newbie question

Rather than memorizing specific rules for every operation and case, you want to use algebra here. The big thing to remember is that the equal sign means “is the same as”. So if you do the same thing to two things that are the same, then they stay the same right?

Example: 1/2=0.5

If you multiply both sides by 2, you get 2(1/2)=2(0.5), which simplifies to 1=1, also true.

So in your above case, you can multiply both sides of X=S/R by R

X=S/R
R(X)=R(S/R)

Since S is being divided into R pieces and then added R times, that’s the same as S (a pizza is cut into 5 pieces. 5 pieces of that pizza are put together, you have the original pizza).

(R)(X)=S
(R)(X)/X=S/X

We divide both sides by X. R times X divided by X gives us R because we have X number of Rs, divided into X groups leaves 1 R per group.

R=S/X

And you’ve successfully found R!
“/“ = “divided by”… ->
X=S/R
->
1/X=R/S
->
S/X=R

X=“S divided by R”

We can “flip” the equation to get “1 divided by X” equals “R divided by S”.

From there it’s multiply by denominator to get 1 times what we’re looking for.

The rule is cool. If X equals something then the “inverse” of X is equal to the inverse of “something.” E.g. X=a/b —>  1/X=b/a
by
Assuming x≠0

x=s÷r

rx=rs÷r

rx=s

rx÷x=s÷x

r=s÷x

Is that what you were looking for?
The division fact

X = S ÷ R

is equivalent to the multiplication fact

X * R = S

and because in multiplication the order of factors does not matter you can say

R * X = S

then say this multiplication statement is equivalent to the division

R = S ÷ X
I edited my previous