This answer key gives worked solutions and a scoring guide for every question on the Grade 6 percents test. Points are given for the correct method, accurate computation, and a clear final answer. Partial credit is explained in each scoring note.
Question 1: Fraction and percent (2 points)
(a) \(45\% = \frac{45}{100} = \frac{9}{20}\).
(b) \(\frac{7}{25} = \frac{28}{100} = 28\%\).
(a) \(\frac{9}{20}\). (b) \(28\%\).
Scoring: 1 point for each correct answer. In part (a), the fraction must be in simplest form.
Question 2: Decimal and fraction to percent (2 points)
(a) \(0.06 \times 100 = 6\), so \(6\%\).
(b) \(3 : 8 = 0.375\), and \(0.375 \times 100 = 37.5\), so \(37.5\%\).
(a) \(6\%\). (b) \(37.5\%\).
Scoring: 1 point for each correct percent.
Question 3: Percent of a number (2 points)
(a) \(0.35 \times 80 = 28\).
(b) \(0.12 \times 150 = 18\).
(a) 28. (b) 18.
Scoring: 1 point for each correct answer.
Question 4: Test score (3 points)
(a) \(42 : 60 = 0.70\), which is \(70\%\).
(b) \(0.90 \times 60 = 54\) points.
(a) \(70\%\). (b) 54 points.
Scoring: (a) 1 point for dividing part by whole, 1 point for \(70\%\). (b) 1 point for 54.
Question 5: Walking to school (3 points)
(a) \(40\%\) of the students is 18, so \(18 : 0.40 = 45\) students.
(b) \(0.20 \times 45 = 9\) students.
(a) 45 students. (b) 9 students.
Scoring: (a) 1 point for a correct method (for example, \(10\% = 4.5\) or dividing by 0.40), 1 point for 45. (b) 1 point for 9; accept follow-through from part (a).
Question 6: Sneaker sale (3 points)
(a) \(0.30 \times 85 = 25.50\), so the discount is \(\$25.50\).
(b) \(85 – 25.50 = 59.50\), so the sale price is \(\$59.50\).
(c) \(100\% – 30\% = 70\%\).
(a) \(\$25.50\). (b) \(\$59.50\). (c) \(70\%\).
Scoring: 1 point for each correct part. Accept follow-through in (b) and (c).
Question 7: Lunch survey (3 points)
(a) Pizza: \(0.45 \times 80 = 36\). Tacos: \(0.30 \times 80 = 24\).
(b) Salad: \(100\% – 45\% – 30\% = 25\%\).
Check: \(25\%\) of 80 is 20, and \(36 + 24 + 20 = 80\).
(a) 36 pizza, 24 tacos. (b) \(25\%\).
Scoring: (a) 1 point for each correct count. (b) 1 point for \(25\%\).
Question 8: Ordering numbers (2 points)
Write each as a decimal: \(65\% = 0.65\), \(0.7\) stays \(0.70\), and \(\frac{3}{4} = 0.75\).
Order: \(0.65 < 0.70 < 0.75\).
\(65\%\), \(0.7\), \(\frac{3}{4}\).
Scoring: 1 point for converting all three to the same form correctly, 1 point for the correct order. Accept follow-through if one conversion is wrong but the order matches it.
20 points
See every chapter on the Grade 6 math page.