Lesson 14.2: Division with Remainders and Real-Life Word Problems
Understand what happens when items cannot be divided evenly, interpret remainders, and solve practical sharing problems.
⏱️ Reading Time: 15 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Division and Equal Sharing
During a school camping trip, 23 students need to travel by minibus. If each minibus seats 5 students, 4 minibuses will carry 20 students, leaving 3 students behind. The camp leader must order a 5th minibus so no child is left behind!
💡 Core Mathematical Concepts: Remainders & Real-Life Problems
Focus areas: Dividend, divisor, quotient, remainder, word problems.
| Concept / Term | Mathematical Definition | Everyday Example |
|---|---|---|
| Dividend | The total amount being divided up | In 23 ÷ 5 = 4 R 3, 23 is the dividend |
| Divisor | The number of groups or group size dividing into the dividend | In 23 ÷ 5, 5 is the divisor |
| Quotient | The whole number result of the division | In 23 ÷ 5 = 4 R 3, 4 is the quotient |
| Remainder (R) | The amount left over when division is not exact; must be strictly less than the divisor | In 23 ÷ 5 = 4 R 3, remainder is 3 (3 < 5) |
🔍 Practical Classroom & Everyday Examples
Example 1: Remainder Rule
The remainder must always be strictly smaller than the divisor. If your remainder is greater than or equal to the divisor, you can make another whole group!
Example 2: Interpreting Remainders in Context
Sometimes you drop the remainder (e.g., number of complete shirts you can buy), and sometimes you round up (e.g., number of buses needed).
⚠️ Watch Out! Common Mistakes to Avoid
Common Error: Leaving a remainder larger than the divisor
Correction: If calculating 35 ÷ 4 and getting 7 R 7, 7 can still be divided by 4 once more to get 8 R 3.
Common Error: Forgetting unit labels in word problems
Correction: Always state what the quotient and remainder represent (e.g., 5 bags and 2 apples left over).
🎯 Quick Self-Check Challenge
A baker has 38 cookies and puts 4 cookies in each decorative box. How many full boxes can he make, and how many cookies remain?
Answer & Explanation:
38 ÷ 4 = 9 with a remainder of 2 (9 × 4 = 36, 38 - 36 = 2). He makes 9 full boxes with 2 cookies left over.
🎯 Key Learning Takeaways
Master Division and Equal Sharing fundamentals.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G3-M-CH14-WS05
A4 • 15 Qs
Division and Equal Sharing — Worksheet 5
Equal Groups, Quotients & Remainders (Library Book Donations Box)
G3-M-CH14-WS04
A4 • 15 Qs
Division and Equal Sharing — Worksheet 4
Equal Groups, Quotients & Remainders (Community Garden Seedlings)
G3-M-CH14-WS03
A4 • 15 Qs
Division and Equal Sharing — Worksheet 3
Equal Groups, Quotients & Remainders (Sports Team Uniform Storage)
G3-M-CH14-WS02
A4 • 15 Qs
Division and Equal Sharing — Worksheet 2
Equal Groups, Quotients & Remainders (Science Lab Experiment Kits)
G3-M-CH14-WS01
A4 • 15 Qs
Division and Equal Sharing — Worksheet 1
Equal Groups, Quotients & Remainders (School Bakery Counter)
✍️ 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
Three friends share a bag of marbles equally and each gets 9 marbles with 1 marble left over. How many marbles were in the bag originally?
A
28 marbles
B
27 marbles
C
29 marbles
D
26 marbles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 marbles
Step-by-Step Explanation:
(Quotient × Divisor) + Remainder = (9 × 3) + 1 = 28 marbles.
2
Short Answer
Hard
2 Marks
A school library received 259 new books. If each shelf holds exactly 9 books, how many shelves will be completely full, and how many more books are needed to fill the last incomplete shelf?
A
28 shelves full, and 2 more book(s) needed
B
29 shelves full, 0 needed
C
27 shelves full, 2 needed
D
28 shelves full, 6 needed
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 shelves full, and 2 more book(s) needed
Step-by-Step Explanation:
(259) ÷ 9 gives the number of full shelves and remainder.
3
Short Answer
Hard
2 Marks
If a number is divisible by both 2 and 3 with zero remainder, which of the following numbers must it also be divisible by?
