# Simplifying expressions containing unit of zero magnitude

I have obtained the following form as a part of a computation:

k (Quantity[0, "Kilohertz"]) + Quantity[1/500, "Kilohertz"]


This is typeset as

Here, k is an atom (representing an integer in my computation). Obviously I would like this to simplify to Quantity[2, "Hertz"], but I cannot figure out how to cause the term with k to vanish. Neither FullSimplify nor UnitSimplify have any effect here:

My best guess is that Mathematica doesn't want to assume things about k, but given that the magnitude of the unit is 0, it should still simplify away.

How can I simplify this as I would expect?

• try Simplify[....,Assumptions->Element[k,Reals]] – george2079 Apr 5 '16 at 2:45
• @george2079 no dice. Same effect as without the Assumptions -- the form is untouched. – thirtythreeforty Apr 5 '16 at 4:11
• Related: (34967) – Mr.Wizard Jun 8 '17 at 2:12

You can do this:

Unprotect[Quantity]
Quantity /: Times[Quantity[mag_, unit_], seq__] :=
Quantity[Times[mag, seq], unit]


This will leads to your desired result, and also works for symbolic Times in Quantity

• That's a good idea. Is it wise to edit builtin rules like Quantity? Also, would Quantity[0, __] := 0 be a better rule or worse? (I don't know general conventions, thanks.) – thirtythreeforty Apr 5 '16 at 5:23
• @thirtythreeforty your idea also "edits" the built-in function (requires Unprotect[ Quantity]) . Which to do depends on your need. – vapor Apr 5 '16 at 5:40

Had the same problem and solved it by simply using a replacement rule.

k (Quantity[0, "Kilohertz"]) + Quantity[1/500, "Kilohertz"]

UnitConvert[Out[1] /. Quantity[0, "Kilohertz"] -> 0, "Hertz"]


Here's what it looks like in a notebook:

• People here generally like users to post code as Mathematica code instead of images or TeX, so they can copy-paste it. It makes it convenient. – user9660 Jun 5 '16 at 8:35
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• Louis, thanks for the formatting suggestion. – T. Zilla Jun 5 '16 at 17:37