← Back to the Unit Analysis worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: N-Q.A.1, N-Q.A.2, N-Q.A.3 · Level: Grade 9 Algebra 1
Problem 1 Hours to minutes
Multiply by 60 min1 h: 4.5 × 60 = 270.
The hours cancel, leaving minutes: 270 minutes.
Problem 2 Feet to miles
7,920 ft × 1 mi5,280 ft = 1.5 mi (check: 5,280 × 1.5 = 7,920).
1.5 miles
Problem 3 Gallons to quarts
3.2 gal × 4 qt1 gal = 12.8 qt (check: 12.8 ÷ 4 = 3.2).
12.8 quarts
Problem 4 Units of a product
$2.751 lb × 6.4 lb = $17.60. The pounds cancel, so the unit is dollars.
$17.60
Problem 5 Cyclist speed
90 min = 1.5 h. Speed = 22.5 mi ÷ 1.5 h = 15 mi/h.
Check: 15 × 1.5 = 22.5.
15 mi/h
Problem 6 Miles per hour to feet per second
45 × 5,280 = 237,600 ft per hour. Divide by 3,600 s per hour: 237,600 ÷ 3,600 = 66.
Check: 66 × 3,600 = 237,600.
66 ft/s
Problem 7 Leaking faucet
Per day: 5 × 24 = 120 fl oz. Convert: 120 ÷ 128 = 0.9375 gal.
Check: 0.9375 × 128 = 120. Rounded: 0.94 gallon
Problem 8 Hose flow rate
Rate per minute: 14 ÷ 8 = 1.75 gal/min. Multiply by 60 min/h: 1.75 × 60 = 105.
Check: 105 gal/h × 860 h = 14 gal.
105 gallons per hour
Problem 9 Square yards to square feet
One square yard contains 3 × 3 = 9 square feet, as the grid shows. So 2 yd² × 9 = 18 ft².
Check: converting with the length factor only (2 × 3 = 6) would be wrong because both dimensions change.
18 square feet
Problem 10 Truncated axis
(a) The bars start at 450, so the heights are 480 − 450 = 30 and 520 − 450 = 70. Ratio 70 ÷ 30 = 7/3 ≈ 2.33.
(b) True ratio: 520 ÷ 480 = 13/12 ≈ 1.08.
The cut-off axis makes Week 2 look about 2.33 times as large, but the true ratio is about 1.08.
Problem 11 Accuracy of an area
Exact product: 8.3 × 5.6 = 46.48 ft². Both measurements have two significant figures, so keep two: 46.
Check: 8 × 6 = 48, close to 46.48.
46 ft²
Problem 12 Crowded parks
Define visitors per acre. Park A: 1,260 ÷ 18 = 70. Park B: 930 ÷ 15 = 62.
Check: 70 × 18 = 1,260 and 62 × 15 = 930.
Park A is more crowded (70 per acre versus 62 per acre).
Problem 13 Days to seconds
3 d × 24 h1 d × 60 min1 h × 60 s1 min = 3 × 24 × 60 × 60 = 259,200.
Check: 259,200 ÷ 86,400 = 3.
259,200 seconds
Problem 14 Conveyor speed
3.5 × 3,600 = 12,600 ft per hour. Divide by 5,280: 12,600 ÷ 5,280 ≈ 2.3864.
Check: 2.39 × 5,280 ≈ 12,619, close to 12,600.
about 2.39 mi/h
Problem 15 Road trip fuel cost
Gallons: 364 mi ÷ 28 mi/gal = 13 gal. Cost: 13 gal × $3.85/gal = $50.05.
Units: mi ÷ (mi/gal) = gal, then gal × (dollars per gal) = dollars.
$50.05
Problem 16 Filling the pool
Volume: 30 × 15 × 4 = 1,800 ft³. Water: 1,800 × 7.5 = 13,500 gal. Time: 13,500 ÷ 450 = 30 h.
Check: 450 × 30 = 13,500.
30 hours
Problem 17 Hiking average speed
Distance: 2.4 + 1.8 = 4.2 mi. Time: 50 + 45 = 95 min = 95/60 h.
Speed: 4.2 ÷ (95/60) = 252/95 ≈ 2.65.
Check: 2.65 × 1.583 ≈ 4.2.
about 2.65 mi/h
Problem 18 Better juice buy
Juice A: $3.84 ÷ 64 = $0.06 = 6 cents per fl oz.
Juice B: 1.5 gal × 128 = 192 fl oz. $10.56 ÷ 192 = $0.055 = 5.5 cents per fl oz.
Check: 5.5 × 192 = 1,056 cents.
Juice B is cheaper (5.5 cents versus 6 cents per fl oz).
Problem 19 Muffin sugar
Sugar needed: 40 × 1.5 = 60 cups. Bags: 60 ÷ 11.25 ≈ 5.33.
Only whole bags are sold, so round up: 6 bags (5 bags give 56.25 cups, not enough).
6 bags
Problem 20 Garden soil bags
Area: 12.5 × 8.25 = 103.125 ft². Bags: 103.125 ÷ 6 ≈ 17.19.
The garden needs full coverage, so round up to 18 bags (17 bags cover only 102 ft²).
18 bags