A
6
B
5
C
8
D
9
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
A number divisible by both 2 and 3 is divisible by their product (2 × 3 = 6).
4
Short Answer
Hard
2 Marks
When any whole number is divided by 5, what are all the possible remainders that can result?
A
0, 1, 2, 3, or 4
B
1, 2, 3, 4, or 5
C
0, 1, 2, 3, 4, or 5
D
Only 0 or 5
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
0, 1, 2, 3, or 4
Step-by-Step Explanation:
A remainder must be strictly smaller than the divisor 5, so possible remainders are 0, 1, 2, 3, 4.
5
Short Answer
Medium
1 Mark
Tariq solved 24 ÷ 3 = 8 and checked his work by doing 8 - 3 = 5. What is the correct way to check a division problem?
A
Multiply the quotient by the divisor (8 × 3 = 24)
B
Add the quotient and divisor (8 + 3 = 11)
C
Subtract 24 - 8
D
Divide 24 by 8 and add 3
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Multiply the quotient by the divisor (8 × 3 = 24)
Step-by-Step Explanation:
Inverse of division is multiplication: quotient × divisor = dividend.
6
Short Answer
Medium
1 Mark
A student calculated 69 ÷ 9 and wrote the answer as '6 R 15'. What is the mistake?
A
The remainder (15) is greater than the divisor (9), meaning more whole groups can be formed
B
The remainder cannot be an even number
C
Division by single digits never produces remainders
D
Quotients can never be less than 10
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The remainder (15) is greater than the divisor (9), meaning more whole groups can be formed
Step-by-Step Explanation:
The remainder must always be strictly less than the divisor (9).
7
Fill in the Blanks
Medium
1 Mark
Find the missing divisor: 189 ÷ [ ? ] = 21
A
9
B
10
C
8
D
18
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
Divide total by quotient: (189) ÷ (21) = 9.
8
Fill in the Blanks
Medium
1 Mark
Find the missing dividend: [ ? ] ÷ 9 = 8
A
72
B
63
C
81
D
63
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
72
Step-by-Step Explanation:
Multiply quotient by divisor: 8 × 9 = 72.
9
Short Answer
Medium
1 Mark
During an event at the Library Book Donations Box, 49 participants need to sit in rows of 9. What is the minimum number of rows needed so everyone has a seat?
A
6 rows
B
5 rows
C
7 rows
D
4 rows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 rows
Step-by-Step Explanation:
49 ÷ 9 = 5 with 4 people remaining. A 6th row is required to seat everyone.
10
Short Answer
Medium
1 Mark
A baker has 68 cupcakes and packs them into boxes of 9. How many full boxes are packed, and how many cupcakes are left over?
A
7 boxes and 5 left over
B
8 boxes and 1 left over
C
6 boxes and 3 left over
D
7 boxes and 2 left over
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 boxes and 5 left over
Step-by-Step Explanation:
68 ÷ 9 = 7 with a remainder of 5 (since 5 < 11).
11
Short Answer
Medium
1 Mark
At the Library Book Donations Box, a supervisor has 126 items to divide equally among 9 work stations. How many items does each station get?
A
14 items
B
12 items
C
17 items
D
10 items
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14 items
Step-by-Step Explanation:
126 ÷ 9 = 14 items per station.
12
Multiple Choice
Easy
1 Mark
Evaluate: 0 ÷ 9 =
A
0
B
1
C
9
D
Undefined
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
0
Step-by-Step Explanation:
Zero divided by any non-zero number is always 0.
13
Multiple Choice
Easy
1 Mark
What is 81 ÷ 9?
A
9
B
8
C
10
D
7
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
Since 9 × 9 = 81, 81 ÷ 9 = 9.
14
Multiple Choice
Easy
1 Mark
Find the quotient and remainder: 66 ÷ 9 =
A
7 R 3
B
6 R 2
C
8 R 1
D
7 R 1
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 R 3
Step-by-Step Explanation:
9 × 7 = 63. 66 - 63 = 3 left over, so 7 R 3.
15
Multiple Choice
Easy
1 Mark
Calculate: 63 ÷ 9 =
A
7
B
6
C
8
D
9
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7
Step-by-Step Explanation:
63 divided by 9 equals 7 because 7 × 9 = 63.
