Simplifying algebric terms

Question

I would like to clarify - when the equation was simplified by dividing both side by 61. why wasnt this equation instead a = 10/61 * b/61 + 230/61

61a = 10b + 230

a = 10/61b + 230

Answer 1

$61a=10b+230$ if we divide both sides by 61, I'd get:

$a=\frac{10b+230}{61}$ which can be distributed into:

$a=\frac{10b}{61}+\frac{230}{61}$ as your first instead would actually have $61^2$ as the denominator since

$\frac{10}{61}*\frac{b}{61}=\frac{10b}{61^2}$ you realize, right? If necessary, consider the pproduct of $\frac{1}{2}$ with itself that is $\frac{1}{2}*\frac{1}{2}=\frac{1}{4} which makes sense as half is a quarter.

Answer 2

I'm not able to comment yet so I am posting this as an "answer"

Your last line, assuming you start with $61a=10b + 230$ and you want to solve for $a$ should be $a=10b/61 +230/61$