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Is there a general consensus regarding which term is the multiplicand, and which is the multiplier in basic arithmetic multiplication?

In my notes I stated that in the expression $a \times b$ the left hand term $a$ is the multiplicand. I don't recall my original source. When viewed in terms of naive usage and Western left to right reading order, the multiplier should be the left term. That is, we read the expression as $a$ times $b$; meaning $b$ appears in the implied sum $a$ times.

A reference to an introductory math book predating Russell and Whitehead's Principia might be instructive.

Steven Thomas Hatton
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    Hmm, I wonder why there is this distinction at all, when in the additive case both $a$ and $b$ are called addends or summands in $c = a +b$ – Jair Taylor Jan 30 '24 at 00:06
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    Where $b$ is the multiplicand is also the convention given in the VNR Concise Encyclopedia of Mathematics by Gellert, et al. (see https://mathworld.wolfram.com/Multiplicand.html). The interpretation of $a \times b$ could be, e.g., "$a$ copies of $b$", or, "$b$ added together $a$ times", as you've stated. But because basic arithmetic multiplication is commutative, it doesn't really matter either way. – K. Jiang Jan 30 '24 at 00:25
  • Transfinite ordinal multiplication forces the order of multiplicand and multiplier. But that's probably not "general" and "basic arithmetic multiplication". – peterwhy Jan 30 '24 at 00:25
  • Since $a + a$ is normally contracted to $2a = 2 \times a$ and not $a \times2$ (which is usually a contraction of $2 + 2 \dots a$ times), I feel the left operand is seen as multiplier. – Tony Mathew Jan 30 '24 at 11:34

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