If you are solving problems that include measurements involving more than one type of measurement, you will need to convert from one unit of measure to another. Each of the units can be converted to one of the other units using the table of equivalents, the conversion factors, and/or the factor label method.
Suppose you want to purchase tubing for a project, and you see two signs in a hardware store: [latex]$1.88[/latex] for [latex]2[/latex] feet of tubing and [latex]$5.49[/latex] for [latex]3[/latex] yards of tubing. If both types of tubing will work equally well for your project, which is the better price? In order to compare, you need to convert the measurements into one single, common unit of measurement.
Let’s solve the tubing problem mentioned above. You are walking through a hardware store and notice two sales on tubing:
[latex]3[/latex] yards of Tubing A costs [latex]$5.49[/latex].
Tubing B sells for [latex]$1.88[/latex] for [latex]2[/latex] feet.
Either tubing is acceptable for your project. Which tubing is less expensive?
Find the unit price for each tubing. This will make it easier to compare.
Tubing A: Find the cost per yard of Tubing A by dividing the cost of [latex]3[/latex] yards of the tubing by [latex]3[/latex].
Compare prices for [latex]1[/latex] yard of each tubing.
Tubing A: [latex]$1.83[/latex] per yard
Tubing B: [latex]$2.82[/latex] per yard
Tubing A is less expensive than Tubing B.
There are times when you will need to perform computations on measurements that are given in different units. In order to do so, you must convert the measurements into one single, common unit of measurement before performing your calculations.
An interior decorator needs border trim for a home she is wallpapering. She needs [latex]15[/latex] feet of border trim for the living room, [latex]10[/latex] yards of border trim for the bedroom, and [latex]27[/latex] feet of border trim for the dining room. How many yards of border trim does she need?
You need to find the total length of border trim that is required for all three rooms in the house. Since the measurements are given in different units we must first convert all measurements to the same unit of measurement. The question asks us to calculate the number of yards of border trim needed so it is best if we use yards as our common unit of measurement.First, we must convert the border trim for the living room. To convert [latex]15[/latex] feet to yards we can use the conversion factor [latex]\frac{1\text{ yard}}{3\text{ feet}}[/latex]:
Since the border trim for the bedroom is given in yards, we can leave it as is.
We now must convert the border trim for the dining room. Just like we did with the border trim for the living room, we can use the conversion factor [latex]\frac{1\text{ yard}}{3\text{ feet}}[/latex]:
Now consider if the question had asked for you to give the total calculation in feet. Do you expect that number to be larger or smaller than the total of the border trim in yards?