# Simplify Mod to subtraction when possible

FullSimplify[Mod[t,10], t>101 && t<109] It's a long shot, but can I get Mathematica to return t-100 or something similar for the above? Currently it returns just Mod[t,10] itself, which is accurate, but I want even more simplification based on my conditions. ================= ================= 1 Answer 1 ================= How about Assuming[101 < t < 109, FullSimplify[PiecewiseExpand[Mod[t, 10]]]] rhermans gives a simpler formulation: PiecewiseExpand[Mod[t, 10], 101 < t < 109] 1 Â  That works, even without the FullSimplify, but I'm not sure why, since PiecewiseExpand[Mod[t, 10]] just returns Mod[t, 10]. I'm guessing Assuming does some sort of Hold on its second argument, hmmm. Will investigate further on my own ðŸ™‚ â€“Â barrycarter Oct 9 '15 at 15:09 Â Â  Â  That too PiecewiseExpand[Mod[t, 10], 101 < t < 109] â€“Â rhermans Oct 9 '15 at 15:10 Â Â  Â  Who knew that Mod was secretly a "nested piecewise function"! â€“Â barrycarter Oct 9 '15 at 15:11 Â Â  Â  Documentation says: "PiecewiseExpand converts such functions as If, Which, Abs, Max, UnitStep, and Floor to Piecewise. " â€“Â rhermans Oct 9 '15 at 15:12 Â Â  Â  I'm confused about the different ways the assumptions are used in each case, see this question â€“Â rhermans Oct 9 '15 at 15:34