Properties of Multiplication (Grade 4)
Properties of multiplication are rules that always hold true when we multiply numbers. Understanding these properties helps students solve problems faster and verify their answers.
In Class 4, students learn five important properties: the commutative, associative, distributive, identity, and zero properties.
What is Properties of Multiplication (Grade 4) - Class 4 Maths (Multiplication (Grade 4))?
A property of multiplication is a mathematical rule that applies to all numbers. These properties do not change regardless of which numbers are used. They are like shortcuts that make calculations easier and help check answers.
Types and Properties
The five properties of multiplication covered in Class 4 are:
| Property | Rule | Example |
|---|---|---|
| Commutative | a × b = b × a | 6 × 4 = 4 × 6 = 24 |
| Associative | (a × b) × c = a × (b × c) | (2 × 3) × 5 = 2 × (3 × 5) = 30 |
| Distributive | a × (b + c) = a × b + a × c | 4 × 23 = 4 × 20 + 4 × 3 = 92 |
| Identity (× 1) | a × 1 = a | 587 × 1 = 587 |
| Zero Property | a × 0 = 0 | 999 × 0 = 0 |
Solved Examples
Example 1: Example 1: Commutative Property
Problem: Show that 15 × 8 = 8 × 15.
Solution:
15 × 8 = 120
8 × 15 = 120
Both products are equal.
Answer: 15 × 8 = 8 × 15 = 120. This confirms the commutative property: changing the order of factors does not change the product.
Example 2: Example 2: Associative Property
Problem: Verify that (4 × 5) × 6 = 4 × (5 × 6).
Solution:
(4 × 5) × 6 = 20 × 6 = 120
4 × (5 × 6) = 4 × 30 = 120
Both give the same result.
Answer: (4 × 5) × 6 = 4 × (5 × 6) = 120. The associative property says we can group factors in any order.
Example 3: Example 3: Distributive Property (Breaking Apart)
Problem: Use the distributive property to find 7 × 46.
Solution:
Break 46 into 40 + 6:
7 × 46 = 7 × (40 + 6)
= 7 × 40 + 7 × 6
= 280 + 42
= 322
Answer: 7 × 46 = 322
Example 4: Example 4: Distributive Property (Subtraction Form)
Problem: Find 8 × 99 using the distributive property.
Solution:
Write 99 as 100 − 1:
8 × 99 = 8 × (100 − 1)
= 8 × 100 − 8 × 1
= 800 − 8
= 792
Answer: 8 × 99 = 792
Example 5: Example 5: Identity Property (Multiply by 1)
Problem: What is 463 × 1?
Solution:
The identity property states that any number multiplied by 1 gives the number itself.
463 × 1 = 463
Answer: 463 × 1 = 463
Example 6: Example 6: Zero Property
Problem: What is 8,752 × 0?
Solution:
The zero property states that any number multiplied by 0 is 0.
8,752 × 0 = 0
Answer: 8,752 × 0 = 0
Example 7: Example 7: Using Commutative Property in Word Problem
Problem: Aman arranges 9 rows with 12 chairs each. Priya arranges 12 rows with 9 chairs each. Who has more chairs?
Solution:
Aman: 9 × 12 = 108 chairs
Priya: 12 × 9 = 108 chairs
By the commutative property, both have the same number.
Answer: Both have 108 chairs. Neither has more.
Example 8: Example 8: Using Associative Property to Simplify
Problem: Find 25 × 7 × 4 quickly.
Solution:
Using the associative property, multiply 25 and 4 first (since 25 × 4 = 100):
25 × 7 × 4 = (25 × 4) × 7 = 100 × 7 = 700
Answer: 25 × 7 × 4 = 700
Example 9: Example 9: Distributive Property in Shopping
Problem: Dev buys 6 items costing ₹52 each. Use the distributive property to find the total cost.
Solution:
6 × 52 = 6 × (50 + 2)
= 6 × 50 + 6 × 2
= 300 + 12
= 312
Answer: Total cost = ₹312
Example 10: Example 10: Identifying the Property
Problem: Name the property used in each statement:
(a) 14 × 6 = 6 × 14
(b) 5 × (3 × 8) = (5 × 3) × 8
(c) 9 × 0 = 0
(d) 7 × (10 + 3) = 7 × 10 + 7 × 3
Solution:
(a) Commutative property — order changed
(b) Associative property — grouping changed
(c) Zero property — multiplied by 0
(d) Distributive property — multiplication distributed over addition
Real-World Applications
Multiplication properties are used in mental maths and problem-solving:
- Mental maths: Using distributive property to break 6 × 98 into 6 × 100 − 6 × 2 = 588.
- Rearranging: Using associative property to pair numbers that give round answers (e.g., 25 × 4 = 100).
- Checking: Using commutative property to verify answers by multiplying in reverse order.
- Simplifying: Breaking complex multiplications into easier parts.
Key Points to Remember
- Commutative property: a × b = b × a — the order of factors does not matter.
- Associative property: (a × b) × c = a × (b × c) — the grouping of factors does not matter.
- Distributive property: a × (b + c) = a × b + a × c — multiply each addend separately, then add.
- Identity property: a × 1 = a — multiplying by 1 gives the same number.
- Zero property: a × 0 = 0 — multiplying by 0 always gives 0.
- These properties work for all whole numbers, no matter how large.
Practice Problems
- Show that 23 × 17 = 17 × 23. Which property is this?
- Use the distributive property to find 8 × 37.
- Find 5 × 13 × 2 by choosing a smart grouping (associative property).
- What is 10,000 × 0? Name the property used.
- Verify: (6 × 4) × 5 = 6 × (4 × 5). What property does this show?
- Use the distributive property to find 9 × 98 mentally.
- Identify the property: 345 × 1 = 345.
- Neha says 4 × (25 × 9) is easier to solve as (4 × 25) × 9. Is she correct? Explain.
Frequently Asked Questions
Q1. What is the commutative property of multiplication?
It states that changing the order of the factors does not change the product. For example, 6 × 9 = 9 × 6 = 54.
Q2. What is the difference between associative and commutative properties?
The commutative property changes the order (a × b = b × a). The associative property changes the grouping: (a × b) × c = a × (b × c). Both keep the product the same.
Q3. How does the distributive property help in multiplication?
It lets you break a number into parts for easier multiplication. For example, 7 × 53 = 7 × 50 + 7 × 3 = 350 + 21 = 371. This is very useful for mental maths.
Q4. Does the distributive property work with subtraction?
Yes. a × (b − c) = a × b − a × c. For example, 6 × 99 = 6 × (100 − 1) = 600 − 6 = 594.
Q5. Why is any number multiplied by 0 equal to 0?
Multiplying by 0 means zero groups of that number, which gives nothing. For example, 5 × 0 means 0 groups of 5, which is 0.
Q6. Why is multiplying by 1 called the identity property?
Because 1 keeps the identity (value) of the number unchanged. Just as looking in a mirror shows your own face, multiplying by 1 returns the same number.
Q7. Do these properties work for division too?
No. Division is not commutative (12 ÷ 3 ≠ 3 ÷ 12) and not associative. The distributive property does work with division over addition in a limited way.
Q8. How can I use properties to check my multiplication?
Multiply in reverse order (commutative property). If 234 × 5 = 1,170, then 5 × 234 should also be 1,170. If both match, the answer is likely correct.
Q9. Are multiplication properties covered in the NCERT Class 4 textbook?
Yes. NCERT Class 4 Maths introduces these properties through patterns, puzzles, and activities. Students use them for mental computation and problem-solving.
