This answer key gives worked solutions and a scoring guide for every question on the Grade 6 unit rates test. Points are given for the correct operation, accurate computation, and a final answer with the proper rate unit.
Question 1: Reading rate (2 points)
(a) \(45 : 90 = 0.5\) page per minute.
(b) \(90 : 45 = 2\) minutes per page.
(a) 0.5 page per minute. (b) 2 minutes per page.
Scoring: 1 point for each correct unit rate with its unit. Award 0 points if the division is reversed.
Question 2: Grape prices (2 points)
(a) \(\$9.75 : 5 = \$1.95\) per pound.
(b) \(1.95 \times 8 = 15.60\).
(a) \(\$1.95\) per pound. (b) \(\$15.60\).
Scoring: 1 point for each part. Accept follow-through on part (b) if part (a) is wrong but used correctly.
Question 3: Highway speed (2 points)
(a) \(210 : 3.5 = 60\) miles per hour.
(b) \(60 \times 5 = 300\) miles.
(a) 60 miles per hour. (b) 300 miles.
Scoring: 1 point for each part. Accept follow-through on part (b).
Question 4: Best buy: snacks (3 points)
18 oz: \(\$4.14 : 18 = \$0.23\) per ounce.
24 oz: \(\$5.28 : 24 = \$0.22\) per ounce.
30 oz: \(\$6.90 : 30 = \$0.23\) per ounce.
The 24-ounce size has the lowest unit price (\(\$0.22\) per ounce).
Scoring: 1 point for a correct method (dividing price by ounces), 1 point for all three unit prices correct, 1 point for naming the 24-ounce size.
Question 5: Typing speeds (3 points)
Ethan: \(150 : 5 = 30\) words per minute.
Aisha: \(222 : 6 = 37\) words per minute.
Difference: \(37 – 30 = 7\).
Aisha types faster, by 7 words per minute.
Scoring: 1 point for Ethan’s rate, 1 point for Aisha’s rate, 1 point for the correct conclusion with the difference of 7.
Question 6: Hourly pay (3 points)
(a) \(13 \times 10 = 130\), so he earns \(\$130\).
(b) \(195 : 13 = 15\) hours.
(c) \(26 : 2 = 13\), so \(\$26\) for 2 hours is also \(\$13\) per hour. The unit rate is the same, so both are equivalent rates.
(a) \(\$130\). (b) 15 hours. (c) Both give \(\$13\) per hour.
Scoring: 1 point for each part. In (c), the explanation must show that \(26 : 2 = 13\), or that doubling both 13 and 1 gives 26 and 2.
Question 7: Honey jars (3 points)
(a) 12-ounce jar: \(\$5.40 : 12 = \$0.45\) per ounce. 16-ounce jar: \(\$6.88 : 16 = \$0.43\) per ounce.
(b) The 16-ounce jar is the better buy. \(0.43 \times 48 = 20.64\).
(a) \(\$0.45\) and \(\$0.43\) per ounce. (b) \(\$20.64\).
Scoring: (a) 1 point for each correct unit price. (b) 1 point for \(\$20.64\), using the lower unit price.
Question 8: Gas mileage (2 points)
(a) \(288 : 9 = 32\) miles per gallon.
(b) \(400 : 32 = 12.5\) gallons.
(a) 32 miles per gallon. (b) 12.5 gallons.
Scoring: 1 point for each part. Accept follow-through on part (b).
20 points
See every chapter on the Grade 6 math page.