The GED Mathematics Exam emphasizes real-life applications of math concepts, and this is especially true of questions about measurement. This article will review the basics of measurement systems used in the United States and other countries, performing mathematical operations with units of measurement, and the process of converting between different units
The use of measurement enables you to form a connection 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 familiarize you with the types, conversions, and units of measurement.
Types of Measurements
Following are the types of measurements used most frequently in the United States.
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.)
Converting Units
When you perform mathematical operations, it is necessary to convert units of measure to simplify a problem. Units of measure are converted by using either multiplication or division:
- To change a larger unit to a smaller unit, simply multiply the specific 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 5 feet, simply multiply 5, the number of larger units, by 12, the number of inches in one foot:
5 feet = how many inches?
5 feet × 12 inches (the number of inches in a single foot) = 60 inches
Therefore, there are 60 inches in 5 feet.
Try another:
Change 3.5 tons to pounds.
3.5 tons = how many pounds?
3.5 tons × 2,000 pounds (the number of pounds in a single ton) = 6,500 pounds
Therefore, there are 6,500 pounds in 3.5 tons.
- To change a smaller unit to a larger unit, simply divide the specific number of smaller units by the number of smaller units in only one of the larger units.
For example, to find the number of pints in 64 ounces, simply divide 64, the smaller unit, by 16, the number of ounces in one pint.
= 4 pints
Therefore, 64 ounces are equal to 4 pints.
Here is one more:
Change 32 ounces to pounds.
= 2 pounds
Therefore, 32 ounces are equal to 2 pounds.
Basic Operations with Measurement
It will be necessary for you to review how to add, subtract, multiply, and divide with measurement. The mathematical rules needed for each of these operations with measurement follow.
Addition with Measurements
To add measurements, follow these two steps:
- Add like units.
- Simplify the answer.
4 pounds 25 ounces =
4 pounds + 1 pound 9 ounces =
5 pounds 9 ounces
Subtraction with Measurements
To subtract measurements, follow these three steps:
- Subtract like units.
- Regroup units when necessary.
- Write the answer in simplest form.
Sometimes, it is necessary to regroup units when subtracting.
Example: Subtract 3 yards 2 feet from 5 yards 1 foot.
From 5 yards, regroup 1 yard to 3 feet. Add 3 feet to 1 foot. Then, subtract feet from feet and yards from yards.
Multiplication with Measurements
To multiply measurements, follow these two steps:
- Multiply like units if units are involved.
- Simplify the answer.
Example: Multiply 9 feet by 4 yards. First, change yards to feet by multiplying the number of feet in a yard (3) by the number of yards in this problem (4).
3 feet in a yard × 4 yards = 12 feet
Then, multiply 9 feet by 12 feet = 108 square feet.
(Note: feet × feet = square feet)
Division with Measurements
For division with measurements, follow these steps:
- Divide into the larger units first.
- Convert the remainder to the smaller unit.
- Add the converted remainder to the existing smaller unit if any.
- Divide into smaller units.
- Write the answer in simplest form.
Metric Measurements
The metric system is an international system of measurement also called the decimal system. Converting units in the metric system is much easier than converting units in the English system of measurement. However, making conversions between the two systems is much more difficult. Luckily, the GED will provide you with the appropriate conversion factor when needed. The basic units of the metric system are the meter, gram, and liter. Here is a general idea of how the two systems compare:
Prefixes are attached to these 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:
Examples
- 1 hectometer = 1 hm = 100 meters
- 1 millimeter = 1 mm = meter = .001 meter
- 1 dekagram = 1 dkg = 10 grams
- 1 centiliter = 1 cL* = liter = .01 liter
- 1 kilogram = 1 kg = 1,000 grams
- 1 deciliter = 1 dL* = liter = .1 liter
*Notice that liter is abbreviated with a capital letter—L.
The following chart illustrates some common relationships used in the metric system:
Conversions within the Metric System
An easy way to do conversions with the metric system is to move the decimal point either to the right or left because the conversion factor is always ten or a power of ten. As you learned previously, when you change from a large unit to a smaller unit you multiply, and when you change from a small unit to a larger unit you divide.
Making Easy Conversions within the Metric System
When you multiply by a power of ten, you move the decimal point to the right. When you divide by a power of ten, you move the decimal point to the left.
To change from a large unit to a smaller unit, move the decimal point to the right.
To change from a small unit to a larger unit, move the decimal point to the left.
Example
Change 520 grams to kilograms.
Step 1: Be aware that changing meters to kilometers is going from small units to larger units; therefore, you will move the decimal point three places to the left.
Step 2: Beginning at the UNIT (for grams), you need to move three prefixes to the left.
Step 3: Move the decimal point from the end of 520 to the left three places:
Place the decimal point before the 5.
Your answer is 520 grams = .520 kilograms.
Example
You are packing your bicycle for a trip from New York City to Detroit. The rack on the back of your bike can hold 20 kilograms. If you exceed that limit, you must buy stabilizers for the rack that cost $2.80 each. Each stabilizer can hold an additional kilogram. If you want to pack 23,000 grams of supplies, how much money will you have to spend on the stabilizers?
Step 1: First, change 23,000 grams to kilograms.
Step 2: Move the decimal point three places to the left:
23,000 g = 23.000 kg = 23 kg
Step 3: Subtract to find the amount over the limit:
Step 4: Because each stabilizer holds 1 kilogram and your supplies exceed the weight limit of the rack by 3 kilograms, you must purchase 3 stabilizers from the bike store.
Step 5: Each stabilizer costs $2.80, so multiply $2.80 by 3: