The practice quiz for this study guide can be found at:
Math for Praxis II ParaPro Test Prep Practice Problems
This section reviews the basics of measurement systems used in the United States (also called the U.S. customary system) and other countries, methods of performing mathematical operations with units of measurement, and the process of converting different units.
The use of measurement enables a connection to be made between mathematics and the real world. To measure any object, assign a number and a unit of measure. For instance, when a fish is caught, it is often weighed in ounces and its length measured in inches. The following lesson will help you become more familiar with the types, conversions, and units of measurement.
Types of Measurements
Length, volume, and weight (or mass) can be measured in either the U.S. customary system or the metric system. It is important to know the U.S. customary measurements.
U.S. Customary Measurements
12 inches (in) = 1 foot (ft)
3 feet = 36 inches = 1 yard (yd)
5,280 feet = 1,760 yards = 1 mile (mi)
8 ounces* (oz) = 1 cup (c)
2 cups = 16 ounces = 1 pint (pt)
2 pints = 4 cups = 32 ounces = 1 quart (qt)
4 quarts = 8 pints = 16 cups = 128 ounces = 1 gallon (gal)
16 ounces* (oz) = 1 pound (lb)
*Notice that ounces are used to measure the dimensions of both volume and weight.
Converting Units
Metric Measurements
The metric system is an international system of measurement also called the decimal system. The unit of length is a meter. The unit of capacity is a liter. The unit of mass is a gram.
Prefixes are attached to the basic metric units to indicate the amount of each unit. For example, the prefix deci means one-tenth (
); therefore, one decigram is one-tenth of a gram, and one decimeter is one-tenth of a meter. The following six prefixes can be used with every metric unit:
Example
So, for example:
- 1 meter is equivalent to 100 centimeters, or 1,000 millimeters.
- 1 gram is equivalent to 1,000 milligrams, or
kilogram.
- 1 liter is equivalent to 1,000 millititers, or kiloliter.
One way to remember the metric prefixes is to remember the mnemonic: King Henry Died Of Drinking Chocolate Milk. The first letter of each word represents a corresponding metric heading from kilo down to milli: King—Kilo, Henry—Hecto, Died—Deka, Of—Original Unit, Drinking—Deci, Chocolate—Centi, and Milk—Milli.
Time
60 seconds (sec) = 1 minute (min)
Converting Units of Measurement
When performing mathematical operations, it may be necessary to convert units to simplify a problem. Units of measure are converted by using either multiplication or division. Note that the ParaPro Assessment may ask you to convert metric units to other metric units or U.S. customary units to other U.S. customary units. It will not likely ask you to convert between systems, such as converting a number of inches to centimeters.
Converting Units in the U.S. Customary System
To convert from a larger unit into a smaller unit, multiply the given number of larger units by the number of smaller units in only one of the larger units.
For example, to find the number of inches in five feet, multiply 5, the number of larger units, by 12, the number of inches in one foot:
5 feet = ? inches
5 feet × 12 (the number of inches in a single foot) = 60 inches:
5 ft = 60 in.
Therefore, there are 60 inches in five feet.
Example
Change 3.5 pounds to ounces.
3.5 pounds = ? ounces
3.5 pounds × 16 ounces per pound = 56 ounces
Therefore, there are 56 ounces in 3.5 pounds.
To change a smaller unit to a larger unit, divide the given number of smaller units by the number of smaller units in only one of the larger units.
Example
Find the number of pints in 64 ounces.
64 ounces = ? pints
64 ounces ÷ 16 ounces per pint = 4 pints
Therefore, 64 ounces equals 4 pints.
Converting Units in the Metric System
An easy way to convert within the metric system is to move the decimal point either to the right or to the left, because the conversion factor is always ten or a power of ten. Remember to multiply when changing from a larger unit to a smaller unit. Divide when changing from a smaller unit to a larger unit.
When multiplying by a power of ten, move the decimal point to the right, because the number becomes larger. When dividing by a power of ten, move the decimal point to the left, because the number becomes smaller. Use the table on page 139 to see how many places to move to the left or right.
Example
Change 2 kilometers to meters.
You are changing a larger unit to a smaller unit, so the number must get bigger. You can move the decimal point three places to the right or solve as shown below:
2 kilometers = ? meters
2 × 1,000 meters per km = 2,000 meters
Therefore, 2 kilometers equals 2,000 meters
Example
Change 520 grams to kilograms.
Changing meters to kilometers requires moving from smaller units to larger units and, thus, requires that the decimal point move to the left. Beginning at the ones unit (for grams), note that the kilo heading is three places away. Therefore, the decimal point will move three places to the left. Move the decimal point from the end of 520 to the left three places. That means you need to place the decimal point before the 5: 0.520.
The answer is 520 grams = 0.520 kilograms
Converting Units of Time
The ParaPro Assessment may ask you to convert units of time. Just like converting U.S. customary or metric units, multiply when changing from a larger unit to a smaller unit and divide when changing from a smaller unit to a larger unit.
Example
A teacher creates a lesson plan for the week that will take four hours. How many minutes will the lesson plan take?
Because minutes are a smaller unit than hours, you need to multiply to convert the units. Remember that there are 60 minutes in an hour.
4 hours = ? minutes
4 hours × 60 minutes per hour = 240
Therefore, there are 240 minutes in 4 hours.
Money
In addition to converting between units of length, capacity, weight, mass, and time, you may also be asked to convert between units of money. Remember that one cent is equal to 
of a dollar, or $0.01. The values of U.S. coins are as follows:
1 penny = 1 cent = 1¢ = $0.01
1 nickel = 5 cents = 5¢ = $0.05
1 dime = 10 cents = 10¢ = $0.10
1 quarter = 25 cents = 25¢ = $0.25
1 dollar = 100 cents = 100¢ = $1.00
Converting Money
As always when converting units, multiply when changing from a larger unit to a smaller unit and divide when changing from a smaller unit to a larger unit. To convert dollars to cents, multiply by 100. To convert cents to dollars, divide by 100.
Example
Jillian has 7 dollars. How many dimes does she have?
To solve this problem, first convert Jillian's dollars to cents. Multiply the number of dollars by 100.
$7 = 7 × 100¢ = 700¢
To convert from cents to dimes, you are going from a smaller unit to a larger unit—which means you have to divide. If Jillian has 700 cents, you need to divide by 10 to find out how many dimes she has.
700¢ ÷ 10 = 70 dimes
The practice quiz for this study guide can be found at:
Math for Praxis II ParaPro Test Prep Practice Problems
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