Primary 5 Mathematics Ratio Quiz

Primary 5 Mathematics Quiz - Ratio (Answer Key)

Total Marks: 50

Section A (Questions 1 to 5: 2 marks each)

1.

• Answer: 5 : 8
• Working: Total fruits = 3 + 5 = 8 parts. Ratio of oranges to total = 5 : 8.
• Explanation: The ratio of apples to oranges is 3:5. This means for every 3 apples, there are 5 oranges. The total number of fruits is 3 + 5 = 8 parts. The question asks for the ratio of oranges (5 parts) to the total (8 parts), so the answer is 5:8.
• Marking: 1 mark for correct ratio parts, 1 mark for correct order.

2.

• Answer: 84 cm
• Working: 2 parts = 24 cm, so 1 part = 24 ÷ 2 = 12 cm. Longer piece = 7 parts = 7 × 12 = 84 cm.
• Explanation: The ratio 2:7 means the ribbon is cut into 2 + 7 = 9 equal parts. The shorter piece is 2 parts, which is 24 cm. Therefore, 1 part is 24 ÷ 2 = 12 cm. The longer piece is 7 parts, so its length is 7 × 12 = 84 cm.
• Marking: 1 mark for finding 1 part, 1 mark for correct final answer.

3.

• Answer: 45 pupils
• Working: 4 parts = 20 boys, so 1 part = 20 ÷ 4 = 5 pupils. Total pupils = 4 + 5 = 9 parts = 9 × 5 = 45 pupils.
• Explanation: The ratio of boys to girls is 4:5. This means there are 4 parts boys and 5 parts girls. 4 parts represent 20 boys, so 1 part is 20 ÷ 4 = 5 pupils. The total number of pupils is 4 + 5 = 9 parts, which is 9 × 5 = 45 pupils.
• Marking: 1 mark for finding 1 part, 1 mark for correct total.

4.

• Answer: 36 years old
• Working: 1 part = 9 years. Father's age = 4 parts = 4 × 9 = 36 years.
• Explanation: The ratio of Ahmad's age to his father's age is 1:4. This means Ahmad's age is 1 part and his father's age is 4 parts. Ahmad is 9 years old, which is 1 part. Therefore, his father's age is 4 × 9 = 36 years.
• Marking: 1 mark for identifying 1 part, 1 mark for correct answer.

5.

• Answer: 30 pears
• Working: 3 parts = 45 apples, so 1 part = 45 ÷ 3 = 15 fruits. Pears = 2 parts = 2 × 15 = 30 pears.
• Explanation: The ratio of apples to pears is 3:2. 3 parts represent 45 apples, so 1 part is 45 ÷ 3 = 15 fruits. The number of pears is 2 parts, which is 2 × 15 = 30 pears.
• Marking: 1 mark for finding 1 part, 1 mark for correct answer.

Section B (Questions 6 to 15: 3 marks each)

6.

• Answer: 104 red marbles
• Working: 5 parts = 65 marbles, so 1 part = 65 ÷ 5 = 13 marbles. Red marbles = 8 parts = 8 × 13 = 104 marbles.
• Explanation: The ratio of blue to red marbles is 5:8. 5 parts represent 65 blue marbles, so 1 part is 65 ÷ 5 = 13 marbles. The number of red marbles is 8 parts, which is 8 × 13 = 104 marbles.
• Marking: 1 mark for finding 1 part, 1 mark for correct method, 1 mark for correct answer.

7.

• Answer: $72
• Working: 3 parts = $27, so 1 part =$27 ÷ 3 = $9. Total sum = 3 + 5 = 8 parts = 8 ×$9 = $72.
• Explanation: The ratio of Ben's share to Chris's share is 3:5. Ben receives $27, which is 3 parts. Therefore, 1 part is$27 ÷ 3 = $9. The total sum is 3 + 5 = 8 parts, which is 8 ×$9 = $72.
• Marking: 1 mark for finding 1 part, 1 mark for correct method, 1 mark for correct answer.

