Talk:multiplicand

Which of the two numbers is the multiplicand?

I have reverted the edit of 10 November 2020 made by user 49.145.136.49

I agree that the multiplicand is the number that is multiplied by the other. But in the expression 5 × 3, it is the number 3 that is multiplied by the other, and so it is 3 that is the multiplicand. 5 × 3 may be read as "5 times 3" as in "5 groups of 3". It does not mean "5 multiplied by 3", but on the contrary it means "3 multiplied by 5".

No doubt the matter is confusing, but what I have set out above is nowadays the standard way of regarding it. See https://mathworld.wolfram.com/Multiplicand.html and https://www.britannica.com/science/multiplicand

A 1932 paper by Saradakanta Ganguli (On the necessity of placing the sign × before the multiplicand, The Mathematical Gazette Vol 16 No 221, Dec 1932) considers the matter. He finds two schools of thought, multiplicand × multiplier, and multiplier × multiplicand; he deplores the inconsistency and calls for standardisation; and for historical reasons he recommends multiplier × multiplicand (which has become standard in the 90 years since his paper was written). Prim Ethics (talk) 01:06, 26 December 2022 (UTC)

@Prim Ethics whenever you change something that's part of a system, please check the other parts. Now multiplier and multiplicand contradict each other.

Thanks, @Chuck Entz. I have changed multiplier now. Prim Ethics (talk) 00:44, 27 December 2022 (UTC)

@Prim Ethics You should also edit Template:arithmetic operations for consistency. 70.172.194.25 00:55, 27 December 2022 (UTC)

Thanks, done. Prim Ethics (talk) 01:54, 27 December 2022 (UTC)

MathWorld is a pretty authoritative reference. And this interpretation is also the one used by e.g. the Common Core curriculum standards in the US, under which 5×3 expands to 3+3+3+3+3, not 5+5+5. So this edit does make sense. Nonetheless, I can find both interpretations in the wild, and the inconsistency/confusion is understandable, since multiplication is commutative for real numbers. I'm not sure whether ⋅ is interpreted the same way as ×, as here's a book that interprets ω ⋅ 2 as ω + ω (in a setting with non-commutative multiplication): [1]. 70.172.194.25 00:55, 27 December 2022 (UTC)

Yes, multiplication of ordinal numbers (which is non-commutative) is always multiplicand · multiplier. That’s a little embarrassing. But it doesn’t alter the fact that, for multiplication of real numbers, multiplier × multiplicand has become standard. Prim Ethics (talk) 02:45, 28 December 2022 (UTC)