Warm-Up 1
A car travels 120 miles in 2 hours. Which of the following is a
rate?
Vocabulary: A rate is a
ratio that compares two quantities with different units (like
miles and hours).
✓Correct! "120 miles per 2 hours" compares miles to hours — two
different units — making it a rate.
✗A rate compares two different units. "120 miles per 2 hours"
compares miles to hours. The answer is B.
Warm-Up 2
If you earn $24 for 3 hours of work, what is your
unit rate (dollars per hour)?
Hint: A unit rate has a
denominator of 1. Divide $24 ÷ 3 hours to find the pay
per one hour.
✓Correct! $24 ÷ 3 = $8 per hour.
✗Divide total dollars by total hours: $24 ÷ 3 = $8. The answer is
B: $8 per hour.
Practice 1
A printer prints 150 pages in 5 minutes. What is the unit rate?
Strategy: Divide pages by minutes: 150 ÷ 5 = ? pages
per minute.
pages per minute
Sentence frame: "I divided ___ pages by ___ minutes to get ___ pages
per minute."
✓Correct! 150 ÷ 5 = 30 pages per minute.
✗Divide 150 pages by 5 minutes: 150 ÷ 5 = 30 pages
per minute.
Practice 2
Store A sells 6 apples for $3.00. Store B sells 8 apples for $4.80.
Which store has the better unit price?
Strategy: Find the price per apple at each store.
Store A: $3.00 ÷ 6. Store B: $4.80 ÷ 8. Compare the unit prices.
Sentence frame: "Store A costs $___ per apple and Store B costs $___
per apple, so Store ___ has the better price."
✓Correct! Store A: $3.00 ÷ 6 = $0.50. Store B: $4.80 ÷ 8 = $0.60.
Store A is cheaper per apple.
✗Store A: $3.00 ÷ 6 = $0.50/apple. Store B: $4.80 ÷ 8 = $0.60/apple.
The answer is A — Store A is cheaper.
Practice 3
Sort each example into the correct category:
Rate or Ratio (not a rate).
Remember: A rate compares
quantities with different units. A ratio that compares the
same kind of unit is not a rate.
60 miles per hour
3 boys to 5 girls
$2.50 per pound
4 red to 6 blue
90 words per minute
2 wins to 3 losses
✓All correct! Rates compare different units (miles/hours,
dollars/pounds). Ratios compare the same kind of unit.
✗Some are in the wrong group. Rates have different units (miles
& hours, dollars & pounds). Try again!
Practice 4
Find each unit rate.
Strategy: Divide the first quantity by the second to
get the rate per 1 unit.
Sentence frame: "I divided ___ by ___ to get a unit rate of ___ per
___."
✓All correct! 60 mph, $3.50 per pound, and 90 words per
minute.
✗Some answers need another look. Divide the total by the number of
units to find each unit rate.
Practice 5
Maria runs 3 miles in 27 minutes. Kevin runs 5 miles in 40 minutes.
Who runs at a faster rate?
Strategy: Find each person's unit rate (minutes per
mile). Maria: 27 ÷ 3. Kevin: 40 ÷ 5. Lower minutes per mile = faster.
Sentence frame: "Maria runs ___ minutes per mile. Kevin runs ___
minutes per mile. ___ is faster because ___."
✓Correct! Kevin runs 8 min/mile vs. Maria's 9 min/mile. Kevin is
faster.
✗Maria: 27 ÷ 3 = 9 min/mile. Kevin: 40 ÷ 5 = 8 min/mile. Lower =
faster. The answer is B.
Challenge
A faucet drips 2.5 gallons of water every 5 hours. At this rate, how
many gallons will it drip in 24 hours?
Think about it: First find the unit rate (gallons per
hour): 2.5 ÷ 5 = ? Then multiply by 24 hours.
Total gallons =
Sentence frame: "The unit rate is ___ gallons per hour. In 24 hours,
the faucet drips ___ × ___ = ___ gallons."
✓Excellent! Unit rate = 0.5 gal/hr. 0.5 × 24 = 12 gallons in 24
hours.
✗Unit rate: 2.5 ÷ 5 = 0.5 gal/hr. Then 0.5 × 24 =
12 gallons.