Why would adding or subtracting the denominator and the numerator with a same number doesn't make an equivalent fraction of the original fraction?

Answer 1

You can divide or multiply the denominator and numerator by the same number and not change the fraction, but you cannot subtract or add to them by the same number.

One way to look at this is algebra

let the fraction be

y = N/D where N = numerator and D = denominator

then

Dy = N

in algebra you do not change the expression if you you do the same operation to both sides

So let's multiply both sides by 10

10Dy = 10N

y = N/D - nothing changed so it's OK to multiply

Now try to subtract 10 from N; you cannot subtract 10 from D since is multiplied by y