Commutative? Who Studies “Commutative”?
It could come in any grade. It could come up in almost any mathematics course in the United States today. But why? What is “the Commutative Property” and why do we study it? Has everyone always studied it?
I may need some help from the mathematicians who read this blog. Which probably means Joel. Maybe Owen. Back in this blog’s heyday I had literally hordes – maybe 8 or 9 – who peaked in. How far I’ve slipped.
A Little Math (skip ahead)
The real numbers (or, for most of us, “numbers”) are commutative under addition. That means that a + b and b + a have the same value, (assuming a and b are numbers, or, in more technical language, “real numbers”). When people say “The Commutative Property” – and by people I mean People who are not Mathematicians – they mean this fact, which educators label “The Commutative Property of Addition.” They label a similar fact “The Commutative Property of Multiplication,” ie ab = ba. Some teachers also teach students that division and subtraction are not commutative, which is usually fine, but sometimes puzzles children who are still wondering why “five minus seven” is different from “take five from seven.”
There are other properties, and they matter just as much. And they all have longer names, or descriptions, than we remember, or than we usually use. We use shorthand. There’s the Associative Property of Addition for Real Numbers, and the Associative Property of Multiplication for Real Numbers. There’s the Distributive Property of Multiplication over Addition or a(b+c) = ab + ac. There’s a special number called the Additive Identity (that’s just zero) and another called the Multiplicative Identity (that’s just one). And there’s a few more fancy sounding properties for pretty simple ideas like CONTINUE READING: Commutative? Who Studies “Commutative”? | JD2718