Lesson 9.1: Multi-Digit Multiplication Strategies
Comprehensive lesson on Multi-Digit Multiplication Strategies in Grade 5 Mathematics.
⏱️ Reading Time: 20 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Multiplication and Division
Eco-Packaging Plant: Calculating bulk box orders of 24 boxes with 35 items per carton.
💡 Core Mathematical Concepts: Multi-Digit Multiplication Strategies
Focus areas: Area model, partial products, and standard column algorithm..
| Concept / Term | Mathematical Meaning | Real-Life Application |
|---|---|---|
| Partial Products | Multiplying tens and ones separately before combining | (20 × 30) + (20 × 5) + (4 × 30) + (4 × 5) |
| Multiplying by Multiples of 10 | Multiply non-zero digits and append zeros | 40 × 600 = 24,000 |
| Distributive Property | a × (b + c) = (a × b) + (a × c) | 18 × 15 = (18 × 10) + (18 × 5) = 180 + 90 = 270 |
📝 Step-by-Step Worked Examples
Worked Example 1: Multiply 245 × 12
245 × 10 = 2,450; 245 × 2 = 490; 2,450 + 490 = 2,940.
Worked Example 2: Multiply 38 × 45
(30 × 40) + (30 × 5) + (8 × 40) + (8 × 5) = 1,200 + 150 + 320 + 40 = 1,710.
⚠️ Common Misconceptions to Avoid
Common Misconception: Forgetting the placeholder zero
Correction: When multiplying by the tens digit, place a 0 in the ones column first.
Common Misconception: Misaligning partial products
Correction: Keep place-value columns strictly aligned when adding partial results.
🎯
Self-Check Challenge
A community library orders 35 boxes of books. Each box contains 24 novels. How many novels were ordered in total?
Answer & Explanation:
35 × 24 = 35 × (20 + 4) = 700 + 140 = 840 novels.
🎯 Key Learning Takeaways
Master core definitions of Multi-Digit Multiplication Strategies.
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-CH09-WS05
A4 • 15 Qs
Multiplication and Division: Worksheet 5
Practice Assessment 5 • Central Botanical Gardens Context
G5-M-CH09-WS04
A4 • 15 Qs
Multiplication and Division: Worksheet 4
Practice Assessment 4 • Eco-Friendly Solar Park Context
G5-M-CH09-WS03
A4 • 15 Qs
Multiplication and Division: Worksheet 3
Practice Assessment 3 • Harbor Marine Terminal Context
G5-M-CH09-WS02
A4 • 15 Qs
Multiplication and Division: Worksheet 2
Practice Assessment 2 • Science & Discovery Museum Context
G5-M-CH09-WS01
A4 • 15 Qs
Multiplication and Division: 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 warehouse packed 3,420 laptops into crates of 36. If each filled crate sells for $14,400, what is the value of all packed crates?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$1,368,000
Step-by-Step Explanation:
Number of crates = 3,420 ÷ 36 = 95 crates. Total value = 95 × $14,400 = $1,368,000.
2
Short Answer
Hard
2 Marks
A mystery 3-digit number multiplied by 18 gives a product ending in 0. When divided by 25, the remainder is 0. If the number is between 300 and 350, find the number.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
325 or 350
Step-by-Step Explanation:
Multiples of 25 between 300 and 350 are 325 and 350. Both satisfy the condition: 325 × 18 = 5,850; 350 × 18 = 6,300.
3
Short Answer
Hard
2 Marks
Why is division considered the inverse operation of multiplication? Show using 48 ÷ 6 = 8.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Division undoes multiplication: if 6 × 8 = 48, then 48 ÷ 6 = 8 and 48 ÷ 8 = 6. They represent the same fact family.
Step-by-Step Explanation:
Multiplication packages equal groups; division unpacks totals into equal groups.
4
Short Answer
Hard
2 Marks
Explain why multiplying any number by 25 is equivalent to multiplying by 100 and then dividing by 4.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Since 25 = 100 ÷ 4, multiplying by 25 is mathematically identical to scaling by 100 and dividing by 4 (e.g. 36 × 25 = 3,600 ÷ 4 = 900).
Step-by-Step Explanation:
25 is 100/4, allowing rapid mental calculation using decimal place shifts.
5
Short Answer
Medium
1 Mark
When dividing 500 by 8, a student writes 'Quotient = 62, Remainder = 8'. What fundamental rule of division was violated?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Remainder must be strictly less than divisor (Remainder is 4, not 8)
Step-by-Step Explanation:
The remainder can never equal or exceed the divisor (8). 500 ÷ 8 = 62 R 4.
