Unit Rates with Fractions Test Answer Key with Scoring – Grade 7

Question 1 Complex Fraction and Unit Rate (2 points)

(a) 38112 miles per hour.

(b) 38 × 12 = 368 = 92.

4 12 miles per hour

Scoring: 1 point for the complex fraction, 1 point for the correct speed.

Question 2 Leaky Pipe (2 points)

710 ÷ 38 = 710 × 83 = 5630 = 2815.

1 1315 quarts per hour

Scoring: 1 point for the correct setup, 1 point for the correct simplified answer.

Question 3 Skater or Runner (3 points)

Skater: 710 × 6 = 4210 = 4 15 mph.

Runner: 12 ÷ 7 = 114 mi per min; × 60 = 6014 = 307 = 4 27 mph.

4 27 > 4 15 because 1035 > 735.

The runner is faster

Scoring: 1 point for the skater’s rate, 1 point for the runner’s rate with the unit conversion, 1 point for the conclusion.

Question 4 Cleaning a Floor Section (2 points)

Area: 56 × 35 = 1530 = 12 sq yd.

12 ÷ 14 = 2.

2 square yards per hour

Scoring: 1 point for the area, 1 point for the rate.

Question 5 Walnut Prices (3 points)

(a) 8.40 ÷ 34 = 8.40 × 43 = 33.60 ÷ 3 = $11.20 per pound.

(b) 11.20 × 2.5 = 28.00.

$11.20 per pound; $28.00

Scoring: 1.5 points for each part (1 for the method, 0.5 for the answer).

Question 6 Robot Speed Conversion (2 points)

Feet per second: 910 × 3 = 2710.

Feet per minute: 2710 × 60 = 162.

162 feet per minute

Scoring: 1 point for feet per second, 1 point for the conversion.

Question 7 Filling a Tub (3 points)

(a) 25 ÷ 34 = 25 × 43 = 815 tub per minute.

(b) 1 ÷ 815 = 158 = 1 78 minutes.

(c) Remaining 35 ÷ 815 = 35 × 158 = 4540 = 1 18 minutes. (Check: 1 78 − 34 = 1 18.)

815 tub per minute; 1 78 min; 1 18 min

Scoring: 1 point per part.

Question 8 Constant Rate Table (3 points)

(a) 58 ÷ 13 = 158 = 1 78 mph.

(b) 1 hour: 1 78 mi. 2 12 hours: 158 × 52 = 7516 = 4 1116 mi.

(c) 154 ÷ 158 = 154 × 815 = 2 hours.

1 78 mph; 1 78 mi and 4 1116 mi; 2 hours

Scoring: 1 point per part.