# Module 13: The US Measurement System

**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*

*U.S. System: Measurements of Length*

foot = inches

yard = feet

mile = feet

Exercises

**1.** How many inches are in

feet?

**2.** How many feet make up

yards?

**3.**

yard is equal to how many inches?

**4.**

mile is equivalent to how many yards?

**5.** How many feet is

inches?

**6.**

feet is what length in yards?

**7.** Convert

feet into miles.

**8.** How many yards are the same as

inches?

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*

*U.S. System: Measurements of Weight or Mass*

pound = ounces

ton = pounds

Exercises

**9.** How many ounces are in

pounds?

**10.** How many pounds are equivalent to

tons?

**11.** Convert

ounces to pounds.

**12.**

ton is equivalent to what number of ounces?

*U.S. System: Measurements of Volume or Capacity*

*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.

Exercises

**13.** How many fluid ounces are in

cups?

**14.** How many pints are in

quarts?

**15.**

gallon is equal to how many pints?

**16.** How many cups equal

quarts?

**17.** Convert

cups into gallons.

**18.** How many fluid ounces are in one half gallon?

*U.S. System: Using Mixed Units of Measurement*

*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.

Exercises

**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.

Exercises

Comet weighs

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?