This answer key gives worked solutions and a scoring guide for each question on the Grade 6 ratios test. Points are awarded for correct setup, correct computation, and a clear final answer. Partial credit is described in each scoring note.
Question 1: Walkers and riders (2 points)
(a) \(16:12\). Divide both by 4: \(4:3\).
(b) \(12:28\). Divide both by 4: \(3:7\).
Scoring: 1 point for each correct ratio in simplest form. An unsimplified ratio such as \(16:12\) earns no point, and the order of the quantities must be correct.
Question 2: Equivalent ratios (2 points)
(a) \(8:12\) simplifies to \(2:3\) and \(6:9\) simplifies to \(2:3\). Yes, they are equivalent.
(b) \(7 \times 5 = 35\), so \(y = 5 \times 5 = \) 25.
Scoring: (a) 1 point for the correct answer with a valid reason. (b) 1 point for 25.
Question 3: Rice and water (2 points)
\(3 \times 3 = 9\) cups of rice go with 15 cups of water.
\(6 \times 2 = 12\), so water is \(10 \times 2 = 20\) cups.
\(3 \times 6 = 18\) cups of rice go with 30 cups of water.
Missing values: 9, 20, 18.
Scoring: 2 points for all three correct; 1 point for two correct; 0 points for one or none.
Question 4: Playlist songs (3 points)
(a) Pop is 5 parts and \(35 : 5 = 7\), so each part is 7 songs. Rock is \(2 \times 7 = 14\) songs.
(b) Total: \(35 + 14 = 49\) songs.
(a) 14 rock songs. (b) 49 songs.
Scoring: (a) 1 point for finding one part equals 7, 1 point for 14. (b) 1 point for 49 (accept follow-through from part a).
Question 5: Lemonade strength (3 points)
Compare using the same amount of water. The least common multiple of 7 and 10 is 70.
Liam: \(2:7 = 20:70\), so 20 cups of juice per 70 cups of water.
Mei: \(3:10 = 21:70\), so 21 cups of juice per 70 cups of water.
Mei’s has more juice for the same water. Mei’s lemonade is stronger.
Scoring: 1 point for a valid common comparison amount, 1 point for both equivalent ratios correct, 1 point for the correct conclusion.
Question 6: Reading pace (3 points)
(a) \(15:20\). Divide by 5: \(3:4\).
(b) \(36 : 4 = 9\), so pages are \(3 \times 9 = \) 27 pages.
(c) \(45 : 3 = 15\), so minutes are \(4 \times 15 = \) 60 minutes.
Scoring: 1 point for each correct part.
Question 7: Class makeup (3 points)
(a) Total parts: \(7 + 8 = 15\). Each part: \(30 : 15 = 2\). Girls: \(7 \times 2 = 14\). Boys: \(8 \times 2 = 16\).
(b) Girls become \(14 + 4 = 18\). The ratio is \(18:16\). Divide by 2: \(9:8\).
(a) 14 girls and 16 boys. (b) \(9:8\).
Scoring: (a) 1 point for finding each part is 2 students, 1 point for both counts correct. (b) 1 point for \(9:8\); accept follow-through from part a.
Question 8: Marble bag (2 points)
(a) Total marbles: \(8 + 5 + 7 = 20\). Red to all: \(8:20 = \) \(2:5\).
(b) Green to yellow: \(5:7\).
Scoring: (a) 1 point for \(2:5\) in simplest form (0 points if the total is wrong). (b) 1 point for \(5:7\) in the correct order.
20 points
See every chapter on the Grade 6 math page.