123 LearnersLast updated on July 5th, 2025
Zero Property of Multiplication
The zero property of multiplication states that multiplying any number by zero always results in zero. This property applies to all types of numbers and is one of the most fundamental rules in math.
What is the Zero Property of Multiplication?
The zero property of multiplication states that the result of multiplying a number by zero is always zero. As multiplication is commutative, the order of multiplication will not affect the result; that is, a × 0 = 0 and 0 × a = 0. This property applies to all types of numbers, including positive and negative integers, fractions, and decimals. The zero property of multiplication is applicable. For example, 10 × 0 = 0, 5624 × 0 = 0, and ⅚ × 0 = 0.
Fundamental Properties of Zero
In mathematics, zero and one are unique numbers. Here are some properties of zero in addition and multiplication.
- Additive property of zero: Zero is the additive identity, so the sum of adding a number to 0 is the number itself. For example, 0 + 5 = 5, 1 + 0 = 1, 56 + 0 = 56.
- Multiplication property of zero: Also known as the zero property of multiplication, it states that the product of multiplying any number and zero is always zero. For example, 523 × 0 = 0, 5 × 0 = 0, 0 × 56 = 0.
- Exponent zero: Any number raised to the power of 0 is 1; that is, n0 = 1 for n ≠ 0. For example, 50 = 1, 9510 = 1
- Exponent of zero: The number 0 raised to any power is 0. For example, 05 = 0, that is 0n = 0.
- Zero as a numerator: Dividing 0 by any nonzero number is 0; that is, 0 ÷ 56 = 0, 0 ÷ 5 = 0
- Zero as a denominator: Dividing any number by 0 is undefined. For example, 62 ÷ 0 = undefined, 5 ÷ 0 = undefined
Difference Between Identity Property and Zero Property of Multiplication
The identity property and zero property of multiplication are the two important properties of multiplication. Let’s learn the difference between them.
|
Identity Property of Multiplication |
Zero Property of Multiplication |
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The identity property of multiplication states that the product of multiplying any number by 1 is 1 itself. |
The zero property of multiplication states that the product of any number with 0 is 0 itself. |
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a × 1 = a |
b × 0 = 0 |
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For example, 5 × 1 = 5, 1 × 562 = 562 |
For example, 5 × 0 = 0, 0 × 56 = 0 |
Tips and Tricks for Zero Property of Multiplication
When we multiply any number by zero, the product will be zero; that is the zero property of multiplication. To master the zero property of multiplication, let’s learn some tips and tricks.
- The black hole trick: Imagine zero as a black hole, which means if we multiply any number by zero, it will disappear. That is 234 × 0 = 0
- The order of multiplying the number by 0 will not affect the result, as multiplication is commutative. For example, 2356 × 0 = 0 and 0 × 2356 = 0.
- Remember zero as a ghost number in multiplication, which means any number multiplied by zero is zero (it vanishes)
- When multiplying more than 2 numbers, if there is zero, the product will be zero; that is 5 × 23 × 0 ×9 = 0
Common Mistakes and How to Avoid Them in Zero Property of Multiplication
The zero property of multiplication is one of the basic properties of multiplication. Most students confuse the property and make errors. To master multiplication, let’s discuss some common mistakes and the ways to avoid them.
Mistake 1
Confusing the zero property of addition with the zero property of multiplication
Students think that the zero property is the same for addition and multiplication, which is wrong. For example, 5 + 0 = 5 and 5 × 0 = 0. It is important to remember that the zero property of addition means adding zero to a number doesn’t change the value, whereas the zero property of multiplication means the product of a number by zero is zero.
Mistake 2
Confusing the identity and zero property of multiplication
Students mix up the identity and the zero property of multiplication. To avoid this error, have a clear idea of what the property is about. The identity property of multiplication states that the product of a number with 1 is the number, a × 1 = a. In contrast, the zero property of multiplication is that the product of a number with zero is zero, that is, a × 0 = 0.
Mistake 3
Thinking the zero property of multiplication applies only to whole numbers
A common error is believing that the zero property only applies to whole numbers. This is incorrect, as the zero property of multiplication applies to all types of numbers, including fractions, decimals, and negative numbers. For example, 0.23 × 0 = 0, 5/2 × 0= 0, p × 0 = 0.
Mistake 4
Thinking that any number raised to the power of zero is zero
As the product of any number by zero is zero, students think that any number raised to the power of zero will also be zero, for example, 50 = 0 instead of 1. So, students should remember that any nonzero number raised to the power of zero is 1. That is 60 = 1, (⅔)0 = 1.
Mistake 5
Not applying the zero property in larger expressions.
When doing the calculation involving multiple factors, check if there is any factor that is zero or not. Because any number multiplied by zero is zero. For example, (5 + 6 × 8) × 0 × 5 = 0.
Solved Examples of Zero Property of Multiplication
Problem 1
What is the product of 56 and zero?
56 × 0 = 0
Explanation
The product of any number by zero is zero. So, 56 × 0 = 0
Problem 2
Find: 12 × 0
12 × 0 = 0
Explanation
According to the zero property of multiplication, the product of 12 and 0 is 0
Problem 3
Find the value of x in the following x × 95 = 0 x × -89 = 0
The value of x in x × 95 = 0 is 0.
In both equations, the value of x is 0 because the product of any number and 0 is 0.
Explanation
If the product of two numbers is zero, then one of the numbers should be zero. So 0 × 95 = 0 and 0 × -89 = 0.
Problem 4
What is 1/2 × 0?
1/2 × 0 = 0
Explanation
The product of a fraction with 0 is 0
Problem 5
Find the value of 0(a + b).
0(a + b) = 0
Explanation
When multiplying any expression by 0, the result is 0. So, 0(a + b) = 0.
FAQs on Zero Property of Multiplication
1.What is the zero property of multiplication?
2.What is the identity property of multiplication?
3.What is the product of 0 multiplied by 0?
4.Can we divide any number by 0?
5.What are the properties of zero in addition?
6.How can children in Indonesia use numbers in everyday life to understand Zero Property of Multiplication?
7.What are some fun ways kids in Indonesia can practice Zero Property of Multiplication with numbers?
8.What role do numbers and Zero Property of Multiplication play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Zero Property of Multiplication skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
