Mnemonic Tricks
Help with a Math Discussion Board Question.?
When we manipulate expressions and equations, we realize that there are basic properties that govern what we can and can’t do. One of those properties is the Commutative Property. Let’s consider this property in our discussion. Is there a commutative property of subtraction? In other words, does order matter when subtracting? Why or Why not? Please provide an example to explain your reasoning. Please share any trick or mnemonic device to help you recall what this property is or how to use it.
This is extremely simple subtraction does NOT commute.
To commute simply means that left-right order doesn’t matter:
i.e. 1 – 2 = 2 – 1 (but this is NOT true and therefore subtraction does NOT commute)
So I guess, the interesting question is why doesn’t it commute.
This is not an answer because the real answer is just because.
However, going on anyways subtraction is the opposite of addition (the inverse). This is NOT a simple function like addition.
so the expression a – b really means
b + ? = a (the answer is ? = a – b but this is how subtraction is accomplished, by answering the original equation)
Likewise division is NOT commutative and is also the inverse of the much simple operation of multiplication which is a generalization of addition (which is probably why it commutes)
Eg a/b != b/a (in general)
However ab = ba (so multiplication DOES commute
Mnemonic – Robots in Disguise
Additional Information
- Generalization analysis of CCNP testing
- Back to Basics: Negative and Non-Real numbers, an Explanation « Its All One Big Adventure
- Building by Subtraction « Greywulf's Lair
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