Question

does the following integer arithmetic property hold?

(m/n)/l == m/(n*l)

At first I thought I knew answer (does not hold), but now am not sure.
Does it hold for all numbers or only for certain conditions, i.e. n > l?

the question pertains to computer arithmetic, namely q = n/m, q*m != n, ignoring overflow.

Answer 1

Case1 assume m = kn+b (b<n),
left = (m/n)/l = ((kn+b)/n)/l = (k+b/n)/l = k/l (b/n=0, because b<n)
right = (kn+b)/(n*l) = k/l + b/(n*l) = k/l (b/(n*l)=0, because b<n)
=> left = right

Case2 assume m = kn,
left = (m/n)/l = (kn/n)/l = k/l
right = kn/(n*l) = k/l
=> left = right

So, (m/n)/l == m/(n*l)