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In this section, we shall learn some interesting properties of multiplication.
The properties of multiplication help us solve multiplication problems quickly and accurately. The main multiplication properties are the Commutative Property, Identity Property and Zero Property. Understanding these properties makes multiplication easier for students and helps build a strong foundation in mathematics.
1. Order Property of Multiplication or Commutative Property:
1. Look at the figures given below:
 |
 |
|
|
3 + 3 = 6 Thus, 3 two times is 6. So, 2 × 3 = 6 |
2 + 2 + 2 = 6 Thus, 2 three times is 6. So, 3 × 2 = 6 |
2. Look and Understand:
What do we conclude?
We conclude that when two numbers are multiplied they may be taken in any order. The result remains the same. This is called the order property.
or
Thus, when two numbers are multiplied in any order, the product remains the same.
More examples: 4 × 3 = 3 × 4, 5 × 6 = 6 × 5 etc.
2. Multiplicative Property of 1 or Identity Property:
1. Look at the figures given below:
|
1 + 1 + 1 = 3 Thus, 1 three times is 3 So, 1 × 3 = 3 Hence, 1 × 3 = 3 × 1 |
Thus, 3 one is 3 So, 3 × 1 = 3 |
2. Look and Understand:
What do we conclude?
When a number is multiplied by 1, the answer is the number itself. This is called multiplicative property of 1.
or
Any number multiplied by 1 is the number itself.
More examples: 1 × 4 = 4, 1 × 8 = 8, 1 × 10 = 10 etc.
3. Multiplicative Property of 0 or Zero Property:
There is no flower in any vase.
We know that: 0 + 0 + 0 + 0 = 0
Thus, 0 four times = 0
So, 0 × 4 = 0
By order property: 0 × 4 = 4 × 0
Hence, 0 × 4 = 4 × 0 = 0
Similarly, 0 + 0 + 0 + 0 + 0 = 0
Thus, 0 six times = 0
So, 0 × 6 = 0
But, 0 × 6 = 6 × 0
Hence, 0 × 6 = 6 × 0 = 0
What do we conclude?
We conclude that when any number is multiplied by zero, the product is always zero.
or
Any number multiplied by 0 is 0.
Basic Properties of Multiplication Video
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Play Properties of Multiplication Quiz Game:
⭐ Score: 0
⏰ Time: 60s
Practice Questions on Properties of Multiplication:
1. Fill in the boxes:
(a) 6 × 1 = ⟎
(b) 17 × 1 = ⟎
(c) 20 × 0 = ⟎
(d) 9 × 0 = ⟎
(e) 21 × 1 = ⟎
(f) 21 × 0 = ⟎
(g) 12 × 1 = ⟎
(h) 25 × 0 = ⟎
(i) 16 × 1 = ⟎
2. Fill in the with the correct number.
(a) 4 × ⟎ = 9 × 4
(b) 8 × 9 = ⟎ × 8
(c) 6 × 3 = ⟎ × 6
(d) ⟎ × 6 = 6 × 9
(e) 2 × 5 = ⟎ × 2
(f) 2 × 7 = ⟎ × 2
3. Find the products:
(a) 9
× 1_
____
(b) 14
× 0_
____
(c) 17
× 1_
____
(d) 25
× 1_
____
4. Complete the multiplication facts.
(a) 7 × ⟎ = 7
(b) 6 × ⟎ = 6
(c) 13 × ⟎ = 13
(d) 29 × ⟎ =0
(e) 14 × ⟎= 14
(f) 19 × ⟎= 19
(g) 17 × ⟎ =17
(h) 12 × ⟎ = 0
(i) 3 × ⟎ = 3
Worksheet on Properties of Multiplication:
1. Fill in the empty boxes by using the properties of multiplication:
(i) 4 × 1 = _____
(ii) 9 × 0 = _____
(iii) 2 × 7 = _____ × 2
(iv) 5 × 0 = _____
(v) 10 × 1 = _____
(vi) 0 × 8 = _____
(vii) 3 × 5 = _____ × 3
(viii) 8 × 1 = _____
(ix) 0 × 7 = 7 × _____
(x) _____ × 13 = 13 × 6
(xi) _____ × 9 = 0
(xii) 6 × _____ = 3 × 6
Answer:
1. (i) 1
(ii) 0
(iii) 7
(iv) 0
(v) 10
(vi) 0
(vii) 5
(viii) 8
(ix) 0
(x) 6
(xi) 0
(xii) 3
FAQs on Properties of Multiplication:
Answer:
The properties of multiplication are Closure Property, Commutative Property, Associative Property, Identity Property, Zero Property, and Distributive Property.
Answer:
The commutative property states that changing the order of factors does not change the product.
Example: 4 × 5 = 5 × 4.
Answer:
The identity property states that multiplying any number by 1 gives the same number.
Answer:
The zero property states that any number multiplied by 0 equals 0.
About Author
Written by Priyanka Ghosh
Mathematics Educator | Founder of Math Only Math
Priyanka Ghosh has been teaching elementary and middle-school mathematics for over 12 years and specializes in creating simple, child-friendly math lessons and worksheets.
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