8.

• Answer: 176 cm
• Working: 7 parts = 56 cm, so 1 part = 56 ÷ 7 = 8 cm. Breadth = 4 parts = 4 × 8 = 32 cm. Perimeter = 2 × (length + breadth) = 2 × (56 + 32) = 2 × 88 = 176 cm.
• Explanation: The ratio of length to breadth is 7:4. The length is 56 cm, which is 7 parts. So 1 part is 56 ÷ 7 = 8 cm. The breadth is 4 parts, which is 4 × 8 = 32 cm. The perimeter of a rectangle is 2 × (length + breadth) = 2 × (56 + 32) = 2 × 88 = 176 cm.
• Marking: 1 mark for finding breadth, 1 mark for correct perimeter formula, 1 mark for correct answer.

9.

• Answer: 12 tables
• Working: 9 parts = 54 chairs, so 1 part = 54 ÷ 9 = 6 items. Tables = 2 parts = 2 × 6 = 12 tables.
• Explanation: The ratio of chairs to tables is 9:2. 9 parts represent 54 chairs, so 1 part is 54 ÷ 9 = 6 items. The number of tables is 2 parts, which is 2 × 6 = 12 tables.
• Marking: 1 mark for finding 1 part, 1 mark for correct method, 1 mark for correct answer.

10.

• Answer: 60 cm
• Working: 1 part = 12 cm. Longest piece = 5 parts = 5 × 12 = 60 cm.
• Explanation: The wire is cut into three pieces in the ratio 1:3:5. The shortest piece is 1 part, which is 12 cm. The longest piece is 5 parts, so its length is 5 × 12 = 60 cm.
• Marking: 1 mark for identifying 1 part, 1 mark for correct method, 1 mark for correct answer.

11.

• Answer: 8 stamps
• Working: 2 parts = 40 stamps, so 1 part = 40 ÷ 2 = 20 stamps. Ali has 40 stamps, Bala has 3 × 20 = 60 stamps. Total stamps = 40 + 60 = 100. To have the same number, each must have 100 ÷ 2 = 50 stamps. Bala must give 60 - 50 = 10 stamps to Ali.
• Explanation: The ratio of Ali's stamps to Bala's stamps is 2:3. Ali has 40 stamps, which is 2 parts, so 1 part is 20 stamps. Bala has 3 × 20 = 60 stamps. The total number of stamps is 40 + 60 = 100. For them to have the same number, each must have 100 ÷ 2 = 50 stamps. Bala currently has 60, so he must give 60 - 50 = 10 stamps to Ali.
• Marking: 1 mark for finding Bala's stamps, 1 mark for finding equal share, 1 mark for correct answer.

12.

• Answer: 1000 ml
• Working: 3 parts = 600 ml, so 1 part = 600 ÷ 3 = 200 ml. Flour = 5 parts = 5 × 200 = 1000 ml.
• Explanation: The ratio of flour to milk is 5:3. 3 parts represent 600 ml of milk, so 1 part is 600 ÷ 3 = 200 ml. The amount of flour needed is 5 parts, which is 5 × 200 = 1000 ml.
• Marking: 1 mark for finding 1 part, 1 mark for correct method, 1 mark for correct answer.

13.

• Answer: 144 pupils
• Working: Difference in ratio parts = 9 - 7 = 2 parts. 2 parts = 18 pupils, so 1 part = 18 ÷ 2 = 9 pupils. Total pupils = 7 + 9 = 16 parts = 16 × 9 = 144 pupils.
• Explanation: The ratio of boys to girls is 7:9. The difference in the number of girls and boys is 9 - 7 = 2 parts. This difference is given as 18 pupils. Therefore, 2 parts = 18 pupils, so 1 part = 18 ÷ 2 = 9 pupils. The total number of pupils is 7 + 9 = 16 parts, which is 16 × 9 = 144 pupils.
• Marking: 1 mark for finding the difference in parts, 1 mark for finding 1 part, 1 mark for correct answer.

