# Is division of rational numbers commutative?

Oct 23, 2014

By rational numbers, you are referring to numbers like 3, $\frac{1}{2}$, -9.5, or 0. (any ratio of two integers that can be written as a fraction)

Give yourself an easy example first: $\frac{10}{2} = 5$, right?
Well, now commute or switch the order of the division: $\frac{2}{10} = \frac{1}{5}$.
They are definitely not the same!

Multiplication, of course, is commutative: $2 \cdot 5 = 5 \cdot 2 = 10$
Division is the inverse operation of multiplication, but it is NOT commutative.

Addition, we know, is commutative as well: 4 + 8 = 8 + 4 = 12.
Subtraction is the inverse operation of addition, but it is NOT commutative: $4 - 8 \ne 8 - 4$ since -4 $\ne$ 4.

I guess it's important to know what operations are inverses of each other, and to test the Commutative Property just in case!