16
Short Answer
Hard
2 Marks
Three friends share a bag of marbles equally and each gets 9 marbles with 1 marble left over. How many marbles were in the bag originally?
A
28 marbles
B
27 marbles
C
29 marbles
D
26 marbles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 marbles
Step-by-Step Explanation:
(Quotient × Divisor) + Remainder = (9 × 3) + 1 = 28 marbles.
17
Short Answer
Hard
2 Marks
A school library received 231 new books. If each shelf holds exactly 8 books, how many shelves will be completely full, and how many more books are needed to fill the last incomplete shelf?
A
28 shelves full, and 1 more book(s) needed
B
29 shelves full, 0 needed
C
27 shelves full, 2 needed
D
28 shelves full, 6 needed
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 shelves full, and 1 more book(s) needed
Step-by-Step Explanation:
(231) ÷ 8 gives the number of full shelves and remainder.
18
Short Answer
Hard
2 Marks
If a number is divisible by both 2 and 3 with zero remainder, which of the following numbers must it also be divisible by?
A
6
B
5
C
8
D
9
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
A number divisible by both 2 and 3 is divisible by their product (2 × 3 = 6).
19
Short Answer
Hard
2 Marks
When any whole number is divided by 5, what are all the possible remainders that can result?
A
0, 1, 2, 3, or 4
B
1, 2, 3, 4, or 5
C
0, 1, 2, 3, 4, or 5
D
Only 0 or 5
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
0, 1, 2, 3, or 4
Step-by-Step Explanation:
A remainder must be strictly smaller than the divisor 5, so possible remainders are 0, 1, 2, 3, 4.
20
Short Answer
Medium
1 Mark
Tariq solved 24 ÷ 3 = 8 and checked his work by doing 8 - 3 = 5. What is the correct way to check a division problem?
A
Multiply the quotient by the divisor (8 × 3 = 24)
B
Add the quotient and divisor (8 + 3 = 11)
C
Subtract 24 - 8
D
Divide 24 by 8 and add 3
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Multiply the quotient by the divisor (8 × 3 = 24)
Step-by-Step Explanation:
Inverse of division is multiplication: quotient × divisor = dividend.
21
Short Answer
Medium
1 Mark
A student calculated 62 ÷ 8 and wrote the answer as '6 R 14'. What is the mistake?
A
The remainder (14) is greater than the divisor (8), meaning more whole groups can be formed
B
The remainder cannot be an even number
C
Division by single digits never produces remainders
D
Quotients can never be less than 10
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The remainder (14) is greater than the divisor (8), meaning more whole groups can be formed
Step-by-Step Explanation:
The remainder must always be strictly less than the divisor (8).
22
Fill in the Blanks
Medium
1 Mark
Find the missing divisor: 168 ÷ [ ? ] = 21
A
8
B
9
C
7
D
16
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
8
Step-by-Step Explanation:
Divide total by quotient: (168) ÷ (21) = 8.
23
Fill in the Blanks
Medium
1 Mark
Find the missing dividend: [ ? ] ÷ 8 = 8
A
64
B
56
C
72
D
56
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
64
Step-by-Step Explanation:
Multiply quotient by divisor: 8 × 8 = 64.
24
Short Answer
Medium
1 Mark
During an event at the Community Garden Seedlings, 44 participants need to sit in rows of 8. What is the minimum number of rows needed so everyone has a seat?
A
6 rows
B
5 rows
C
7 rows
D
4 rows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 rows
Step-by-Step Explanation:
44 ÷ 8 = 5 with 4 people remaining. A 6th row is required to seat everyone.
25
Short Answer
Medium
1 Mark
A baker has 61 cupcakes and packs them into boxes of 8. How many full boxes are packed, and how many cupcakes are left over?
A
7 boxes and 5 left over
B
8 boxes and 1 left over
C
6 boxes and 3 left over
D
7 boxes and 2 left over
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 boxes and 5 left over
Step-by-Step Explanation:
61 ÷ 8 = 7 with a remainder of 5 (since 5 < 10).
26
Short Answer
Medium
1 Mark
At the Community Garden Seedlings, a supervisor has 112 items to divide equally among 8 work stations. How many items does each station get?
A
14 items
B
12 items
C
17 items
D
10 items
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14 items
Step-by-Step Explanation:
112 ÷ 8 = 14 items per station.
