# 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.