Weird square root disappearing and flipping fraction upside down?So here I was, making 2 math...

babyagelesszj

babyagelesszj

Answered

2022-07-08

Weird square root disappearing and flipping fraction upside down?
So here I was, making 2 math problems, I was able to solve them, but 2 operations seem a bit intractable to me. Maybe you can help me understand why this is true:
The first problem:
x = 1 5 4 y
4 y = 1 5 x
4 y = 1 5 x 5
y 4 = 5 1 5 x
Why is it possible to turn y 4 upside down?
y = 20 / 1 5 x
The second problem:
4 A B B = 3
B ( 4 A 1 ) = 3
Where does the -√B go? I understand that the -1 comes from the - sign in front of the square root. But where does the other √B go?
B = 3 ( 4 A 1 )
B = ( 3 ( 4 A 1 ) ) 2
B = 9 ( 4 A 1 ) 2
Everything, except above the bold text I understand. Maybe I do not understand the full extent of a certain rule which I am familiar with in simpler situations. That's why I think an example would be very useful. I really want to have a deep understand of why these things are true.
Greetings, Bowser.

Answer & Explanation

Ashley Parks

Ashley Parks

Expert

2022-07-09Added 11 answers

First question: if two fractions are equal, then their reciprocals are equal too (the reciprocal of a fraction is the same fraction "turned upside down", using your terminology).
Second question: the B is still there: if you multiply B ( 4 A 1 ) you get indeed 4 A B B . It's called "distributive law".

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