You may use a calculator throughout this module.
This system used to be called the English system, but now the U.S. has the dubious honor of being associated with the system that uses inches, feet, miles, ounces, pounds, cups, gallons, etc. To convert from one unit to another, we often have to perform messy calculations like dividing by
or multiplying by .
We could solve these unit conversions using proportions, but there is another method than is more versatile, especially when a conversion requires more than one step. This method goes by various names, such as dimensional analysis or the factor label method. The basic idea is to begin with the measurement you know, then multiply it by a conversion ratio that will cancel the units you don’t want and replace it with the units you do want.
It’s okay if you don’t have the conversion ratios memorized; just be sure to have them available. If you discover other conversion ratios that aren’t provided here, go ahead and write them down!
U.S. System: Measurements of Length
foot = inches
yard = feet
mile = feet
1. How many inches are in
2. How many feet make up
yard is equal to how many inches?
mile is equivalent to how many yards?
5. How many feet is
feet is what length in yards?
feet into miles.
8. How many yards are the same as
Notice that Exercises 3 & 4 give us two more conversion ratios that we could add to our list.
U.S. System: Measurements of Weight or Mass
pound = ounces
ton = pounds
9. How many ounces are in
10. How many pounds are equivalent to
ounces to pounds.
ton is equivalent to what number of ounces?
U.S. System: Measurements of Volume or Capacity
cup = fluid ounces
pint = cups
quart = pints
gallon = quarts
There are plenty of other conversions that could be provided, such as the number of fluid ounces in a gallon, but let’s keep the list relatively short.
13. How many fluid ounces are in
14. How many pints are in
gallon is equal to how many pints?
16. How many cups equal
cups into gallons.
18. How many fluid ounces are in one half gallon?
U.S. System: Using Mixed Units of Measurement
Measurements are frequently given with mixed units, such as a person’s height being given as
ft in instead of in, or a newborn baby’s weight being given as lb oz instead of oz. This can sometimes make the calculations more complicated, but if you can convert between improper fractions and mixed numbers, you can handle this.
19. A bag of apples weighs
ounces. What is its weight in pounds and ounces?
20. A carton of orange juice contains
fluid ounces. Determine its volume in cups and fluid ounces.
21. A hallway is
inches long. Give its length in feet and inches.
22. The maximum loaded weight of a Ford F-150 pickup truck is
lb. Convert this weight into tons and pounds.
We’ll finish up this module by adding and subtracting with mixed units. Again, it may help to think of them as mixed numbers, with a whole number part and a fractional part.
lb oz and Fred weighs lb oz.
23. Comet and Fred are being put into a cat carrier together. What is their combined weight?
24. How much heavier is Fred than Comet?
Two tables are
ft in long and ft in long.
25. If the two tables are placed end to end, what is their combined length?
26. What is the difference in length between the two tables?