Measurement for Praxis I: Pre-Professional Skills Test Study Guide (page 3)
This section reviews the basics of measurement systems used in the United States (sometimes called customary measurement) and other countries, methods of performing mathematical operations with units of measurement, and the process of converting between 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
The types of measurements used most frequently in the United States are listed here:
- Units of Length
- 12 inches (in.) = 1 foot (ft.)
- 3 feet = 36 inches = 1 yard (yd.)
- 5,280 feet = 1,760 yards = 1 mile (mi.)
- Units of Volume
- 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.)
- Units of Weight
- 16 ounces* (oz.) = 1 pound (lb.)
- 2,000 pounds = 1 ton (T.)
- Units of Time
- 60 seconds (sec.) = 1 minute (min.)
- 60 minutes = 1 hour (hr.)
- 24 hours = 1 day
- 7 days = 1 week
- 52 weeks = 1 year (yr.)
- 12 months = 1 year
- 365 days = 1 year
- *Notice that ounces are used to measure the dimensions of both volume and weight.
When performing mathematical operations, it may be necessary to convert units of measure to simplify a problem. Units of measure are converted by using either multiplication or division.
- 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:
- 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:
(given number of the larger units) × (the number of smaller units per larger unit) = answer in smaller 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.
Change 3.5 tons to pounds.
3.5 tons = ? pounds
3.5 tons × = 7,000 pounds
Therefore, there are 7,000 pounds in 3.5 tons.
For example, to find the number of pints in 64 ounces, divide 64, the number of smaller units, by 16, the number of ounces in one pint.
64 ounces = ? pints
Therefore, 64 ounces equals four pints.
Change 32 ounces to pounds.
32 ounces = ? pounds
Therefore, 32 ounces equals two pounds.
Basic Operations with Measurement
You may need 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 by converting smaller units into larger units when possible.
Add 4 pounds 5 ounces to 20 ounces.
Be sure to add ounces to ounces.
Because 25 ounces is more than 16 ounces (1 pound), simplify by dividing by 16:
Then add the 1 pound to the 4 pounds:
4 pounds 25 ounces = 4 pounds + 1 pound 9 ounces = 5 pounds 9 ounces
Subtraction with Measurements
- Subtract like units if possible.
- If not, regroup units to allow for subtraction.
- Write the answer in simplest form.
For example, 6 pounds 2 ounces subtracted from 9 pounds 10 ounces.
Subtract ounces from ounces.
Then subtract pounds from pounds.
Sometimes, it is necessary to regroup units when subtracting.
Subtract 3 yards 2 feet from 5 yards 1 foot.
Because 2 feet cannot be taken from 1 foot, regroup 1 yard from the 5 yards and convert the 1 yard to 3 feet. Add 3 feet to 1 foot. Then subtract feet from feet and yards from yards:
Therefore, 5 yards 1 foot – 3 yards 2 feet = 1 yard 2 feet.
Multiplication with Measurements
- Multiply like units if units are involved.
- Simplify the answer.
Multiply 5 feet 7 inches by 3.
Multiply 7 inches by 3, then multiply 5 feet by 3. Keep the units separate.
Because 12 inches = 1 foot, simplify 21 inches.
15 ft. 21 in. = 15 ft. + 1 ft. 9 in. = 16 ft. 9 in.
Multiply 9 feet by 4 yards.
First, decide on a common unit: either change the 9 feet to yards, or change the 4 yards to feet. Both options are explained below:
To change yards to feet, multiply 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 × 12 feet = 108 square feet.
(Note: feet · feet = square feet = ft.2)
To change feet to yards, divide the number of feet given (9), by the number of feet in a yard (3).
- 9 feet ÷ 3 feet in a yard = 3 yards
Then multiply 3 yards by 4 yards = 12 square yards.
(Note: yards × yards = square yards = yd.2)
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