Unit Rates and Unit Conversion
Grade 6 · Math · Study Guide
Master unit rates and learn to convert between units using dimensional analysis.
A unit rate tells you the amount of something per one unit of something else. 'Miles per hour,' 'calories per serving,' and 'dollars per pound' are all unit rates. To find a unit rate, divide the first quantity by the second. If a car travels 240 miles in 4 hours, the unit rate is 240 ÷ 4 = 60 miles per hour.
Unit conversion means changing a measurement from one unit to another — like converting inches to feet, or minutes to hours. The key tool is a conversion factor, which is a fraction equal to 1 because the numerator and denominator represent the same amount in different units. For example: 12 inches = 1 foot, so the fraction 12 in/1 ft equals 1.
Dimensional analysis is the technique of multiplying by conversion factors to cancel unwanted units. To convert 3.5 feet to inches: 3.5 ft × (12 in / 1 ft) = 42 inches. The 'ft' units cancel, leaving only inches. You can chain multiple conversion factors together for complex conversions.
Unit conversion is everywhere — athletes convert their race times, engineers convert between metric and imperial, and cooks convert tablespoons to cups. The metric system is based on powers of 10, making conversions much simpler: 1 kilometer = 1,000 meters, 1 meter = 100 centimeters.
| From | To | Conversion |
|---|---|---|
| Feet | Inches | 1 ft = 12 in |
| Yards | Feet | 1 yd = 3 ft |
| Miles | Feet | 1 mi = 5,280 ft |
| Pounds | Ounces | 1 lb = 16 oz |
| Kilometers | Meters | 1 km = 1,000 m |
Key terms
- Unit Rate
- A rate with a denominator of 1 — tells you the amount per one unit
- Conversion Factor
- A fraction equal to 1 that converts one unit to another, like 12 in/1 ft
- Dimensional Analysis
- Multiplying by conversion factors to cancel units and convert measurements
- Metric Prefix
- Prefixes like kilo- (1,000) and centi- (1/100) that modify base metric units
Flashcards
- Unit rate
- Amount per 1 unit — e.g. 60 miles per 1 hour
- Finding a unit rate
- Divide first quantity by second — 180 miles ÷ 3 hours = 60 mph
- Conversion factor
- A fraction = 1 that changes units — e.g. (100 cm / 1 m)
- Dimensional analysis
- Multiply by conversion factors; units in numerator and denominator cancel
- 1 foot = ? inches
- 12 inches
- 1 kilometer = ? meters
- 1,000 meters
Practice questions
A car travels 360 miles in 6 hours. What is the unit rate in miles per hour?
- 60 mph
- 54 mph
- 2160 mph
- 66 mph
Show answer
Answer: 60 mph
360 miles ÷ 6 hours = 60 miles per hour.
Convert 5 feet to inches.
- 60 inches
- 15 inches
- 5 inches
- 17 inches
Show answer
Answer: 60 inches
5 ft × 12 in/ft = 60 inches.
A conversion factor is a fraction equal to 1.
Show answer
Answer: True
Conversion factors equal 1 because they equate the same quantity in different units — multiplying by 1 doesn't change the value.
There are ___ centimeters in 1 meter.
Show answer
Answer: 100
The metric prefix centi- means 1/100, so 1 meter = 100 centimeters.
Juice costs $2.40 for 6 oz and $3.50 for 10 oz. Which is the better deal?
- $3.50 for 10 oz (35¢/oz)
- $2.40 for 6 oz (40¢/oz)
- They are the same price per ounce
- Cannot be compared
Show answer
Answer: $3.50 for 10 oz (35¢/oz)
$2.40÷6=40¢/oz; $3.50÷10=35¢/oz. The larger bottle costs less per ounce.
Fun facts
- In 1999, NASA lost a $125 million Mars orbiter because one engineering team used metric units and another used imperial — a unit conversion error sent it off course.
- The world record for the 100-meter dash is about 10.49 meters per second — roughly 23.5 miles per hour!
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