Zero Property of Multiplication
According to the zero property of multiplication, the product of any number and zero is always zero. This property applies to all kinds of numbers, and should not be mistaken for the identity property of multiplication, which involves 1 as the identity element and in which the product is the number itself. Let us learn more about the zero property of multiplication.
1.  What is the Zero Property of Multiplication? 
2.  Difference Between Identity Property and Zero Property of Multiplication 
3.  FAQs on Zero Property of Multiplication 
What is the Zero Property of Multiplication?
The zero property of multiplication states that when we multiply a number by zero, the product is always zero. It should be noted that this zero can come before or after the number. In other words, the position of zero does not affect the property. This property applies to all types of numbers, whether they are integers, fractions, decimals, or even algebraic terms. For example, 5 × 0 = 0, 8.4 × 0 = 0, 0 × 1/2 = 0, y × 0 = 0
Another important point to be kept in mind is that the operation of division does not have any zero property even though division is the inverse operation of multiplication. If we divide a number by zero, it does not result in zero.
Difference Between Identity Property and Zero Property of Multiplication
The zero property of multiplication should not be mistaken for the Identity property of multiplication. The Identity property of multiplication states that when we multiply 1 by any number, the product is the number itself. For example, 7 × 1 = 7. Here, '1' is the multiplicative identity of a number and the property is represented as: a × 1 = a = 1 × a. On the other hand, the zero property of multiplication states that when we multiply a number by zero, the product is always zero. For example, 7 × 0 = 0.
Related Links
Check out the following pages related to the zero property of multiplication.
Zero Property of Multiplication Examples

Example 1: Which of the following is an example of Zero Property of Multiplication?
a.) 5 + 0 = 5
b.) 5 × 1 = 5
c.) 5 × 0 = 0
Solution:
a.) In the first case, 5 + 0 = 5, the numbers are added and not multiplied, hence, it does not denote the zero property of multiplication.
b.) In the second case, 5 × 1 = 5, the number is not multiplied by 0, therefore, it does not denote the zero property of multiplication.
c.) In the third case, 5 × 0 = 0, the number is multiplied with 0, and the product is zero, therefore, it shows the zero property of multiplication.

Example 2: Use the Zero Property of Multiplication to find the missing numbers.
a.) 32 × 0 = __
b.) 65 × __ = 0
c.) __ × 78 = 0
Solution:
a.) 32 × 0 = 0
b.) 65 × 0 = 0
c.) 0 × 78 = 0
FAQs on Zero Property of Multiplication
What is the Zero Property of Multiplication?
The zero property of multiplication states that when a number is multiplied by zero, the product is always zero. Whether this zero is placed before or after the number, the result will always be zero. This property applies to all types of numbers, like integers, fractions, decimals, or even algebraic terms. For example, 67 × 0 = 0, 98.4 × 0 = 0, 0 × 31/72 = 0, b × 0 = 0
How is the Identity Property of Multiplication Different From the Zero Property of Multiplication?
The Identity property of multiplication is different from the zero property of multiplication. According to the identity property of multiplication, if we multiply 1 by any number the product is the number itself. For example, 42 × 1 = 42. Here, '1' is the multiplicative identity of the number and the property is represented as, a × 1 = a = 1 × a. On the other hand, the zero property of multiplication says that when we multiply a number by 0, the product is always 0. For example, 98 × 0 = 0.
What is the Difference Between the Associative Property of Multiplication and Zero Property of Multiplication?
The associative property of multiplication is different from the zero property of multiplication. According to the associative property of multiplication, the product of three or more numbers remains the same irrespective of the way in which they are grouped, which means changing the grouping of the factors does not change the product. For example, (2 × 5) × 3 = 2 × (5 × 3) = 30. On the other hand, the zero property of multiplication says that whenever a number is multiplied by zero, the result is zero. For example, 23 × 0 = 0.
What is the Difference Between the Commutative Property of Multiplication and Zero Property of Multiplication?
According to the commutative property of multiplication, changing the order of the operands or factors does not change the product. For example, 5 × 4 = 4 × 5 = 20. While we know that the zero property of multiplication says that whenever a number is multiplied by zero, the product is zero. For example, 6 × 0 = 0.
What are the 3 Properties of Multiplication?
There are three main properties of multiplication:
 Commutative Property: According to the commutative property of multiplication, if we change the order of the multiplicands, it does change the product. For example, 3 × 2 = 6 and 2 × 3 = 6.
 Associative Property: According to the associative property of multiplication, the way in which the multiplicands are grouped does not change the product of those numbers. For example, (4 × 2) × 3 = 24 and 4 × (2 × 3) = 24
 Distributive Property: According to the distributive property of multiplication, when a number is multiplied with the sum of two or more addends, the result is equal to the result that is obtained when each addend is separately multiplied by the number. For example, if we need to solve 5(10 + 3), we can solve it in the usual way where we solve the brackets first, that is, 5(10 + 3) = 5(13) = 65. Now, if we apply the distributive property of multiplication to solve this question, 5(10 + 3), we will have to multiply the number with both the addends separately and we will get the same result. That means, 5(10 + 3) = (5 × 10) + (5 × 3) = 50 + 15 = 65.
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