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Several of the basic arithmetic operations can be described in spoken words such as:

  • $x + y$ - Add $y$ to $x$
  • $x - y$ - Subtract $y$ from $x$
  • $x \times y$ - Multiply $x$ by $y$
  • $x \div y$ - Divide $x$ by $y$

I'm wondering if there is a similar way to describe the modulo operation ($x \mod y$) in spoken words.

kuenzign
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    $x \operatorname{mod} y$ remainder of $x$ divided by $y$ – Theo Diamantakis Sep 12 '23 at 15:25
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    It's usually read as "$x$ modulo $y$". If you don't like that, you could say "the remainder of $x$ on division by $y$". – Robert Israel Sep 12 '23 at 15:27
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    The "active" analog of what you wrote is "mod (out) $x$ by $y$" (compare "cast out nines"). This is less common than those mentioned above. – Bill Dubuque Sep 12 '23 at 15:34
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    If there were a verb form for the "mod" operator, it would be a keyword in COBOL. – Dan Sep 12 '23 at 15:54
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    @Dan COBOL does have a keyword for the mod operator, REMAINDER, which is an optional clause for the DIVIDE statement. For example: DIVIDE A BY B GIVING C REMAINDER D. This seems fairly similar to some of the other comments. – kuenzign Sep 12 '23 at 18:05
  • The word residue is also sometimes used in place of remainder. – user170231 Sep 12 '23 at 18:48

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If you need it to be a verb phrase, I'd go with “Find the remainder when x is divided by y”, or some obvious synonym (“Calculate”, “Compute”, “Determine”, etc.) thereof.

You could also try @Bill Dubuque's suggestion of “Mod (out) x by y”, using “mod” as a verb, but verbing weirds language, so this might be harder to understand.

Note that there are multiple definitions of mod depending on the associated integer division operator (truncated, floored, ceiling, Euclidean, or rounded), so if you're writing documentation for operator% in a computer math library, you might want to clarify which one you mean.

Dan
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    "Mod out $x$ by $y$" is more common (so much so that it is even in Wikipedia). $\ \ $ – Bill Dubuque Sep 12 '23 at 18:39
  • True, but even Wikipedia claims that it is an informal term. – kuenzign Sep 12 '23 at 19:01
  • But "factor out" ideals, congruences, equivalence relations, etc. is widely used in formal math, so it makes no sense to deem informal its associated operational form "mod out". Likely this occurs because some writers denigrate anything to do with computation - here normal form operations. In any case, Wikipedia is very far from being authoritative on such matters. – Bill Dubuque Sep 12 '23 at 19:18