6
Short Answer
Medium
1 Mark
A student calculates 304 × 12 as follows: 304 × 10 = 3040, 304 × 2 = 608, sum = 9120. Identify the mistake and write the correct product.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3,648
Step-by-Step Explanation:
The student misaligned the partial products during addition. Correct sum = 3,040 + 608 = 3,648.
7
Fill in the Blanks
Medium
1 Mark
Complete the division equation: [ ? ] ÷ 16 = 25.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
400
Step-by-Step Explanation:
25 × 16 = 400.
8
Fill in the Blanks
Medium
1 Mark
Find the missing factor: 45 × [ ? ] = 1,350.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
30
Step-by-Step Explanation:
1,350 ÷ 45 = 30.
9
Short Answer
Medium
1 Mark
A school field trip has 285 students. Each tour bus holds 48 passengers. How many buses must be chartered so every student has a seat?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 buses
Step-by-Step Explanation:
285 ÷ 48 = 5 with remainder 45. To seat all students, 6 buses are needed.
10
Short Answer
Medium
1 Mark
A carton holds 24 bottles of mineral water. If a charity receives 1,560 bottles, how many complete cartons can be packed?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
65 cartons
Step-by-Step Explanation:
1,560 ÷ 24 = 65 complete cartons.
11
Short Answer
Medium
1 Mark
At the Central Botanical Gardens, an auditorium has 28 rows of seats with 35 seats in each row. What is the total seating capacity?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
980 seats
Step-by-Step Explanation:
Multiply rows by seats per row: 28 × 35 = 980 seats.
12
Multiple Choice
Easy
1 Mark
Which multiplication strategy uses the distributive property to solve 24 × 15?
A
(24 × 10) + (24 × 5)
B
(20 × 10) + (4 × 5)
C
(24 + 10) × 5
D
24 × 10 × 5
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(24 × 10) + (24 × 5)
Step-by-Step Explanation:
Distributive property splits 15 into 10 + 5: (24 × 10) + (24 × 5) = 240 + 120 = 360.
13
Multiple Choice
Easy
1 Mark
What is the remainder when 487 is divided by 15?
A
7
B
5
C
12
D
0
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7
Step-by-Step Explanation:
487 ÷ 15 = 32 with a remainder of 7 (15 × 32 = 480; 487 - 480 = 7).
14
Multiple Choice
Easy
1 Mark
Divide: 2,040 ÷ 12.
A
170
B
160
C
182
D
175
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
170
Step-by-Step Explanation:
2,040 ÷ 12 = 170.
15
Multiple Choice
Easy
1 Mark
Evaluate: 305 × 22.
A
6,710
B
6,690
C
6,810
D
6,610
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6,710
Step-by-Step Explanation:
Multiply 305 × 22 = 6,710.
16
Short Answer
Hard
2 Marks
A warehouse packed 3,420 laptops into crates of 36. If each filled crate sells for $14,400, what is the value of all packed crates?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$1,368,000
Step-by-Step Explanation:
Number of crates = 3,420 ÷ 36 = 95 crates. Total value = 95 × $14,400 = $1,368,000.
17
Short Answer
Hard
2 Marks
A mystery 3-digit number multiplied by 18 gives a product ending in 0. When divided by 25, the remainder is 0. If the number is between 300 and 350, find the number.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
325 or 350
Step-by-Step Explanation:
Multiples of 25 between 300 and 350 are 325 and 350. Both satisfy the condition: 325 × 18 = 5,850; 350 × 18 = 6,300.
18
Short Answer
Hard
2 Marks
Why is division considered the inverse operation of multiplication? Show using 48 ÷ 6 = 8.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Division undoes multiplication: if 6 × 8 = 48, then 48 ÷ 6 = 8 and 48 ÷ 8 = 6. They represent the same fact family.
Step-by-Step Explanation:
Multiplication packages equal groups; division unpacks totals into equal groups.
19
Short Answer
Hard
2 Marks
Explain why multiplying any number by 25 is equivalent to multiplying by 100 and then dividing by 4.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Since 25 = 100 ÷ 4, multiplying by 25 is mathematically identical to scaling by 100 and dividing by 4 (e.g. 36 × 25 = 3,600 ÷ 4 = 900).
Step-by-Step Explanation:
25 is 100/4, allowing rapid mental calculation using decimal place shifts.
20
Short Answer
Medium
1 Mark
When dividing 500 by 8, a student writes 'Quotient = 62, Remainder = 8'. What fundamental rule of division was violated?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Remainder must be strictly less than divisor (Remainder is 4, not 8)
Step-by-Step Explanation:
The remainder can never equal or exceed the divisor (8). 500 ÷ 8 = 62 R 4.