14.

• Answer: 20 red pens
• Working: 3 parts = 30 blue pens, so 1 part = 30 ÷ 3 = 10 pens. Red pens = 2 parts = 2 × 10 = 20 red pens.
• Explanation: The ratio of red to blue to green pens is 2:3:5. 3 parts represent 30 blue pens, so 1 part is 30 ÷ 3 = 10 pens. The number of red pens is 2 parts, which is 2 × 10 = 20 red pens.
• Marking: 1 mark for finding 1 part, 1 mark for correct method, 1 mark for correct answer.

15.

• Answer: 2 $5 notes
• Working: Let the number of $2 notes be 4 units and the number of$5 notes be 1 unit. Total value = (4 units × $2) + (1 unit ×$5) = 8 units + 5 units = 13 units. 13 units = $52, so 1 unit =$52 ÷ 13 = $4. Number of$5 notes = 1 unit = 2 notes.
• Explanation: The ratio of $2 notes to$5 notes is 4:1. Let the number of $2 notes be 4 units and the number of$5 notes be 1 unit. The total value is (4 units × $2) + (1 unit ×$5) = 8 units + 5 units = 13 units. This total value is $52, so 13 units =$52. Therefore, 1 unit = $52 ÷ 13 =$4. Since each $5 note is counted as 1 unit, the number of$5 notes is 1 unit, which is 2 notes.
• Marking: 1 mark for setting up the value equation, 1 mark for finding 1 unit, 1 mark for correct answer.

Section C (Questions 16 to 20: 4 marks each)

16.

• Answer: 60 stickers
• Working: Let May's stickers be 5 units and June's stickers be 2 units. Total stickers = 5 + 2 = 7 units. After May gives 18 stickers to June, they have the same number, so each has 7 units ÷ 2 = 3.5 units. May gives away 5 units - 3.5 units = 1.5 units. 1.5 units = 18 stickers, so 1 unit = 18 ÷ 1.5 = 12 stickers. May at first = 5 units = 5 × 12 = 60 stickers.
• Explanation: The initial ratio of May's stickers to June's stickers is 5:2. Let May have 5 units and June have 2 units. The total number of stickers is 5 + 2 = 7 units. After May gives 18 stickers to June, they have the same number. This means each has half of the total, which is 7 units ÷ 2 = 3.5 units. May gives away 5 units - 3.5 units = 1.5 units. This 1.5 units is equal to 18 stickers. Therefore, 1 unit = 18 ÷ 1.5 = 12 stickers. May initially had 5 units, which is 5 × 12 = 60 stickers.
• Marking: 1 mark for finding the number of units each has after transfer, 1 mark for finding the number of units given away, 1 mark for finding 1 unit, 1 mark for correct answer.

17.

• Answer: 15 50-cent coins
• Working: Let the number of 20-cent coins be 5 units and the number of 50-cent coins be 3 units. Total value = (5 units × $0.20) + (3 units ×$0.50) = 1 unit + 1.5 units = 2.5 units. 2.5 units = $12.50, so 1 unit =$12.50 ÷ 2.5 = $5.00. Number of 50-cent coins = 3 units = 3 × 5 = 15 coins.
• Explanation: The ratio of 20-cent coins to 50-cent coins is 5:3. Let the number of 20-cent coins be 5 units and the number of 50-cent coins be 3 units. The total value is (5 units × $0.20) + (3 units ×$0.50) = $1.00 per unit +$1.50 per unit = $2.50 per unit. This total value is$12.50, so 2.5 units = $12.50. Therefore, 1 unit =$12.50 ÷ 2.5 = $5.00. The number of 50-cent coins is 3 units, which is 3 × 5 = 15 coins.
• Marking: 1 mark for setting up the value equation, 1 mark for finding 1 unit, 1 mark for correct method, 1 mark for correct answer.

