I ask this in relation to ” /(x/y) ” = ” *(y/x) ”
My mathematical ignorance does not allow me to perceive exactly what it is that confuses me about these manoeuvres and so perhaps my question is vague.
I have no difficulty with it as a technique; as something through which I can put an expression, and out at the other end the right result will appear. What I am trying to understand is *why it works*, contrasted with remembering it as a kind of magical spell.
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**EDIT:**
It was very rewarding for me to read all of your comments. Thank you most kindly for enlightening me.
For those interested in the cause of my previous confusion:
The gaps in my understanding of going from y*x=z to y=z/x were definitions of the equal sign and division.
I can see now that I previously considered the = sign to mean «result» or «answer» in some sort of final sense, like a conclusion; I now see that it only states that this is equal to that.
Following this fundamental piece of knowledge, I can belatedly understand what an equation is. From there, via the definition of division as the opposite of multiplication, I can see that if I divide something while also multiplying it with the same number, these actions cancel each other out.
And so the magical spell between y*x=z and y=z/x is the logic above expressed mathematically as x/(y*x)=z/x.
In: 25
So far, I’ve only seen one ACTUAL “like I’m 5” answer, so here’s my stab at it:
Multiplication is just adding a certain number together as many times as you’re told to, so if you have 6 * 7, you would add 6 together 7 times.
6+6+6+6+6+6+6=42
Division is similarly SUBTRACTING a certain number of times until you reach zero, so like above, if you’re asked “What is 42 / 7” then you subtract 7 until you reach zero.
42 – 7 = 35 (1 time)
35 – 7 = 28 (2 times)
28 – 7 = 21 (3 times)
21 – 7 = 14 (4 times)
14 – 7 = 7 (5 times)
7 – 7 = 0 (6 times)
So 42 / 7 = 6.
6(y) * 7(x) = 42(z), and 42(z) / 7(x) = 6(y).
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