Solve for r

[greatwhiteshark]

S = a/1 - r

MY WORK:

s(1 - r) = a

1 - r = a/s

-r = a/s - 1

r = a/s - 1 OVER -1

Is this correct?

 

[tkhunny]

S = a/1 - r

I would have added parentheses: S = a/(1-r)

r = a/s - 1 OVER -1

Icky notation.

Maybe: r = ((a/s)-1)/(-1)

Better: r = 1-(a/s)

Do you know that "solve for" DOES NOT mean it has to end up on the left hand side? Many people do not know this.

From 1-r = a/s

Subtract r, not 1

1 = (a/s) + r

Subtract (a/s)

1 - (a/s) = r

Almost magic.

 

[Denis]

Just another way:

if a/b = c/d, then a*d = b*c : known as criss cross multiplication

if a = c/d, then a/1 = c/d; so a*d = 1*c : criss cross multiplication again

Doing that with your equation:
S = a/(1 - r), then S/1 = a/(1 - r); so apply criss cross multiplication:
S * (1 - r) = 1 * a
S - Sr = a
Sr = S - a
r = (S - a) / S : same as TK's "1 - (a/s) = r "

 

[greatwhiteshark]

Denis

Thank you Denis.