I’m interested for personal reasons on how these mathematical operations work. I know they’re quite simple, but I never quite understood them, so it’s something that got stuck with me. Any explanations are welcome!
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For equations, let’s take an example:
There is your salary, the taxes, and the money you get at the end. The formula is simply:
* Salary – Taxes = Money
For example, you get paid 10 and taxed 2, you have 8 at the end because
* 10 – 2 = 8
More precisely, if you known that Salary = 10 and the Taxes = 2, then you have
* 10 – 2 = Money
So you can deduce that Money = 8. On the other hand, if you know that the Salary = 20 and Money = 16, then you have
* 20 – Taxes = 16
And if you want to deduce what were the taxes, this is called a linear equation, which mathematicians will write “20-x=16”. To solve this equation, you can either use trial and error and see that Taxes = 4 works, because
* 20 – 4 = 16
Instead of using trial and error, you can use a set of mathematical methods to solve those equations. For example, one method is:
* Starting from “16 = 20-Taxes”, if I undo the “-Taxes” by adding “+Taxes” I obtain “16+Taxes = 20”
* Continuing with “Taxes+16 = 20”, if I undo the “+16” by doing “-16”, I obtain “Taxes = 20-16”, hence “Taxes = 4”.
As you say, a lot of the resolution of equations is knowing “what mathematical operation is undoing which other mathematical operation”. That’s how you get fractions most of the time, you were “undoing a multiplication”, and that’s called creating a fraction.
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