Rate Racers Worksheet
MATH 7 Unit Rates with Fractional Quantities (7.RP.A.1)
RATE RACERS PRACTICE
Name:
Date:
Period:
Unit Rate Rule: To find \(\text{Unit Rate} = \frac{\text{Quantity}}{\text{Single Unit}}\), divide by multiplying the numerator by the denominator's reciprocal.
\(\frac{a/b}{c/d} = \frac{a}{b} \times \frac{d}{c}\)
1 Part 1: Speed & Distance Trials
Compute the unit rate in miles per hour (mph).
1. An electric delivery cart travels \(\frac{3}{5}\) mile in \(\frac{1}{10}\) hour. What is its speed in miles per hour?
Show Work
Unit Rate:
mph
2. A runner jogs \(\frac{5}{8}\) mile in \(\frac{1}{4}\) hour. Calculate the runner's average pace in miles per hour.
Show Work
Unit Rate:
mph
3. A hiker walks \(\frac{2}{3}\) mile in each \(\frac{1}{2}\) hour. How many miles does the hiker walk in 1 hour?
Show Work
Unit Rate:
mph
2 Part 2: Area & Surface Coverage
Find coverage per 1 whole unit of material.
4. A painter uses \(\frac{1}{3}\) gallon of paint to cover \(\frac{4}{5}\) square meter of a bedroom wall. How many square meters can 1 full gallon cover?
Show Work
Unit Rate:
\(\text{m}^2/\text{gal}\)
5. A landscaper covers \(\frac{3}{4}\) square yard of lawn using \(\frac{2}{5}\) bag of grass fertilizer. What is the coverage rate in square yards per bag?
Show Work
Unit Rate:
sq yd/bag
Rate Racers Student Worksheet Page 1 of 2
SECTION 2 RATE RACERS: ADVANCED PROBLEM SOLVING
Page 2
3 Part 3: Rates of Flow & Mixtures
Carefully identify the dividend and divisor.
6. A scientific dropper dispenses \(\frac{7}{10}\) milliliter of liquid reagent every \(\frac{1}{5}\) second. What is the dispensing rate in milliliters per second?
Unit Rate:
mL/sec
7. A baker uses \(\frac{3}{4}\) cup of cocoa powder for each \(\frac{2}{3}\) batch of brownies. How many cups of cocoa are needed per full batch?
Unit Rate:
cups/batch
4 Part 4: The Drone Grand Prix (Comparison)
Multi-Step Challenge
8. Two robotic test drones are timed on an obstacle course:
• Drone Alpha: flies \(\frac{5}{6}\) mile in \(\frac{1}{12}\) hour.
• Drone Beta: flies \(\frac{7}{8}\) mile in \(\frac{1}{10}\) hour.
A. Drone Alpha Unit Rate
Alpha Rate: _________ mph
B. Drone Beta Unit Rate
Beta Rate: _________ mph
C. Comparison & Speed Difference:
5 Part 5: Mathematical Reasoning & Error Analysis
Spot the Slip
9. Problem: A snail crawls \(\frac{2}{5}\) meter in \(\frac{3}{10}\) hour. Marcus calculated the speed as: \(\frac{3}{10} \div \frac{2}{5} = \frac{3}{10} \times \frac{5}{2} = \frac{15}{20} = \frac{3}{4}\text{ m/hr}\).
Marcus's Error:
Correct Calculation & Unit Rate:
Self-Check: Did you include proper compound units (mph, m²/gal, mL/s)?
Needs Review Getting There Mastered!