A ratio that compares two quantities measured in different units
What Makes a Rate Different from a Ratio?
A rate is a special type of ratio that compares two quantities with different units. While a ratio like 3:5 compares the same kind of thing, a rate compares different things — like miles and hours, dollars and pounds, or heartbeats and minutes.
Common Rates You Already Know
Speed: 60 miles per hour (miles ÷ hours)
Price: $3.50 per gallon (dollars ÷ gallons)
Heart rate: 72 beats per minute (beats ÷ minutes)
Pay: $18 per hour (dollars ÷ hours)
The Word "Per"
The word "per" is the signal for a rate. It means "for each" or "divided by." When you see "per," you're dealing with a rate.
Miles per hour. Dollars per pound. Words per minute. The unit after "per" is what you're dividing by.
Writing Rates
Rates can be written several ways:
60 miles per hour
With words: 60 miles per hour
As a fraction: 60 miles / 1 hour
Abbreviated: 60 mph
💡 Rate vs unit rate: A rate can be any comparison (150 miles in 3 hours). A unit rate is simplified so the second quantity is 1 (50 miles per 1 hour = 50 mph). Unit rates are easier to compare and use.
🎯 Practice Problems
1. Which of these is a rate?
A) 3 boys to 5 girls
B) 12 red marbles to 8 blue
C) 45 miles per hour
D) 2:7
2. A car travels 240 miles in 4 hours. What is the rate?
A) 240 miles per 4 hours
B) 4 hours per 240 miles
C) 60 miles per hour
D) Both A and C
3. What does the word 'per' mean in a rate?
A) Plus
B) Times
C) For each (divided by)
D) Minus
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🎯 Bonus Practice
1. A printer prints 120 pages in 10 minutes. Express this as a rate.
A) 120 pages per 10 minutes
B) 12 pages per minute
C) Both A and B
D) 10 minutes per 120 pages
2. Which is NOT a rate?
A) $5.99 per pound
B) 30 students per class
C) 3 wins to 2 losses
D) 80 beats per minute
3. You earn $540 in 36 hours. What is your hourly rate?
A) $36 per hour
B) $15 per hour
C) $540 per hour
D) $54 per hour
4. A recipe uses 3 cups of flour for 24 cookies. What is the rate?
A) 3 cups per 24 cookies
B) 8 cookies per cup
C) 0.125 cups per cookie
D) All of these
5. Water flows at 5 gallons per minute. How much in 12 minutes?