Commutation of Multiplication is the rule that says “a*b = b*a”.
Commutation of Multiplication is an axiom. We don’t claim that we can prove it from our collection of starting rules, rather, it is one of the rules in our collection of starting rules.
However, we at Mockingbird Academy maintain that there is a way to visualize why commutation of multiplication is true.
Assume we spend a lot of money to put gold dots on an expensive stone tablet, and we end up with this:
As we analyze it, first we notice there are twenty dots on it (we had to pay for each one) and we wanted to make sure we got what we paid for. Now for the magic–can you look at the tablet and see that it says “five times four”? We can’t force you to see it, you are free in your own mind. If yes, then look at the next picture of the same tablet:
Using the same thinking as used for the previous view, can you see the above as representing “four times five”?
We still have twenty dots, we paid a lot of money so we wouldn’t have to worry about the number of dots changing when we slowly and carefully move the tablet.
5*4 = 4*5
If we think about what we have done here, we should be able to agree that if our strategy is to represent the multiplication a*b by a grid of dots on a tablet, we can rotate the table by 90 degrees–as was done above–and we will have b*a.
a*b = b*a
Similar work has been done to illustration Commutation of Addition.
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