Properties of Multiplication
Properties of multiplication are rules that multiplication always follows. These rules make calculations faster and easier. In Class 3, you learn four main properties: commutative, associative, distributive, and the identity property.
Knowing these properties helps you solve problems mentally and check your answers quickly.
What is Properties of Multiplication - Class 3 Maths (Multiplication)?
A property of multiplication is a rule that is true for every pair of numbers. No matter which numbers you pick, the rule always works.
Properties of Multiplication Formula
Commutative: a × b = b × a
Associative: (a × b) × c = a × (b × c)
Distributive: a × (b + c) = a × b + a × c
Identity: a × 1 = a
Types and Properties
The four properties taught in Class 3 are:
| Property | Rule | Example |
|---|---|---|
| Commutative (Order property) | Changing the order does not change the product. | 4 × 7 = 7 × 4 = 28 |
| Associative (Grouping property) | Changing the grouping does not change the product. | (2 × 3) × 5 = 2 × (3 × 5) = 30 |
| Distributive | Multiply a number by a sum by breaking it apart. | 3 × 12 = 3 × (10 + 2) = 30 + 6 = 36 |
| Identity (Multiply by 1) | Any number × 1 = the number itself. | 9 × 1 = 9 |
Solved Examples
Example 1: Commutative Property
Question: Show that 6 × 9 = 9 × 6.
Think:
- 6 × 9 = 54
- 9 × 6 = 54
- Both products are the same.
Answer: 6 × 9 = 9 × 6 = 54. The order does not matter.
Example 2: Commutative Property — Word Problem
Question: Aman arranges 5 rows of 8 chairs. Priya arranges 8 rows of 5 chairs. Who has more chairs?
Think:
- Aman: 5 × 8 = 40
- Priya: 8 × 5 = 40
- Both have the same number of chairs.
Answer: Both have 40 chairs. (Commutative property)
Example 3: Associative Property
Question: Find 2 × 4 × 5 using two different groupings.
Think:
- Grouping 1: (2 × 4) × 5 = 8 × 5 = 40
- Grouping 2: 2 × (4 × 5) = 2 × 20 = 40
Answer: Both groupings give 40.
Example 4: Associative Property — Easier Calculation
Question: Find 5 × 7 × 2.
Think:
- Multiply 5 × 2 first (easy pair) = 10
- Then 10 × 7 = 70
Answer: 5 × 7 × 2 = 70. Grouping 5 and 2 together made it simpler.
Example 5: Distributive Property — Breaking Apart
Question: Find 4 × 13 using the distributive property.
Think:
- Break 13 into 10 + 3
- 4 × 13 = 4 × (10 + 3)
- = 4 × 10 + 4 × 3
- = 40 + 12 = 52
Answer: 4 × 13 = 52.
Example 6: Distributive Property — Shopping Problem
Question: One book costs ₹15. Ria buys 6 books. Find the total cost using the distributive property.
Think:
- 6 × 15 = 6 × (10 + 5)
- = 6 × 10 + 6 × 5
- = 60 + 30 = 90
Answer: Total cost = ₹90.
Example 7: Identity Property
Question: What is 85 × 1?
Think:
- Any number multiplied by 1 gives the number itself.
- 85 × 1 = 85
Answer: 85 × 1 = 85.
Example 8: Zero Property
Question: What is 47 × 0?
Think:
- Any number multiplied by 0 gives 0.
- 47 × 0 = 0
Answer: 47 × 0 = 0.
Example 9: Identify the Property
Question: Name the property used: 3 × (2 + 8) = 3 × 2 + 3 × 8.
Think:
- A number is multiplied by a sum.
- The sum is broken apart and each part is multiplied separately.
Answer: This is the Distributive Property.
Key Points to Remember
- Commutative: a × b = b × a — order does not change the product.
- Associative: (a × b) × c = a × (b × c) — grouping does not change the product.
- Distributive: a × (b + c) = a × b + a × c — break apart to make multiplication easier.
- Identity: a × 1 = a — multiplying by 1 keeps the number the same.
- Zero property: a × 0 = 0 — multiplying by 0 always gives 0.
- These properties help in mental maths and checking answers.
- The distributive property is especially useful for multiplying larger numbers.
Practice Problems
- Show that 7 × 5 = 5 × 7. Which property is this?
- Find 4 × 3 × 5 by grouping 3 and 5 first. Which property did you use?
- Use the distributive property to find 5 × 14.
- What is 63 × 1? Name the property.
- What is 99 × 0? Name the property.
- Rewrite 8 × (6 + 4) using the distributive property and solve.
- Find 2 × 9 × 5. Which grouping makes it easiest?
Frequently Asked Questions
Q1. What is the commutative property of multiplication?
It means the order of numbers does not change the product. For example, 3 × 8 = 8 × 3 = 24.
Q2. What is the associative property of multiplication?
It means the grouping of numbers does not change the product. For example, (2 × 3) × 4 = 2 × (3 × 4) = 24.
Q3. How does the distributive property help?
It lets you break a hard multiplication into two easier ones. For example, 7 × 12 becomes 7 × 10 + 7 × 2 = 70 + 14 = 84.
Q4. Why is multiplying by 1 called the identity property?
Because the number keeps its identity — it stays the same. 25 × 1 = 25. The number does not change.
Q5. Is there a commutative property for subtraction?
No. Subtraction is not commutative. 8 − 3 = 5 but 3 − 8 is not the same. This property works only for addition and multiplication.
Q6. What happens when you multiply any number by 0?
The answer is always 0. This is called the zero property of multiplication. For example, 1000 × 0 = 0.
Q7. Can I use these properties to check my answer?
Yes. For example, if you calculated 6 × 9 = 54, check by doing 9 × 6. If you also get 54, your answer is correct (commutative property).
Q8. Do these properties work for all numbers?
Yes. The commutative, associative, distributive, identity, and zero properties work for all whole numbers. They are universal rules of multiplication.
Q9. Is the distributive property in the NCERT Class 3 textbook?
NCERT Class 3 introduces the idea of breaking numbers apart for easier multiplication. The formal name "distributive property" may appear in higher classes, but the concept is practised in Class 3.
Related Topics
- Multiplication Concept (Grade 3)
- Multiplication by 10 and 100
- Multiplication Tables of 3 and 4
- Multiplication Tables of 6 and 7
- Multiplication Tables of 8 and 9
- Multiplication of 2-Digit by 1-Digit
- Multiplication Word Problems (Grade 3)
- Multiplying by 0 and 1
- Multiplication Tables (2 to 10)
- Multiplication of 2-Digit Numbers (Grade 3)