18.

• Answer: 27 pupils
• Working: Let Class A have 3 units and Class B have 4 units. Total pupils = 3 + 4 = 7 units. After transfer, Class A has 3 units + 6 and Class B has 4 units - 6. The new ratio is (3 units + 6) : (4 units - 6) = 5 : 6. Cross-multiply: 6(3 units + 6) = 5(4 units - 6) → 18 units + 36 = 20 units - 30 → 36 + 30 = 20 units - 18 units → 66 = 2 units → 1 unit = 33. Class A at first = 3 units = 3 × 33 = 99 pupils.
• Explanation: The initial ratio of Class A to Class B is 3:4. Let Class A have 3 units and Class B have 4 units. The total number of pupils is 7 units. After 6 pupils transfer from Class B to Class A, Class A has 3 units + 6 pupils and Class B has 4 units - 6 pupils. The new ratio is (3 units + 6) : (4 units - 6) = 5 : 6. Cross-multiplying gives 6(3 units + 6) = 5(4 units - 6). This simplifies to 18 units + 36 = 20 units - 30. Rearranging gives 36 + 30 = 20 units - 18 units, so 66 = 2 units. Therefore, 1 unit = 33 pupils. Class A initially had 3 units, which is 3 × 33 = 99 pupils.
• Marking: 1 mark for setting up the before-after expressions, 1 mark for forming the ratio equation, 1 mark for solving for 1 unit, 1 mark for correct answer.

19.

• Answer: 60 vanilla cakes
• Working: Let chocolate cakes be 7 units and vanilla cakes be 3 units. After selling 40 chocolate cakes, chocolate cakes become 7 units - 40. The new ratio is (7 units - 40) : 3 units = 3 : 2. Cross-multiply: 2(7 units - 40) = 3(3 units) → 14 units - 80 = 9 units → 14 units - 9 units = 80 → 5 units = 80 → 1 unit = 16. Vanilla cakes = 3 units = 3 × 16 = 60 vanilla cakes.
• Explanation: The initial ratio of chocolate cakes to vanilla cakes is 7:3. Let chocolate cakes be 7 units and vanilla cakes be 3 units. After selling 40 chocolate cakes, the number of chocolate cakes becomes 7 units - 40. The new ratio is (7 units - 40) : 3 units = 3 : 2. Cross-multiplying gives 2(7 units - 40) = 3(3 units). This simplifies to 14 units - 80 = 9 units. Rearranging gives 14 units - 9 units = 80, so 5 units = 80. Therefore, 1 unit = 16 cakes. The number of vanilla cakes is 3 units, which is 3 × 16 = 60 vanilla cakes.
• Marking: 1 mark for setting up the before-after expressions, 1 mark for forming the ratio equation, 1 mark for solving for 1 unit, 1 mark for correct answer.

20.

• Answer: 840 girls
• Working: Let boys be 5 units and girls be 7 units. After 60 new boys join, boys become 5 units + 60. The new ratio is (5 units + 60) : 7 units = 3 : 4. Cross-multiply: 4(5 units + 60) = 3(7 units) → 20 units + 240 = 21 units → 240 = 21 units - 20 units → 240 = 1 unit. Girls = 7 units = 7 × 240 = 1680 girls.
• Explanation: The initial ratio of boys to girls is 5:7. Let boys be 5 units and girls be 7 units. After 60 new boys join, the number of boys becomes 5 units + 60. The new ratio is (5 units + 60) : 7 units = 3 : 4. Cross-multiplying gives 4(5 units + 60) = 3(7 units). This simplifies to 20 units + 240 = 21 units. Rearranging gives 240 = 21 units - 20 units, so 240 = 1 unit. The number of girls is 7 units, which is 7 × 240 = 1680 girls.
• Marking: 1 mark for setting up the before-after expressions, 1 mark for forming the ratio equation, 1 mark for solving for 1 unit, 1 mark for correct answer.