Lesson 5.1: Fraction of a Collection
Comprehensive lesson on Fraction of a Collection in Grade 5 Mathematics.
⏱️ Reading Time: 20 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Fractions of a Number
Fruit Orchard Harvesting: Packing 3/4 of a batch of 120 organic honeycrisp apples into export crates.
💡 Core Mathematical Concepts: Fraction of a Collection
Focus areas: Divide by the denominator, then multiply by the numerator..
| Concept / Term | Mathematical Meaning | Real-Life Application |
|---|---|---|
| Unit Fraction of a Number | 1/n of Total = Total ÷ n | 1/5 of 60 = 12 |
| Non-Unit Fraction | (a/b) of Total = (Total ÷ b) × a | 3/4 of 48 = (48 ÷ 4) × 3 = 12 × 3 = 36 |
| Collection Division | Splitting an inventory into equal groups | Sharing quantities fairly |
📝 Step-by-Step Worked Examples
Worked Example 1: Find 2/3 of 45
45 ÷ 3 = 15; 15 × 2 = 30.
Worked Example 2: Find 5/8 of 64
64 ÷ 8 = 8; 8 × 5 = 40.
⚠️ Common Misconceptions to Avoid
Common Misconception: Multiplying before dividing
Correction: Dividing by the denominator first keeps numbers small and prevents arithmetic errors.
Common Misconception: Forgetting to multiply by numerator
Correction: Finding 1/4 of 40 = 10, but failing to multiply by 3 for 3/4.
🎯
Self-Check Challenge
A sports shop has 150 footballs. If 3/5 of them are sold during the weekend sale, how many footballs are left?
Answer & Explanation:
Sold: (150 ÷ 5) × 3 = 30 × 3 = 90. Left: 150 - 90 = 60 footballs.
🎯 Key Learning Takeaways
Master core definitions of Fraction of a Collection.
Apply mathematical principles to everyday scenarios.
Avoid common calculation and conceptual pitfalls.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G5-M-CH05-WS05
A4 • 15 Qs
Fractions of a Number: Worksheet 5
Practice Assessment 5 • Central Botanical Gardens Context
G5-M-CH05-WS04
A4 • 15 Qs
Fractions of a Number: Worksheet 4
Practice Assessment 4 • Eco-Friendly Solar Park Context
G5-M-CH05-WS03
A4 • 15 Qs
Fractions of a Number: Worksheet 3
Practice Assessment 3 • Harbor Marine Terminal Context
G5-M-CH05-WS02
A4 • 15 Qs
Fractions of a Number: Worksheet 2
Practice Assessment 2 • Science & Discovery Museum Context
G5-M-CH05-WS01
A4 • 15 Qs
Fractions of a Number: Worksheet 1
Practice Assessment 1 • City Regional Airport Context
✍️ Lesson Practice Questions (50 Questions)
Solve these real-world challenges online, test your understanding, and reveal instant step-by-step explanations.
1
Short Answer
Hard
2 Marks
A runner has completed 3/7 of a marathon course and has 24 km remaining. What is the total length of the marathon course?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
42 km
Step-by-Step Explanation:
Remaining fraction = 1 - 3/7 = 4/7. If 4/7 = 24 km, then 1/7 = 6 km. Total course = 6 × 7 = 42 km.
2
Short Answer
Hard
2 Marks
In a botanical garden, 2/5 of the 150 trees are flowering trees, and 1/3 of the flowering trees are cherry blossoms. How many cherry blossom trees are there?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
20 trees
Step-by-Step Explanation:
Flowering trees = 150 × 2/5 = 60. Cherry blossoms = 60 × 1/3 = 20 trees.
3
Short Answer
Hard
2 Marks
Show why 3/5 of 50 is equal to (3 × 50) ÷ 5 and explain whether order of operations matters.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3/5 of 50 = (50 ÷ 5) × 3 = 10 × 3 = 30. Also (3 × 50) ÷ 5 = 150 ÷ 5 = 30. Multiplication and division have equal priority, so order does not change the result.
Step-by-Step Explanation:
Multiplication and division are associative and commutative in rational scaling.
4
Short Answer
Hard
2 Marks
Explain why finding 1/4 of 48 gives the same result as dividing 48 by 4.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A fraction 1/n represents one equal share out of n equal parts. Dividing 48 into 4 equal shares distributes 12 into each part, which is mathematically identical to 1/4 of 48.
Step-by-Step Explanation:
Multiplying by 1/n is operationally equivalent to division by n.
5
Short Answer
Medium
1 Mark
Ella writes: '3/4 of 20 is equal to 3/4 + 20 = 20 3/4.' Correct Ella's conceptual misunderstanding and provide the right answer.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
'Of' indicates multiplication/grouping, not addition. 20 ÷ 4 = 5; 5 × 3 = 15.
