Grade 6 Mathematics
A RATE is a special ratio that compares two quantities with DIFFERENT UNITS.
Examples: miles per hour, dollars per pound, words per minute
A UNIT RATE is a rate with 1 in the denominator (like $3 per 1 pound or 60 miles per 1 hour).
Rate: A ratio comparing two quantities with different units
Unit Rate: A rate where the second quantity is 1 (per ONE)
"Per": Means "for each" or "for every one"
Problem: A car travels 180 miles in 3 hours. What is the speed in miles per hour?
Identify the rate: 180 miles / 3 hours (This compares miles to hours - different units!)
Divide to find "per 1": 180 / 3 = 60
Write with units: 60 miles per hour (or 60 mph)
180 miles / 3 hours = 60 miles per 1 hour
Problem: A pack of 8 pencils costs $4.00. What is the price per pencil?
Identify the rate: $4.00 / 8 pencils
Divide: $4.00 / 8 = $0.50
Write with units: $0.50 per pencil
Which is the better buy?
Brand A: 6 oz for $2.40 Brand B: 8 oz for $2.80
Find unit rate for Brand A: $2.40 / 6 oz = $0.40 per oz
Find unit rate for Brand B: $2.80 / 8 oz = $0.35 per oz
Compare: $0.35 < $0.40, so Brand B is the better buy! (lower price per ounce)
WRONG: "The unit rate is 60." (60 what? Per what?)
RIGHT: "The unit rate is 60 miles per hour." Always include BOTH units!
WRONG: For "$12 for 4 items," dividing 4/12 = 0.33 items per dollar
RIGHT: For "price per item," divide $12/4 = $3 per item. Put what you want "per one" of in the denominator!
1. A cyclist rides 45 miles in 3 hours.
Unit rate: miles per hour
2. A store sells 5 pounds of apples for $10.00.
Unit price: $ per pound
3. Maria types 120 words in 4 minutes.
Unit rate: words per minute
4. A car uses 8 gallons of gas to travel 240 miles.
Unit rate: miles per gallon
5. Which is the better buy? Show your work!
Store A: 4 notebooks for $6.00 Store B: 6 notebooks for $8.40
Store A unit price: $ per notebook
Store B unit price: $ per notebook
Better buy: Store