21
Short Answer
Medium
1 Mark
A student calculates 304 × 12 as follows: 304 × 10 = 3040, 304 × 2 = 608, sum = 9120. Identify the mistake and write the correct product.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3,648
Step-by-Step Explanation:
The student misaligned the partial products during addition. Correct sum = 3,040 + 608 = 3,648.
22
Fill in the Blanks
Medium
1 Mark
Complete the division equation: [ ? ] ÷ 16 = 25.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
400
Step-by-Step Explanation:
25 × 16 = 400.
23
Fill in the Blanks
Medium
1 Mark
Find the missing factor: 45 × [ ? ] = 1,350.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
30
Step-by-Step Explanation:
1,350 ÷ 45 = 30.
24
Short Answer
Medium
1 Mark
A school field trip has 285 students. Each tour bus holds 48 passengers. How many buses must be chartered so every student has a seat?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 buses
Step-by-Step Explanation:
285 ÷ 48 = 5 with remainder 45. To seat all students, 6 buses are needed.
25
Short Answer
Medium
1 Mark
A carton holds 24 bottles of mineral water. If a charity receives 1,560 bottles, how many complete cartons can be packed?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
65 cartons
Step-by-Step Explanation:
1,560 ÷ 24 = 65 complete cartons.
26
Short Answer
Medium
1 Mark
At the Eco-Friendly Solar Park, an auditorium has 28 rows of seats with 35 seats in each row. What is the total seating capacity?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
980 seats
Step-by-Step Explanation:
Multiply rows by seats per row: 28 × 35 = 980 seats.
27
Multiple Choice
Easy
1 Mark
Which multiplication strategy uses the distributive property to solve 24 × 15?
A
(24 × 10) + (24 × 5)
B
(20 × 10) + (4 × 5)
C
(24 + 10) × 5
D
24 × 10 × 5
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(24 × 10) + (24 × 5)
Step-by-Step Explanation:
Distributive property splits 15 into 10 + 5: (24 × 10) + (24 × 5) = 240 + 120 = 360.
28
Multiple Choice
Easy
1 Mark
What is the remainder when 487 is divided by 15?
A
7
B
5
C
12
D
0
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7
Step-by-Step Explanation:
487 ÷ 15 = 32 with a remainder of 7 (15 × 32 = 480; 487 - 480 = 7).
29
Multiple Choice
Easy
1 Mark
Divide: 1,920 ÷ 12.
A
160
B
150
C
172
D
165
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
160
Step-by-Step Explanation:
1,920 ÷ 12 = 160.
30
Multiple Choice
Easy
1 Mark
Evaluate: 290 × 20.
A
5,800
B
5,780
C
5,900
D
5,700
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5,800
Step-by-Step Explanation:
Multiply 290 × 20 = 5,800.
31
Short Answer
Hard
2 Marks
A warehouse packed 3,420 laptops into crates of 36. If each filled crate sells for $14,400, what is the value of all packed crates?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$1,368,000
Step-by-Step Explanation:
Number of crates = 3,420 ÷ 36 = 95 crates. Total value = 95 × $14,400 = $1,368,000.
32
Short Answer
Hard
2 Marks
A mystery 3-digit number multiplied by 18 gives a product ending in 0. When divided by 25, the remainder is 0. If the number is between 300 and 350, find the number.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
325 or 350
Step-by-Step Explanation:
Multiples of 25 between 300 and 350 are 325 and 350. Both satisfy the condition: 325 × 18 = 5,850; 350 × 18 = 6,300.
33
Short Answer
Hard
2 Marks
Why is division considered the inverse operation of multiplication? Show using 48 ÷ 6 = 8.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Division undoes multiplication: if 6 × 8 = 48, then 48 ÷ 6 = 8 and 48 ÷ 8 = 6. They represent the same fact family.
Step-by-Step Explanation:
Multiplication packages equal groups; division unpacks totals into equal groups.
34
Short Answer
Hard
2 Marks
Explain why multiplying any number by 25 is equivalent to multiplying by 100 and then dividing by 4.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Since 25 = 100 ÷ 4, multiplying by 25 is mathematically identical to scaling by 100 and dividing by 4 (e.g. 36 × 25 = 3,600 ÷ 4 = 900).
Step-by-Step Explanation:
25 is 100/4, allowing rapid mental calculation using decimal place shifts.
35
Short Answer
Medium
1 Mark
When dividing 500 by 8, a student writes 'Quotient = 62, Remainder = 8'. What fundamental rule of division was violated?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Remainder must be strictly less than divisor (Remainder is 4, not 8)
Step-by-Step Explanation:
The remainder can never equal or exceed the divisor (8). 500 ÷ 8 = 62 R 4.
