Multiplication Of Whole Numbers Lesson– Concepts, Techniques & Practice
Lesson Overview
- What Are Whole Numbers?
- What Is Multiplication?
- Why Is Multiplication Important?
- Multiplication Vocabulary
- Basic Multiplication Facts
- Properties of Multiplication
- Multi-Digit Multiplication Strategies
- Word Problems Using Multiplication
- Common Mistakes and How to Avoid Them
- Practice Questions With Explanations
- Self-Check Table
- Test Yourself:
- Key Takeaway
Imagine this: you're organizing chairs for 12 rows in your school auditorium, and each row needs exactly 25 chairs. Counting them one by one takes too long. What if you could multiply instead?
This lesson on Multiplication of Whole Numbers solves everyday problems like this quickly. We'll explore how multiplying isn't just faster-it's smarter.
What Are Whole Numbers?
Whole numbers are all the counting numbers starting from 0 and going up (0, 1, 2, 3, 4...). They do not include fractions or decimals.
Examples:
- 0 is a whole number.
- 57 is a whole number.
- 5.5 is not a whole number.
What Is Multiplication?
Multiplication is the operation of repeated addition. For example, 4 × 3 means 4 groups of 3.
Equation: 4 × 3 = 3 + 3 + 3 + 3 = 12
Symbols used:
- × (most common in primary grades)
- (used in programming)
- (used in programming)
- · (used in higher mathematics)
Why Is Multiplication Important?
- Speeds up repeated addition
- Helps in solving area and volume problems
- Used in daily life: shopping, cooking, building
- Essential in advanced topics like algebra and geometry
Multiplication Vocabulary
| Term | Meaning | Example |
| Factor | A number being multiplied | 6 and 4 in 6 × 4 |
| Product | The answer to a multiplication problem | 24 is the product of 6 × 4 |
| Multiplier | The number of groups | 6 in 6 × 4 |
| Multiplicand | The size of each group | 4 in 6 × 4 |
Basic Multiplication Facts
Learning multiplication tables (1 to 12) builds a strong foundation.
Here are a few:
| × | 1 | 2 | 3 | 4 |
| 3 | 3 | 6 | 9 | 12 |
| 4 | 4 | 8 | 12 | 16 |
| 5 | 5 | 10 | 15 | 20 |
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Properties of Multiplication
Understanding these helps solve problems faster:
A. Commutative Property
Changing the order doesn't change the product.
6 × 4 = 4 × 6
B. Associative Property
Grouping doesn't affect the product.
(2 × 3) × 4 = 2 × (3 × 4)
C. Identity Property
Multiplying any number by 1 keeps it the same.
7 × 1 = 7
D. Zero Property
Any number multiplied by 0 equals 0.
12 × 0 = 0
Multi-Digit Multiplication Strategies
A. Place Value Method
Multiply each digit separately using place values.
Example:
73 × 45
→ Multiply 73 × 5 = 365
→ Multiply 73 × 40 = 2920
→ Add: 365 + 2920 = 3285
B. Lattice Method (Optional for visual learners)
Use a grid and diagonals to multiply large numbers step-by-step.
Word Problems Using Multiplication
Example 1:
A bakery makes 6 trays of cookies. Each tray has 18 cookies. How many cookies in total?
Solution:
6 × 18 = 108 cookies
Example 2:
You save ₹75 every week. How much will you save in 12 weeks?
Solution:
₹75 × 12 = ₹900
Common Mistakes and How to Avoid Them
| Mistake | Why It Happens | Fix |
| Misplacing digits in multi-digit multiplication | Not aligning by place value | Use lined paper and work step-by-step |
| Forgetting to carry over | Happens in mental math | Always double-check carries |
| Switching the order in word problems | Misreading the question | Label each number (e.g., "number of groups") |
Practice Questions With Explanations
Q1: Which symbol represents multiplication?
Answer: ×
Why: It's the standard symbol used in early grades and quizzes.
Q2: Is "Multiplication is repeated addition" true?
Answer: True
Why: You add the same number multiple times.
Q3: Solve 7 × 6
Answer: 42
Explanation: Use the multiplication table or repeated addition.
Q4: Solve 8 × 19
Breakdown:
8 × 9 = 72 → write 2, carry 7
8 × 1 = 8 → 8 + 7 = 15 → Final answer: 152
Q5: Solve 73 × 45
Breakdown:
73 × 5 = 365
73 × 40 = 2920
365 + 2920 = 3285 (correcting explanation from source)
Q6: Solve 62 × 104
Use standard multiplication steps
→ Answer: 6,448
Self-Check Table
| Problem | Method | Correct Answer |
| 7 × 6 | Basic Fact | 42 |
| 8 × 19 | Traditional | 152 |
| 73 × 45 | Place Value | 3285 |
| 62 × 104 | Long Multiplication | 6448 |
Test Yourself:
- Can multiplication always replace repeated addition?
- Why is it easier to multiply with powers of 10?
- How does multiplication connect with area and volume?
Key Takeaway
Mastering the Multiplication of Whole Numbers means more than memorizing tables. It involves understanding the "how" and "why" behind every step. This skill prepares you for algebra, science problems, and even smart shopping. Use this lesson to build your confidence-and ace that quiz!
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