6
Short Answer
Medium
1 Mark
Ben calculates 2/3 of 18 as: '18 ÷ 2 = 9, then 9 × 3 = 27.' What did Ben do wrong and what is the correct answer?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
12
Step-by-Step Explanation:
Ben divided by the numerator and multiplied by denominator. He should divide by 3 (18÷3=6) and multiply by 2 (6×2=12).
7
Fill in the Blanks
Medium
1 Mark
Fill in the missing fraction: [ ? ] of 40 = 25.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5/8
Step-by-Step Explanation:
25/40 simplified by dividing by 5 gives 5/8.
8
Fill in the Blanks
Medium
1 Mark
Find the mystery quantity: 2/3 of [ ? ] = 18.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
27
Step-by-Step Explanation:
If 2 parts = 18, then 1 part = 9. Whole quantity = 9 × 3 = 27.
9
Short Answer
Medium
1 Mark
A charity fundraiser collected $360. If 1/4 was spent on venue setup and 1/3 on food, how much total money was spent on these two items?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$210
Step-by-Step Explanation:
Venue: 360 ÷ 4 = $90. Food: 360 ÷ 3 = $120. Total spent = 90 + 120 = $210.
10
Short Answer
Medium
1 Mark
A school sports club has 80 members. 5/8 of the members play soccer. How many members play soccer?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
50 members
Step-by-Step Explanation:
80 ÷ 8 = 10. 10 × 5 = 50 soccer players.
11
Short Answer
Medium
1 Mark
At the Central Botanical Gardens, an orchard harvests 120 baskets of apples. If 3/5 of the baskets are red apples and the rest are green, how many baskets of red apples were harvested?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
72 baskets
Step-by-Step Explanation:
120 ÷ 5 = 24. 24 × 3 = 72 baskets of red apples.
12
Multiple Choice
Easy
1 Mark
Calculate 3/8 of 64.
A
24
B
16
C
32
D
28
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24
Step-by-Step Explanation:
64 ÷ 8 = 8; 8 × 3 = 24.
13
Multiple Choice
Easy
1 Mark
What is 5/6 of 72?
A
60
B
55
C
64
D
48
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
60
Step-by-Step Explanation:
72 ÷ 6 = 12; 12 × 5 = 60.
14
Multiple Choice
Easy
1 Mark
Evaluate 2/5 of 150 km.
A
60 km
B
50 km
C
75 km
D
40 km
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
60 km
Step-by-Step Explanation:
150 ÷ 5 = 30; 30 × 2 = 60 km.
15
Multiple Choice
Easy
1 Mark
Find 3/4 of 84.
A
63
B
42
C
21
D
67
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
63
Step-by-Step Explanation:
Divide by 4 (84 ÷ 4 = 21), then multiply by 3: 63.
16
Short Answer
Hard
2 Marks
A runner has completed 3/7 of a marathon course and has 24 km remaining. What is the total length of the marathon course?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
42 km
Step-by-Step Explanation:
Remaining fraction = 1 - 3/7 = 4/7. If 4/7 = 24 km, then 1/7 = 6 km. Total course = 6 × 7 = 42 km.
17
Short Answer
Hard
2 Marks
In a botanical garden, 2/5 of the 150 trees are flowering trees, and 1/3 of the flowering trees are cherry blossoms. How many cherry blossom trees are there?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
20 trees
Step-by-Step Explanation:
Flowering trees = 150 × 2/5 = 60. Cherry blossoms = 60 × 1/3 = 20 trees.
18
Short Answer
Hard
2 Marks
Show why 3/5 of 50 is equal to (3 × 50) ÷ 5 and explain whether order of operations matters.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3/5 of 50 = (50 ÷ 5) × 3 = 10 × 3 = 30. Also (3 × 50) ÷ 5 = 150 ÷ 5 = 30. Multiplication and division have equal priority, so order does not change the result.
Step-by-Step Explanation:
Multiplication and division are associative and commutative in rational scaling.
19
Short Answer
Hard
2 Marks
Explain why finding 1/4 of 48 gives the same result as dividing 48 by 4.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A fraction 1/n represents one equal share out of n equal parts. Dividing 48 into 4 equal shares distributes 12 into each part, which is mathematically identical to 1/4 of 48.
Step-by-Step Explanation:
Multiplying by 1/n is operationally equivalent to division by n.
20
Short Answer
Medium
1 Mark
Ella writes: '3/4 of 20 is equal to 3/4 + 20 = 20 3/4.' Correct Ella's conceptual misunderstanding and provide the right answer.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
'Of' indicates multiplication/grouping, not addition. 20 ÷ 4 = 5; 5 × 3 = 15.
