Zero Property of Multiplication — Definition & Examples

The multiplicative property of zero doesn't take very long to explain.

Here it is:

...and that's it. The only trick is that the zero can come first or second. That is, for any real number $a$,

$$a \times 0 = 0$$ $$0 \times a = 0$$

The product of any number with $0$ is $0$.

Both of these statements work. That's thanks to the commutative property of multiplication. Also, don't mix it up with the identity property of addition. That property says what happens if you add $0$.

Let's try one or two practice problems just to make sure you've got it.

Multiplication Property of Zero

The multiplication property of zero is about multiplying $0$. If you multiply a number by zero, the product will be zero. It doesn't matter you multiplied zero with.

What happens on the number line? We get dragged right to the middle of it. Multiply a number by $0$, you go right to the middle of the number line.

Let's look at some examples. $$3 \times 0 = 0$$ $$-5 \times 0 = 0$$ We conclude that $x \times 0 = 0$.

Let's take a look at some problems. All of them will be about the zero property of multiplication.

By the multiplication property of zero, $$5 \times 0 = 0$$

When items are organized into rows and columns, counting them is a simple matter of multiplication. To get the total number of items, we use: $$\text{Number of Rows} \times \text{Number of Columns} = \text{Number of Items}$$ For this problem, the number of rows is $0$ and there are $4$ columns, the total number of books is: $$0 \times 4 = 0$$

(Video) Multiplication Properties of 0 and 1

by mathman1024

Here's a video by mathman1024. It explains two big formulas. The first is the multiplication property of zero. The other is the multiplication property of one.

$\large{\text{Summary}}$

The Multiplication Property of Zero states: $$a\times0=0$$

You might see this written as $$a(0) = 0$$

as well. This means that any number multiplied by $0$ will give a $0$.

For example, $$8742(0)=0$$