This answer key shows a full worked solution for each of the 10 unit rates problems. Each solution divides to find the unit rate and then checks the result by multiplying. Compare your steps and your rate units with the bold final answers.
Problem 1: Unit rate of speed
Divide miles by hours: \(150 : 3 = 50\).
Check: \(50 \times 3 = 150\).
50 miles per hour.
Problem 2: Unit price
Divide the cost by the number of notebooks: \(\$9.00 : 6 = \$1.50\).
Check: \(6 \times 1.50 = 9.00\).
\(\$1.50\) per notebook.
Problem 3: Typing rate
Divide words by minutes: \(180 : 4 = 45\).
Check: \(45 \times 4 = 180\).
45 words per minute.
Problem 4: Filling a tank
Divide gallons by minutes: \(15 : 6 = 2.5\).
Check: \(2.5 \times 6 = 15\).
2.5 gallons per minute.
Problem 5: Cost from a unit price
Multiply the unit price by the number of pounds: \(1.80 \times 5 = 9.00\).
\(\$9.00\).
Problem 6: Better buy: juice
4-pack: \(\$5.20 : 4 = \$1.30\) per bottle.
6-pack: \(\$7.50 : 6 = \$1.25\) per bottle.
The 6-pack has the lower price per bottle.
The 6-pack is the better buy (\(\$1.25\) versus \(\$1.30\)).
Problem 7: Constant speed train
Unit rate: \(240 : 4 = 60\) miles per hour.
(a) \(60 \times 7 = 420\) miles.
(b) \(360 : 60 = 6\) hours.
(a) 420 miles. (b) 6 hours.
Problem 8: Babysitting pay
Unit rate: \(\$63 : 7 = \$9\) per hour.
(a) \(9 \times 12 = 108\).
(b) \(144 : 9 = 16\).
(a) \(\$108\). (b) 16 hours.
Problem 9: Comparing three sizes
12 oz: \(\$2.40 : 12 = \$0.20\) per ounce.
20 oz: \(\$3.80 : 20 = \$0.19\) per ounce.
32 oz: \(\$6.40 : 32 = \$0.20\) per ounce.
The lowest unit price is \(\$0.19\).
The 20-ounce size is the best buy.
Problem 10: Road trip
(a) First part: \(60 \times 3 = 180\) miles. Second part: \(45 \times 2 = 90\) miles. Total: \(180 + 90 = 270\) miles.
(b) Total time: \(3 + 2 = 5\) hours.
(c) Average speed: \(270 : 5 = 54\) miles per hour.
(a) 270 miles. (b) 5 hours. (c) 54 miles per hour.
See every chapter on the Grade 6 math page.