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.