Is there a convention on the order of scalar multiplication? I know there were questions before mine, but I would like to know if such distinction is culturally dependent.

This came from a news in Taiwan reporting a question appeared in a 2nd grade test. The question roughly translates as

A dozen of pencils has twelve pencils, and each pencil is sold at $\$8$. What is the total price?

  1. $8\times12$
  2. $12\times8$
  3. $8+12$
  4. $12+8$

(News report in Chinese, sorry)

And the only "correct"/"best" answer was $8\times12$. One teacher claimed that this is correct (and option 2 is not) because $8$ carries the unit and $12$ denotes the quantity. The teacher also claimed that $8$ as the multiplicand must goes before $12$ the multiplier, so the following sum should be written in this following way:

$$8+8+8+8+8+8+8+8+8+8+8+8 = 8\times12$$

And Wolfram MathWorld said otherwise. Instead of looking for a global convention, I would like to know is such convention affected by culture or language?

I have left elementary school long ago, and I cannot remember how I was taught.

  • $\begingroup$ I don't think I understand your question. It seems like the answer should just be "Yes, the convention is affected by culture/language; for example, compare this Taiwanese test question and MathWorld." $\endgroup$ – Mark S. Nov 24 '13 at 16:34

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