Mathematics
Grade 9
15 min
Convert rates and measurements customary units
Convert rates and measurements customary units
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Introduction & Learning Objectives
Learning Objectives
Identify common customary units for length, weight, and capacity.
Use conversion factors to convert single-unit measurements within the customary system.
Apply dimensional analysis to convert rates with compound units (e.g., miles per hour to feet per second).
Correctly convert measurements of area and volume by applying exponents to conversion factors.
Set up and solve multi-step real-world problems involving customary unit conversions.
Analyze units to determine the correct conversion pathway and verify the reasonableness of their answers.
Ever wondered if a cheetah running at 70 miles per hour is faster than a car driving at 100 feet per second? 🐆💨 Let's learn the math to find out!
This tutorial will guide you through converting rates and measu...
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Key Concepts & Vocabulary
TermDefinitionExample
Customary SystemThe system of measurement primarily used in the United States. It includes units like inches, feet, miles for length; ounces, pounds, tons for weight; and cups, pints, quarts, gallons for capacity.A road sign in the U.S. shows a speed limit of 65 miles per hour, using customary units of length (miles) and time (hours).
Conversion FactorA ratio or fraction of two equivalent measurements, which is equal to one. It is used to convert from one unit to another without changing the value of the measurement.The relationship 1 foot = 12 inches can be written as the conversion factor (12 inches / 1 foot) or (1 foot / 12 inches).
Dimensional AnalysisA problem-solving method that uses conversion factors to change units. By strategically multiplying by fractions...
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Core Formulas
Single Unit Conversion
Q_{original} \times \frac{U_{desired}}{U_{original}} = Q_{converted}
To convert a single measurement, multiply the original quantity by a conversion factor. The conversion factor should be set up so that the original unit is in the denominator to cancel it out, leaving the desired unit in the numerator.
Rate Conversion
\frac{A}{B} \times \frac{C}{A} \times \frac{D}{C} = \frac{D}{B}
To convert a rate, you may need to use multiple conversion factors. One factor converts the numerator unit, and another converts the denominator unit. Ensure units cancel diagonally, leaving you with the desired final rate.
Area and Volume Conversion
For Area: Q_{original} \times (\frac{U_{desired}}{U_{original}})^2 = Q_{converted} \newline For Volume: Q_{original} \ti...
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Challenging
A cylindrical grain silo has a volume of 5,000 cubic feet. Grain flows out of the silo at a rate of 400 quarts per minute. If the grain has a density such that 1 cubic foot holds approximately 29.9 quarts, how many hours will it take to empty the silo? Round to the nearest hour.
A.1 hour
B.6 hours
C.25 hours
D.374 hours
Challenging
The kinetic energy of an object is given by E = 0.5 * m * v², where m is mass and v is velocity. A 4,000-pound car is traveling at 30 miles per hour. What is its velocity in feet per second, and which conversion pathway is most direct for finding it?
A.44 ft/s; Pathway: Convert mph to ft/hr, then ft/hr to ft/s.
B.88 ft/s; Pathway: Convert mph to miles/s, then miles/s to ft/s.
C.44 ft/s; Pathway: Use two factors simultaneously: (5280 ft / 1 mile) and (1 hr / 3600 s).
D.22 ft/s; Pathway: Convert pounds to tons before calculating velocity.
Challenging
A developer is selling a square plot of land with a side length of 1/8 of a mile. A buyer wants to know the area in acres. Which of the following calculations correctly determines the area? (1 mile = 5280 ft, 1 acre = 43560 ft²)
A.(1/8 * 5280)² / 43560
B.(1/8)² * 5280 / 43560
C.(1/8 * 5280) / 43560
D.(1/8) * (5280)² / 43560
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