21
Short Answer
Medium
1 Mark
Ben calculates 2/3 of 18 as: '18 ÷ 2 = 9, then 9 × 3 = 27.' What did Ben do wrong and what is the correct answer?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
12
Step-by-Step Explanation:
Ben divided by the numerator and multiplied by denominator. He should divide by 3 (18÷3=6) and multiply by 2 (6×2=12).
22
Fill in the Blanks
Medium
1 Mark
Fill in the missing fraction: [ ? ] of 40 = 25.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5/8
Step-by-Step Explanation:
25/40 simplified by dividing by 5 gives 5/8.
23
Fill in the Blanks
Medium
1 Mark
Find the mystery quantity: 2/3 of [ ? ] = 18.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
27
Step-by-Step Explanation:
If 2 parts = 18, then 1 part = 9. Whole quantity = 9 × 3 = 27.
24
Short Answer
Medium
1 Mark
A charity fundraiser collected $360. If 1/4 was spent on venue setup and 1/3 on food, how much total money was spent on these two items?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$210
Step-by-Step Explanation:
Venue: 360 ÷ 4 = $90. Food: 360 ÷ 3 = $120. Total spent = 90 + 120 = $210.
25
Short Answer
Medium
1 Mark
A school sports club has 80 members. 5/8 of the members play soccer. How many members play soccer?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
50 members
Step-by-Step Explanation:
80 ÷ 8 = 10. 10 × 5 = 50 soccer players.
26
Short Answer
Medium
1 Mark
At the Eco-Friendly Solar Park, an orchard harvests 120 baskets of apples. If 3/5 of the baskets are red apples and the rest are green, how many baskets of red apples were harvested?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
72 baskets
Step-by-Step Explanation:
120 ÷ 5 = 24. 24 × 3 = 72 baskets of red apples.
27
Multiple Choice
Easy
1 Mark
Calculate 3/8 of 64.
A
24
B
16
C
32
D
28
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24
Step-by-Step Explanation:
64 ÷ 8 = 8; 8 × 3 = 24.
28
Multiple Choice
Easy
1 Mark
What is 5/6 of 72?
A
60
B
55
C
64
D
48
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
60
Step-by-Step Explanation:
72 ÷ 6 = 12; 12 × 5 = 60.
29
Multiple Choice
Easy
1 Mark
Evaluate 2/5 of 150 km.
A
60 km
B
50 km
C
75 km
D
40 km
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
60 km
Step-by-Step Explanation:
150 ÷ 5 = 30; 30 × 2 = 60 km.
30
Multiple Choice
Easy
1 Mark
Find 3/4 of 72.
A
54
B
36
C
18
D
58
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
54
Step-by-Step Explanation:
Divide by 4 (72 ÷ 4 = 18), then multiply by 3: 54.
31
Short Answer
Hard
2 Marks
A runner has completed 3/7 of a marathon course and has 24 km remaining. What is the total length of the marathon course?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
42 km
Step-by-Step Explanation:
Remaining fraction = 1 - 3/7 = 4/7. If 4/7 = 24 km, then 1/7 = 6 km. Total course = 6 × 7 = 42 km.
32
Short Answer
Hard
2 Marks
In a botanical garden, 2/5 of the 150 trees are flowering trees, and 1/3 of the flowering trees are cherry blossoms. How many cherry blossom trees are there?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
20 trees
Step-by-Step Explanation:
Flowering trees = 150 × 2/5 = 60. Cherry blossoms = 60 × 1/3 = 20 trees.
33
Short Answer
Hard
2 Marks
Show why 3/5 of 50 is equal to (3 × 50) ÷ 5 and explain whether order of operations matters.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3/5 of 50 = (50 ÷ 5) × 3 = 10 × 3 = 30. Also (3 × 50) ÷ 5 = 150 ÷ 5 = 30. Multiplication and division have equal priority, so order does not change the result.
Step-by-Step Explanation:
Multiplication and division are associative and commutative in rational scaling.
34
Short Answer
Hard
2 Marks
Explain why finding 1/4 of 48 gives the same result as dividing 48 by 4.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A fraction 1/n represents one equal share out of n equal parts. Dividing 48 into 4 equal shares distributes 12 into each part, which is mathematically identical to 1/4 of 48.
Step-by-Step Explanation:
Multiplying by 1/n is operationally equivalent to division by n.
35
Short Answer
Medium
1 Mark
Ella writes: '3/4 of 20 is equal to 3/4 + 20 = 20 3/4.' Correct Ella's conceptual misunderstanding and provide the right answer.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
'Of' indicates multiplication/grouping, not addition. 20 ÷ 4 = 5; 5 × 3 = 15.
