# Identity Property of Multiplication

**Identity property of multiplication**:

$$$\color{purple}{a\times 1=a}$$$

What does it mean?

It means, that multiplication of the number with one will result in original number.

Recall, that multiplication is shorthand for addition.

$$$a\times 1$$$ means, that we use $$$a$$$ one times. In other words, we are left with original number $$$a$$$.

Using commutative property of multiplication, we can write that $$${a}\times{1}={1}\times{a}$$$.

Thus, $$$\color{purple}{a\times 1=1\times a=a}$$$.

This is also true, if we divide by one: $$$\frac{a}{1}=a$$$.

In fact, identity property is true for any real number.

**Example 1.** $$${3}\times{1}={3}$$$.

**Example 2.** $$${\left(-\sqrt{{{2}}}\right)}\times{1}=-\sqrt{{{2}}}$$$.

**Example 3.** $$${1}\times\frac{{5}}{{8}}=\frac{{5}}{{8}}$$$.

**Conclusion.** Multiplication or division by 1 doesn't change things.