27
Multiple Choice
Easy
1 Mark
Evaluate: 0 ÷ 8 =
A
0
B
1
C
8
D
Undefined
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
0
Step-by-Step Explanation:
Zero divided by any non-zero number is always 0.
28
Multiple Choice
Easy
1 Mark
What is 72 ÷ 8?
A
9
B
8
C
10
D
7
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
Since 9 × 8 = 72, 72 ÷ 8 = 9.
29
Multiple Choice
Easy
1 Mark
Find the quotient and remainder: 59 ÷ 8 =
A
7 R 3
B
6 R 2
C
8 R 1
D
7 R 1
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 R 3
Step-by-Step Explanation:
8 × 7 = 56. 59 - 56 = 3 left over, so 7 R 3.
30
Multiple Choice
Easy
1 Mark
Calculate: 56 ÷ 8 =
A
7
B
6
C
8
D
9
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7
Step-by-Step Explanation:
56 divided by 8 equals 7 because 7 × 8 = 56.
31
Short Answer
Hard
2 Marks
Three friends share a bag of marbles equally and each gets 9 marbles with 1 marble left over. How many marbles were in the bag originally?
A
28 marbles
B
27 marbles
C
29 marbles
D
26 marbles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 marbles
Step-by-Step Explanation:
(Quotient × Divisor) + Remainder = (9 × 3) + 1 = 28 marbles.
32
Short Answer
Hard
2 Marks
A school library received 175 new books. If each shelf holds exactly 6 books, how many shelves will be completely full, and how many more books are needed to fill the last incomplete shelf?
A
28 shelves full, and 5 more book(s) needed
B
29 shelves full, 0 needed
C
27 shelves full, 2 needed
D
28 shelves full, 6 needed
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 shelves full, and 5 more book(s) needed
Step-by-Step Explanation:
(175) ÷ 6 gives the number of full shelves and remainder.
33
Short Answer
Hard
2 Marks
If a number is divisible by both 2 and 3 with zero remainder, which of the following numbers must it also be divisible by?
A
6
B
5
C
8
D
9
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
A number divisible by both 2 and 3 is divisible by their product (2 × 3 = 6).
34
Short Answer
Hard
2 Marks
When any whole number is divided by 5, what are all the possible remainders that can result?
A
0, 1, 2, 3, or 4
B
1, 2, 3, 4, or 5
C
0, 1, 2, 3, 4, or 5
D
Only 0 or 5
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
0, 1, 2, 3, or 4
Step-by-Step Explanation:
A remainder must be strictly smaller than the divisor 5, so possible remainders are 0, 1, 2, 3, 4.
35
Short Answer
Medium
1 Mark
Tariq solved 24 ÷ 3 = 8 and checked his work by doing 8 - 3 = 5. What is the correct way to check a division problem?
A
Multiply the quotient by the divisor (8 × 3 = 24)
B
Add the quotient and divisor (8 + 3 = 11)
C
Subtract 24 - 8
D
Divide 24 by 8 and add 3
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Multiply the quotient by the divisor (8 × 3 = 24)
Step-by-Step Explanation:
Inverse of division is multiplication: quotient × divisor = dividend.
36
Short Answer
Medium
1 Mark
A student calculated 48 ÷ 6 and wrote the answer as '6 R 12'. What is the mistake?
A
The remainder (12) is greater than the divisor (6), meaning more whole groups can be formed
B
The remainder cannot be an even number
C
Division by single digits never produces remainders
D
Quotients can never be less than 10
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
The remainder (12) is greater than the divisor (6), meaning more whole groups can be formed
Step-by-Step Explanation:
The remainder must always be strictly less than the divisor (6).
37
Fill in the Blanks
Medium
1 Mark
Find the missing divisor: 126 ÷ [ ? ] = 21
A
6
B
7
C
5
D
12
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
Divide total by quotient: (126) ÷ (21) = 6.
38
Fill in the Blanks
Medium
1 Mark
Find the missing dividend: [ ? ] ÷ 6 = 8
A
48
B
42
C
54
D
42
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
48
Step-by-Step Explanation:
Multiply quotient by divisor: 8 × 6 = 48.
39
Short Answer
Medium
1 Mark
During an event at the Sports Team Uniform Storage, 34 participants need to sit in rows of 6. What is the minimum number of rows needed so everyone has a seat?
