Proportional Reasoning with Rates — Drills
Proportional Reasoning with Rates has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 1 idea from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Better buy — The option with the lower unit price.
Unit rate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A machine produces 360 words in 9 minutes. Find the rate in words per minute.
Worked answer
40
360 ÷ 9 = 40
40 words every minute.
Problem 2
A machine produces 60 miles in 6 hours. Find the rate in miles per hour.
Worked answer
10
60 ÷ 6 = 10
10 miles every hour.
Fracrate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A pump moves 34 of a tank in 43 of an hour. How many tanks per hour?
Worked answer
9/16
34 ÷ 43 = 34 × 34
= 916
Problem 2
A pump moves 12 of a tank in 14 of an hour. How many tanks per hour?
Worked answer
2
12 ÷ 14 = 12 × 4
= 2
Userate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A printer runs at 22 pages per minute. How many minutes to print 308 pages?
Worked answer
14
308 ÷ 22 = 14 minutes
Problem 2
A printer runs at 7 pages per minute. How many minutes to print 77 pages?
Worked answer
11
77 ÷ 7 = 11 minutes
Comparing
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A 12-ounce pack costs $5.04. A 18-ounce pack costs $8.46. Which is the better buy?
- The 12-ounce pack
- The 18-ounce pack
Worked answer
The 12-ounce pack
5.04 ÷ 12 = 0.42 per ounce
8.46 ÷ 18 = 0.47 per ounce
0.42 < 0.47, so the 12-ounce pack wins.
Problem 2
A 10-ounce pack costs $2.20. A 18-ounce pack costs $3.06. Which is the better buy?
- The 10-ounce pack
- The 18-ounce pack
Worked answer
The 18-ounce pack
2.20 ÷ 10 = 0.22 per ounce
3.06 ÷ 18 = 0.17 per ounce
0.17 < 0.22, so the 18-ounce pack wins.
Avgrate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Theo drives 180 miles at 30 mph, then 180 miles at 60 mph. Find the average speed for the whole trip.
Worked answer
40
Time going out: 180 ÷ 30 = 6 h
Time coming back: 180 ÷ 60 = 3 h
Total: 360 miles in 9 h
360 ÷ 9 = 40 mph
Problem 2
Nina drives 60 miles at 30 mph, then 60 miles at 90 mph. Find the average speed for the whole trip.
Worked answer
45
Time going out: 60 ÷ 30 = 2 h
Time coming back: 60 ÷ 90 = 23 h
Total: 120 miles in 83 h
120 ÷ 83 = 45 mph