Identity Property of Multiplication

Identity property of multiplication:

` huge 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, `huge color(purple)(a times 1=1 times a=a)`.

This is also true, if we divide by one: `a/1=a`.

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

Example 1. `3 times 1=3`.

Example 2. `(-sqrt(2)) times 1=-sqrt(2)`.

Example 3. `1 times 5/8=5/8`.

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