A
6 rows
B
5 rows
C
7 rows
D
4 rows
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 rows
Step-by-Step Explanation:
34 ÷ 6 = 5 with 4 people remaining. A 6th row is required to seat everyone.
40
Short Answer
Medium
1 Mark
A baker has 47 cupcakes and packs them into boxes of 6. How many full boxes are packed, and how many cupcakes are left over?
A
7 boxes and 5 left over
B
8 boxes and 1 left over
C
6 boxes and 3 left over
D
7 boxes and 2 left over
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 boxes and 5 left over
Step-by-Step Explanation:
47 ÷ 6 = 7 with a remainder of 5 (since 5 < 8).
41
Short Answer
Medium
1 Mark
At the Sports Team Uniform Storage, a supervisor has 84 items to divide equally among 6 work stations. How many items does each station get?
A
14 items
B
12 items
C
17 items
D
10 items
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14 items
Step-by-Step Explanation:
84 ÷ 6 = 14 items per station.
42
Multiple Choice
Easy
1 Mark
Evaluate: 0 ÷ 6 =
A
0
B
1
C
6
D
Undefined
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
0
Step-by-Step Explanation:
Zero divided by any non-zero number is always 0.
43
Multiple Choice
Easy
1 Mark
What is 54 ÷ 6?
A
9
B
8
C
10
D
7
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
9
Step-by-Step Explanation:
Since 9 × 6 = 54, 54 ÷ 6 = 9.
44
Multiple Choice
Easy
1 Mark
Find the quotient and remainder: 45 ÷ 6 =
A
7 R 3
B
6 R 2
C
8 R 1
D
7 R 1
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7 R 3
Step-by-Step Explanation:
6 × 7 = 42. 45 - 42 = 3 left over, so 7 R 3.
45
Multiple Choice
Easy
1 Mark
Calculate: 42 ÷ 6 =
A
7
B
6
C
8
D
9
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7
Step-by-Step Explanation:
42 divided by 6 equals 7 because 7 × 6 = 42.
46
Short Answer
Hard
2 Marks
Three friends share a bag of marbles equally and each gets 9 marbles with 1 marble left over. How many marbles were in the bag originally?
A
28 marbles
B
27 marbles
C
29 marbles
D
26 marbles
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 marbles
Step-by-Step Explanation:
(Quotient × Divisor) + Remainder = (9 × 3) + 1 = 28 marbles.
47
Short Answer
Hard
2 Marks
A school library received 147 new books. If each shelf holds exactly 5 books, how many shelves will be completely full, and how many more books are needed to fill the last incomplete shelf?
A
28 shelves full, and 3 more book(s) needed
B
29 shelves full, 0 needed
C
27 shelves full, 2 needed
D
28 shelves full, 6 needed
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
28 shelves full, and 3 more book(s) needed
Step-by-Step Explanation:
(147) ÷ 5 gives the number of full shelves and remainder.
48
Short Answer
Hard
2 Marks
If a number is divisible by both 2 and 3 with zero remainder, which of the following numbers must it also be divisible by?
A
6
B
5
C
8
D
9
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6
Step-by-Step Explanation:
A number divisible by both 2 and 3 is divisible by their product (2 × 3 = 6).
49
Short Answer
Hard
2 Marks
When any whole number is divided by 5, what are all the possible remainders that can result?
A
0, 1, 2, 3, or 4
B
1, 2, 3, 4, or 5
C
0, 1, 2, 3, 4, or 5
D
Only 0 or 5
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
0, 1, 2, 3, or 4
Step-by-Step Explanation:
A remainder must be strictly smaller than the divisor 5, so possible remainders are 0, 1, 2, 3, 4.
50
Short Answer
Medium
1 Mark
Tariq solved 24 ÷ 3 = 8 and checked his work by doing 8 - 3 = 5. What is the correct way to check a division problem?
A
Multiply the quotient by the divisor (8 × 3 = 24)
B
Add the quotient and divisor (8 + 3 = 11)
C
Subtract 24 - 8
D
Divide 24 by 8 and add 3
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Multiply the quotient by the divisor (8 × 3 = 24)
Step-by-Step Explanation:
Inverse of division is multiplication: quotient × divisor = dividend.