with feet,
which is what we are looking for.
We now continue by multiplying by the next conversion factor.
We see that there are 3,600 seconds per hour.
You may also use conversion such as there are 60 seconds in a minute
and 60 seconds in an hour.
We will be using this one.
We see that hours was originally in the denominator
so we will need to put it in the opposite
or the numerator for it to be able to be reduced.
We therefore have hours on top and seconds on bottom.
The hours on top is 1 hour per 3,600 seconds.
We can now reduce the hours and we are left with seconds,
which is what we are looking for.
Now that we have found both sets of units,
we can finish solving by multiplying all of the numerators
and all of the denominators.
This will give us 184,800 feet per 3,600 seconds.
We continue to divide in which we get 51.333 repeated
which we will round to the 10's giving us
51.3 feet per second.
You can write it as a slash or over one another
as we did in the example at the top.
Example 2, 45 ounces per minute
and we would like to convert this to pounds per hour.
Once again, it is helpful to sometimes write them vertically
as ounces per minute and pounds per hour.
We can see that we are changing from ounces to pounds
and minutes to hours.
We will start by writing down what we have.
We have 45 ounces per minute.
We also have a reference A table
to come up with some conversions that will be helpful.
We find one value that says that there are 16 ounces
and it equals 1 pound.
We also found another value that says that there are 60 minutes
and that that equals 1 hour.
After we have found these two values,
we can now continue to solve.
We start by multiplying by a first conversion factor
and we can either change the ounces or the minutes but let us start with the ounces.
We know that the ounces need to be diagonal;
therefore, the pounds are on top.
We know that 16 goes with the ounces
and 1 goes with the pound.
We can now reduce the ounces and we have gotten pounds.
We now continue on and we focus on minutes to hours.
We see that we have minutes on the bottom
so we must put them on the top
or in the numerator to reduce them.
We also see that we need to put hours in the denominators.
The numbers that go with them are
60 minutes and 1 hour.
We can now reduce giving us hours,
which is what we are looking for.
We now multiply across all of the numerators giving us 2,700 pounds
and we multiply all the denominators giving us 16 hours.
We now divide the 2 and this will give us 168.75 pounds per hour.
We have now converted ounces per minute to pounds per hour.
Remember when converting dual units that the word per is the fraction bar
and with dual units you can only covert one unit at a time.