← Back to the Unit Rates With Fractions worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: 7.RP.A.1 · Level: Grade 7
Problem 1 Reading a Complex Fraction
(a) 4516 miles per hour.
(b) 45 ÷ 16 = 45 × 6 = 245 = 4 45.
Answer: 4 45 miles per hour
Problem 2 Hose Filling a Bucket
56 ÷ 29 = 56 × 92 = 4512 = 154.
Answer: 3 34 gallons per minute
Problem 3 Sugar per Batch
58 ÷ 14 = 58 × 4 = 208 = 52.
Answer: 2 12 cups per batch
Problem 4 Hiking Speed
910 ÷ 35 = 910 × 53 = 4530 = 32.
Check: 32 × 35 = 910.
Answer: 1 12 miles per hour
Problem 5 Price of Cashews
$6.75 ÷ 34 = $6.75 × 43 = $27.00 ÷ 3 = $9.00.
Check: 9 × 0.75 = 6.75.
Answer: $9.00 per pound
Problem 6 Toy Car Both Ways
(a) 35 ÷ 110 = 35 × 10 = 6 feet per second.
(b) 110 ÷ 35 = 110 × 53 = 530 = 16 second per foot.
Answer: 6 feet per second; 16 second per foot
Problem 7 Which Hiker Is Faster
A: 34 × 3 = 94 = 2 14 mph.
B: 23 × 4 = 83 = 2 23 mph.
2 23 > 2 14 because 812 > 312.
Answer: Hiker B is faster (2 23 mph vs. 2 14 mph)
Problem 8 Better Paint Buy
X: 12 ÷ 23 = 12 × 32 = $18.00 per gallon.
Y: 14.25 ÷ 34 = 14.25 × 43 = 57 ÷ 3 = $19.00 per gallon.
19 − 18 = 1.
Answer: Brand X costs $1.00 less per gallon
Problem 9 Conveyor Belt Units
Yards per minute: 56 × 73 = 3518.
1 yard = 3 feet, so 3518 × 3 = 356 = 5 56.
Answer: 5 56 feet per minute
Problem 10 Minutes to Hours
2 12 = 52. Miles per minute: 38 × 25 = 640 = 320.
Per hour: 320 × 60 = 9.
Answer: 9 miles per hour
Problem 11 Painting a Panel
Area = 34 × 23 = 612 = 12 square yard.
12 ÷ 16 = 12 × 6 = 3.
Answer: 3 square yards per hour
Problem 12 Filling a Pool
(a) 16 ÷ 34 = 16 × 43 = 418 = 29 pool per hour.
(b) 1 ÷ 29 = 92 = 4 12 hours. (Also 34 × 6 = 184.)
Answer: 29 pool per hour; 4 12 hours
Problem 13 Distance at a Steady Pace
Rate: 56 × 4 = 206 = 103 mph.
Distance: 103 × 32 = 306 = 5.
Answer: 5 miles
Problem 14 Rate Table for a Model Train
Rate: 78 × 4 = 288 = 3 12 feet per minute.
12 min: 3 12 × 12 = 1 34 ft. 1 min: 3 12 ft. 2 12 min: 72 × 52 = 354 = 8 34 ft.
Answer: 3 12 ft per min; 1 34 ft, 3 12 ft, 8 34 ft
Problem 15 Mural Painting Time
Area = 52 × 65 = 3010 = 3 square feet.
Painted: 38 × 3 = 98 sq ft in 32 h.
(a) 98 ÷ 32 = 98 × 23 = 1824 = 34 sq ft per hour.
(b) Remaining: 3 − 98 = 158 sq ft. 158 ÷ 34 = 158 × 43 = 6024 = 52.
Answer: 34 square foot per hour; 2 12 more hours
Problem 16 Trail Schedule
Speed: 94 ÷ 34 = 94 × 43 = 3 mph.
Hiking time: 274 ÷ 3 = 94 = 2 14 h. Add lunch: 2 14 + 12 = 2 34 h = 2 h 45 min.
8:15 AM + 2 h 45 min = 11:00 AM.
Answer: 11:00 AM
Problem 17 Printer Race
A: 34 × 8 = 6 pages per minute. B: 52 × 2 = 5 pages per minute.
A needs 45 ÷ 6 = 7 12 min. B needs 45 ÷ 5 = 9 min.
9 − 7 12 = 1 12.
Answer: A: 7 12 min; B: 9 min; A finishes 1 12 minutes sooner
Problem 18 Storm Rainfall
(a) 58 × 2 = 108 = 1 14 in per hour.
(b) 154 ÷ 54 = 154 × 45 = 3 hours.
(c) 12 inches = 1 foot: 54 ÷ 12 = 548 foot per hour.
Answer: 1 14 in/h; 3 hours; 548 ft/h
Problem 19 Mixing Paint Tint
23 ÷ 34 = 23 × 43 = 89 cup per gallon.
89 × 92 = 7218 = 4.
Answer: 89 cup per gallon; 4 cups for 4 12 gallons
Problem 20 Three Athletes Compared
Leo: 32 × 4 = 6 mph.
Nia: 310 ÷ 3 = 110 mi per min; × 60 = 6 mph.
Omar: 58 ÷ 6 = 548 mi per min; × 60 = 30048 = 6 14 mph.
Answer: Omar (6 14 mph) is fastest; Leo and Nia tie at 6 mph