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Zero Property of Multiplication – Definition with Examples

Jo-ann Caballes

Updated on September 29, 2026

The zero property of multiplication states that any number multiplied by zero equals zero. In symbols, a × 0 = 0, no matter what number a is. For example, 7 × 0 = 0 and 0 × 582 = 0.

This is one of the first multiplication properties children learn, usually around third grade, and it lays the groundwork for later work in arithmetic and algebra.

What Is the Zero Property of Multiplication?

The zero property of multiplication — also called the multiplication property of zero — states that the product of any number and zero is always zero. Written as a rule, a × 0 = 0 for any number a. It does not matter how large or small the number is: multiplying by zero always gives zero.

Why Does Multiplying by Zero Equal Zero?

Multiplication is repeated addition, and that explains why multiplying by zero gives zero. The expression 4 × 0 means “add four zeros together,” which is 0 + 0 + 0 + 0 = 0. In the other order, 0 × 4 means “add zero four times,” which is also 0. Either way, the result is zero — a rule that connects to the properties of zero itself.

Zero Property of Multiplication Examples

No matter what number you start with, multiplying by zero gives zero. The table below shows the rule in action with different kinds of numbers.

Once a child sees that any number times zero is zero, the rule tends to stick — and elementary math tutors can reinforce it with quick mental math practice.

Zero Property vs Identity Property of Multiplication

The zero property and the identity property are easy to mix up, but they do opposite things. The identity property of multiplication says any number times one stays the same (a × 1 = a), while the zero property says any number times zero becomes zero (a × 0 = 0).

Zero Property vs Zero Product Property

These two similar-sounding rules are not the same. The zero property of multiplication tells you the result of multiplying by zero: a × 0 = 0. The zero product property works in reverse — it says that if a product of two numbers is zero, then at least one of them must be zero: if a × b = 0, then a = 0 or b = 0. The zero product property is used later to solve equations by factoring.

Solved Examples on the Zero Property

These worked examples apply the zero property of multiplication.

• Example 1: 25 × 0 = 0, because any number times zero is zero.
• Example 2: 0 × 1,439 = 0, since the order does not matter.
• Example 3: (8 + 5) × 0 = 13 × 0 = 0 — even a sum multiplied by zero gives zero.

Practice Questions

Try these problems, then check the answers below.

1. What is 15 × 0?
2. Calculate 0 × 200.
3. If x × 0 = 0, what can the value of x be?
4. Multiply −50 by 0.

Answers: 1) 0. 2) 0. 3) x can be any number, because every number times zero is zero. 4) 0.

Zero Property of Multiplication: Practice Test

Try these questions, then check the marked answers.

Jo-ann Caballes

30 articles

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.