36
Short Answer
Medium
1 Mark
A student calculates 304 × 12 as follows: 304 × 10 = 3040, 304 × 2 = 608, sum = 9120. Identify the mistake and write the correct product.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3,648
Step-by-Step Explanation:
The student misaligned the partial products during addition. Correct sum = 3,040 + 608 = 3,648.
37
Fill in the Blanks
Medium
1 Mark
Complete the division equation: [ ? ] ÷ 16 = 25.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
400
Step-by-Step Explanation:
25 × 16 = 400.
38
Fill in the Blanks
Medium
1 Mark
Find the missing factor: 45 × [ ? ] = 1,350.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
30
Step-by-Step Explanation:
1,350 ÷ 45 = 30.
39
Short Answer
Medium
1 Mark
A school field trip has 285 students. Each tour bus holds 48 passengers. How many buses must be chartered so every student has a seat?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 buses
Step-by-Step Explanation:
285 ÷ 48 = 5 with remainder 45. To seat all students, 6 buses are needed.
40
Short Answer
Medium
1 Mark
A carton holds 24 bottles of mineral water. If a charity receives 1,560 bottles, how many complete cartons can be packed?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
65 cartons
Step-by-Step Explanation:
1,560 ÷ 24 = 65 complete cartons.
41
Short Answer
Medium
1 Mark
At the Harbor Marine Terminal, an auditorium has 28 rows of seats with 35 seats in each row. What is the total seating capacity?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
980 seats
Step-by-Step Explanation:
Multiply rows by seats per row: 28 × 35 = 980 seats.
42
Multiple Choice
Easy
1 Mark
Which multiplication strategy uses the distributive property to solve 24 × 15?
A
(24 × 10) + (24 × 5)
B
(20 × 10) + (4 × 5)
C
(24 + 10) × 5
D
24 × 10 × 5
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(24 × 10) + (24 × 5)
Step-by-Step Explanation:
Distributive property splits 15 into 10 + 5: (24 × 10) + (24 × 5) = 240 + 120 = 360.
43
Multiple Choice
Easy
1 Mark
What is the remainder when 487 is divided by 15?
A
7
B
5
C
12
D
0
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
7
Step-by-Step Explanation:
487 ÷ 15 = 32 with a remainder of 7 (15 × 32 = 480; 487 - 480 = 7).
44
Multiple Choice
Easy
1 Mark
Divide: 1,800 ÷ 12.
A
150
B
140
C
162
D
155
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
150
Step-by-Step Explanation:
1,800 ÷ 12 = 150.
45
Multiple Choice
Easy
1 Mark
Evaluate: 275 × 18.
A
4,950
B
4,930
C
5,050
D
4,850
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4,950
Step-by-Step Explanation:
Multiply 275 × 18 = 4,950.
46
Short Answer
Hard
2 Marks
A warehouse packed 3,420 laptops into crates of 36. If each filled crate sells for $14,400, what is the value of all packed crates?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
$1,368,000
Step-by-Step Explanation:
Number of crates = 3,420 ÷ 36 = 95 crates. Total value = 95 × $14,400 = $1,368,000.
47
Short Answer
Hard
2 Marks
A mystery 3-digit number multiplied by 18 gives a product ending in 0. When divided by 25, the remainder is 0. If the number is between 300 and 350, find the number.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
325 or 350
Step-by-Step Explanation:
Multiples of 25 between 300 and 350 are 325 and 350. Both satisfy the condition: 325 × 18 = 5,850; 350 × 18 = 6,300.
48
Short Answer
Hard
2 Marks
Why is division considered the inverse operation of multiplication? Show using 48 ÷ 6 = 8.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Division undoes multiplication: if 6 × 8 = 48, then 48 ÷ 6 = 8 and 48 ÷ 8 = 6. They represent the same fact family.
Step-by-Step Explanation:
Multiplication packages equal groups; division unpacks totals into equal groups.
49
Short Answer
Hard
2 Marks
Explain why multiplying any number by 25 is equivalent to multiplying by 100 and then dividing by 4.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Since 25 = 100 ÷ 4, multiplying by 25 is mathematically identical to scaling by 100 and dividing by 4 (e.g. 36 × 25 = 3,600 ÷ 4 = 900).
Step-by-Step Explanation:
25 is 100/4, allowing rapid mental calculation using decimal place shifts.
50
Short Answer
Medium
1 Mark
When dividing 500 by 8, a student writes 'Quotient = 62, Remainder = 8'. What fundamental rule of division was violated?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Remainder must be strictly less than divisor (Remainder is 4, not 8)
Step-by-Step Explanation:
The remainder can never equal or exceed the divisor (8). 500 ÷ 8 = 62 R 4.