36
Short Answer
Medium
1 Mark
Ben calculates 2/3 of 18 as: '18 ÷ 2 = 9, then 9 × 3 = 27.' What did Ben do wrong and what is the correct answer?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
12
Step-by-Step Explanation:
Ben divided by the numerator and multiplied by denominator. He should divide by 3 (18÷3=6) and multiply by 2 (6×2=12).
37
Fill in the Blanks
Medium
1 Mark
Fill in the missing fraction: [ ? ] of 40 = 25.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5/8
Step-by-Step Explanation:
25/40 simplified by dividing by 5 gives 5/8.
38
Fill in the Blanks
Medium
1 Mark
Find the mystery quantity: 2/3 of [ ? ] = 18.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
27
Step-by-Step Explanation:
If 2 parts = 18, then 1 part = 9. Whole quantity = 9 × 3 = 27.
39
Short Answer
Medium
1 Mark
A charity fundraiser collected $360. If 1/4 was spent on venue setup and 1/3 on food, how much total money was spent on these two items?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$210
Step-by-Step Explanation:
Venue: 360 ÷ 4 = $90. Food: 360 ÷ 3 = $120. Total spent = 90 + 120 = $210.
40
Short Answer
Medium
1 Mark
A school sports club has 80 members. 5/8 of the members play soccer. How many members play soccer?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
50 members
Step-by-Step Explanation:
80 ÷ 8 = 10. 10 × 5 = 50 soccer players.
41
Short Answer
Medium
1 Mark
At the Harbor Marine Terminal, an orchard harvests 120 baskets of apples. If 3/5 of the baskets are red apples and the rest are green, how many baskets of red apples were harvested?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
72 baskets
Step-by-Step Explanation:
120 ÷ 5 = 24. 24 × 3 = 72 baskets of red apples.
42
Multiple Choice
Easy
1 Mark
Calculate 3/8 of 64.
A
24
B
16
C
32
D
28
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
24
Step-by-Step Explanation:
64 ÷ 8 = 8; 8 × 3 = 24.
43
Multiple Choice
Easy
1 Mark
What is 5/6 of 72?
A
60
B
55
C
64
D
48
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
60
Step-by-Step Explanation:
72 ÷ 6 = 12; 12 × 5 = 60.
44
Multiple Choice
Easy
1 Mark
Evaluate 2/5 of 150 km.
A
60 km
B
50 km
C
75 km
D
40 km
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
60 km
Step-by-Step Explanation:
150 ÷ 5 = 30; 30 × 2 = 60 km.
45
Multiple Choice
Easy
1 Mark
Find 3/4 of 60.
A
45
B
30
C
15
D
49
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
45
Step-by-Step Explanation:
Divide by 4 (60 ÷ 4 = 15), then multiply by 3: 45.
46
Short Answer
Hard
2 Marks
A runner has completed 3/7 of a marathon course and has 24 km remaining. What is the total length of the marathon course?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
42 km
Step-by-Step Explanation:
Remaining fraction = 1 - 3/7 = 4/7. If 4/7 = 24 km, then 1/7 = 6 km. Total course = 6 × 7 = 42 km.
47
Short Answer
Hard
2 Marks
In a botanical garden, 2/5 of the 150 trees are flowering trees, and 1/3 of the flowering trees are cherry blossoms. How many cherry blossom trees are there?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
20 trees
Step-by-Step Explanation:
Flowering trees = 150 × 2/5 = 60. Cherry blossoms = 60 × 1/3 = 20 trees.
48
Short Answer
Hard
2 Marks
Show why 3/5 of 50 is equal to (3 × 50) ÷ 5 and explain whether order of operations matters.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3/5 of 50 = (50 ÷ 5) × 3 = 10 × 3 = 30. Also (3 × 50) ÷ 5 = 150 ÷ 5 = 30. Multiplication and division have equal priority, so order does not change the result.
Step-by-Step Explanation:
Multiplication and division are associative and commutative in rational scaling.
49
Short Answer
Hard
2 Marks
Explain why finding 1/4 of 48 gives the same result as dividing 48 by 4.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A fraction 1/n represents one equal share out of n equal parts. Dividing 48 into 4 equal shares distributes 12 into each part, which is mathematically identical to 1/4 of 48.
Step-by-Step Explanation:
Multiplying by 1/n is operationally equivalent to division by n.
50
Short Answer
Medium
1 Mark
Ella writes: '3/4 of 20 is equal to 3/4 + 20 = 20 3/4.' Correct Ella's conceptual misunderstanding and provide the right answer.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
15
Step-by-Step Explanation:
'Of' indicates multiplication/grouping, not addition. 20 ÷ 4 = 5; 5 × 3 = 15.