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Here, we will go over the customary system of measurements used in the United States. It includes linear measurements for length and distance, weight (or how heavy a given object is), volume (the amount a container can hold), and temperature (how hot or cold something is). Most other countries use the metric system to express the same things in standard terms, and you'll ultimately end up studying both of them. Even though you can convert customary units to metric units and metric units to customary units, this article will only talk about customary units themselves.

There is a different customary unit for each type of measurement. For example, the typical customary units for measuring length are the inch, foot, yard, and mile:

- $12\mathrm{inches}\left(\mathrm{in.}\right)=1\mathrm{foot}\left(\mathrm{ft.}\right)$
- $3\mathrm{feet}\left(\mathrm{ft.}\right)=1\mathrm{yard}\left(\mathrm{yd.}\right)$
- $5280\mathrm{feet}\left(\mathrm{ft.}\right)=1\mathrm{mile}$

You could also say that there are 1760 yards in a mile, but the conversion is generally given in feet instead. Common examples of these measurements include a standard 12-inch ruler, a football field measuring 100 yards, and how many miles you'll have to travel by car to get somewhere.

Similarly, the customary units for measuring weight are ounces, pounds, and tons.

- $16\mathrm{ounces}\left(\mathrm{oz.}\right)=1\mathrm{pound}\left(\mathrm{1b}\right)$
- $2000\mathrm{pounds}\left(\mathrm{lbs}\right)=1\mathrm{ton}\left(T\right)$

Many foodstuffs are sold by weight, in either ounces or pounds, and a person's weight is commonly expressed in pounds. Tons are only used to convey the weight of really heavy things, such as huge trucks and construction equipment.

The customary system has five different units for measuring volume or capacity: fluid ounces, cups, pints, quarts, and gallons:

- $8\mathrm{fluid\; ounces}\left(\mathrm{fl\; oz.}\right)=1\mathrm{cup}\left(c\right)$
- $2\mathrm{cups}\left(c\right)=1\mathrm{pint}\left(\mathrm{pt}\right)$
- $2\mathrm{pints}\left(\mathrm{pt}\right)=1\mathrm{quart}\left(\mathrm{qt}\right)$
- $4\mathrm{quarts}\left(\mathrm{qt}\right)=1\mathrm{gallon}\left(\mathrm{gal}\right)$

Again, you'll find many of these units of measurement at the grocery store, especially if you're buying liquids such as juice or milk. Half-gallons are also a common unit, which is 2 quarts.

There's only one customary unit for measuring temperature in the U. S.: Fahrenheit. It's expressed in degrees, and you'll hear it frequently on weather broadcasts. The point at which water freezes (32 degrees) and the point at which it boils (212 degrees) are two important points of reference. When it was first introduced, the average human body temperature was supposed to be 100 degrees, but due to imprecise measurements and drifting over time, that is now 98.6 degrees.

Each grouping of customary measurements is best seen as its own system. A fluid ounce doesn't have the same weight as an ounce, and there's no way to express gallons in terms of miles or tons because there are too many variables at play. For instance, a gallon of oil isn't the same weight as a gallon of water, even if both fit in the same container. Therefore, it's important to choose the right unit of measurement for whatever you are measuring.

If you want to convert larger units to smaller units, multiply by the appropriate unit ratio. For instance, there are 2 cups in a pint. If you have 3 pints of something and you wanted to know how many cups you had, you would multiply that by two to determine that it's equivalent to 6 cups.

If you want to convert smaller units to larger units, multiply by the reciprocal of the appropriate unit ratio. For example, there are 16 ounces in a pound. If you have something that weighs 48 ounces, you would divide by 16 to determine that it's three pounds.

Remember that multiplying or dividing by a unit ratio is mathematically equivalent to using a proportion to convert between units of measurement.

a. How many cups are in one gallon?

4 cups to a quart, and 4 quarts to a gallon

$4\times 4=16$

$16\mathrm{cups}$

b. If your school has a track measuring 90 feet, how many yards do you need to run to go across it?

$\mathrm{yards}=\frac{\mathrm{feet}}{3}$

$\mathrm{yards}=\frac{90}{3}=30$

$30\mathrm{yards}$

c. If your uncle weighs 150 lbs., how many ounces does he weigh?

at 16 oz to the lbs.

$150\times 16=2400\u2060\mathrm{oz.}$

e. How many quarts are in a half-gallon of milk?

since there are 4 quarts to a gallon, half of that is 2 qt.

f. How many feet are there in three miles?

$5280\u2060\mathrm{ft\; per\; mile}\times 3\u2060\mathrm{miles}=15840\u2060\mathrm{ft.}$

Choosing Appropriate Units of Measure

Common Core: 3rd Grade Math Diagnostic Tests

Americans encounter customary units of measurement every day, and your student needs to understand how they work. Furthermore, measurement provides a practical application of concepts such as proportions and ratios that can help your student realize how much math they'll encounter in daily life. If your student isn't keeping up with their math teacher, a private tutor can help identify what the learning obstacle is and determine how to best address it. Contact the Educational Directors at Varsity Tutors right now to learn more about 1-on-1 tutoring and how it could help the student in your life.

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