Is division of rational numbers commutative?

1 Answer
MrsRudolph221
Oct 23, 2014

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

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

Multiplication, of course, is commutative: #2*5 = 5*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 != 8 - 4# since -4 #!=# 4.

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

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